Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.5% → 41.3%

Time: 1.5min

Alternatives: 37

Speedup: 2.6×

• 88.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 41.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := b \cdot y4 - i \cdot y5\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot t\_4 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ t_6 := t \cdot j - y \cdot k\\ t_7 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t\_6\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;y1 \leq -1.36 \cdot 10^{+229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -4.6 \cdot 10^{+156}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y1 \leq -2.5 \cdot 10^{+136}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_6 + y1 \cdot t\_4\right) + c \cdot t\_2\right)\\ \mathbf{elif}\;y1 \leq -0.0005:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y1 \leq -2.1 \cdot 10^{-160}:\\ \;\;\;\;t\_4 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(t\_6 \cdot t\_3 + t\_1\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot t\_2\right)\\ \mathbf{elif}\;y1 \leq -9.2 \cdot 10^{-201}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;y1 \leq -2.5 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t\_3 + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 4.7 \cdot 10^{-253}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot t\_2\right)\\ \mathbf{elif}\;y1 \leq 2.9 \cdot 10^{-118}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;y1 \leq 1.1 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y3 (* z (- (* a y1) (* c y0)))))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (- (* b y4) (* i y5)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5
         (*
          y1
          (+
           (* i (- (* x j) (* z k)))
           (+ (* y4 t_4) (* a (- (* z y3) (* x y2)))))))
        (t_6 (- (* t j) (* y k)))
        (t_7
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 t_6))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= y1 -1.36e+229)
     t_1
     (if (<= y1 -4.6e+156)
       t_5
       (if (<= y1 -2.5e+136)
         (* y4 (+ (+ (* b t_6) (* y1 t_4)) (* c t_2)))
         (if (<= y1 -0.0005)
           t_5
           (if (<= y1 -2.1e-160)
             (+
              (* t_4 (- (* y1 y4) (* y0 y5)))
              (+ (+ (* t_6 t_3) t_1) (* (- (* c y4) (* a y5)) t_2)))
             (if (<= y1 -9.2e-201)
               t_7
               (if (<= y1 -2.5e-276)
                 (*
                  t
                  (+
                   (+ (* j t_3) (* z (- (* c i) (* a b))))
                   (* y2 (- (* a y5) (* c y4)))))
                 (if (<= y1 4.7e-253)
                   (*
                    c
                    (+
                     (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
                     (* y4 t_2)))
                   (if (<= y1 2.9e-118)
                     t_7
                     (if (<= y1 1.1e+35)
                       (* c (* y3 (- (* y y4) (* z y0))))
                       t_5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * (z * ((a * y1) - (c * y0)));
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (b * y4) - (i * y5);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))));
	double t_6 = (t * j) - (y * k);
	double t_7 = b * (((a * ((x * y) - (z * t))) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (y1 <= -1.36e+229) {
		tmp = t_1;
	} else if (y1 <= -4.6e+156) {
		tmp = t_5;
	} else if (y1 <= -2.5e+136) {
		tmp = y4 * (((b * t_6) + (y1 * t_4)) + (c * t_2));
	} else if (y1 <= -0.0005) {
		tmp = t_5;
	} else if (y1 <= -2.1e-160) {
		tmp = (t_4 * ((y1 * y4) - (y0 * y5))) + (((t_6 * t_3) + t_1) + (((c * y4) - (a * y5)) * t_2));
	} else if (y1 <= -9.2e-201) {
		tmp = t_7;
	} else if (y1 <= -2.5e-276) {
		tmp = t * (((j * t_3) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y1 <= 4.7e-253) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2));
	} else if (y1 <= 2.9e-118) {
		tmp = t_7;
	} else if (y1 <= 1.1e+35) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = y3 * (z * ((a * y1) - (c * y0)))
    t_2 = (y * y3) - (t * y2)
    t_3 = (b * y4) - (i * y5)
    t_4 = (k * y2) - (j * y3)
    t_5 = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))))
    t_6 = (t * j) - (y * k)
    t_7 = b * (((a * ((x * y) - (z * t))) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))))
    if (y1 <= (-1.36d+229)) then
        tmp = t_1
    else if (y1 <= (-4.6d+156)) then
        tmp = t_5
    else if (y1 <= (-2.5d+136)) then
        tmp = y4 * (((b * t_6) + (y1 * t_4)) + (c * t_2))
    else if (y1 <= (-0.0005d0)) then
        tmp = t_5
    else if (y1 <= (-2.1d-160)) then
        tmp = (t_4 * ((y1 * y4) - (y0 * y5))) + (((t_6 * t_3) + t_1) + (((c * y4) - (a * y5)) * t_2))
    else if (y1 <= (-9.2d-201)) then
        tmp = t_7
    else if (y1 <= (-2.5d-276)) then
        tmp = t * (((j * t_3) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
    else if (y1 <= 4.7d-253) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2))
    else if (y1 <= 2.9d-118) then
        tmp = t_7
    else if (y1 <= 1.1d+35) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * (z * ((a * y1) - (c * y0)));
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (b * y4) - (i * y5);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))));
	double t_6 = (t * j) - (y * k);
	double t_7 = b * (((a * ((x * y) - (z * t))) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (y1 <= -1.36e+229) {
		tmp = t_1;
	} else if (y1 <= -4.6e+156) {
		tmp = t_5;
	} else if (y1 <= -2.5e+136) {
		tmp = y4 * (((b * t_6) + (y1 * t_4)) + (c * t_2));
	} else if (y1 <= -0.0005) {
		tmp = t_5;
	} else if (y1 <= -2.1e-160) {
		tmp = (t_4 * ((y1 * y4) - (y0 * y5))) + (((t_6 * t_3) + t_1) + (((c * y4) - (a * y5)) * t_2));
	} else if (y1 <= -9.2e-201) {
		tmp = t_7;
	} else if (y1 <= -2.5e-276) {
		tmp = t * (((j * t_3) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y1 <= 4.7e-253) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2));
	} else if (y1 <= 2.9e-118) {
		tmp = t_7;
	} else if (y1 <= 1.1e+35) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y3 * (z * ((a * y1) - (c * y0)))
	t_2 = (y * y3) - (t * y2)
	t_3 = (b * y4) - (i * y5)
	t_4 = (k * y2) - (j * y3)
	t_5 = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))))
	t_6 = (t * j) - (y * k)
	t_7 = b * (((a * ((x * y) - (z * t))) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if y1 <= -1.36e+229:
		tmp = t_1
	elif y1 <= -4.6e+156:
		tmp = t_5
	elif y1 <= -2.5e+136:
		tmp = y4 * (((b * t_6) + (y1 * t_4)) + (c * t_2))
	elif y1 <= -0.0005:
		tmp = t_5
	elif y1 <= -2.1e-160:
		tmp = (t_4 * ((y1 * y4) - (y0 * y5))) + (((t_6 * t_3) + t_1) + (((c * y4) - (a * y5)) * t_2))
	elif y1 <= -9.2e-201:
		tmp = t_7
	elif y1 <= -2.5e-276:
		tmp = t * (((j * t_3) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
	elif y1 <= 4.7e-253:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2))
	elif y1 <= 2.9e-118:
		tmp = t_7
	elif y1 <= 1.1e+35:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y3 * Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(Float64(b * y4) - Float64(i * y5))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y4 * t_4) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))))
	t_6 = Float64(Float64(t * j) - Float64(y * k))
	t_7 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_6)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (y1 <= -1.36e+229)
		tmp = t_1;
	elseif (y1 <= -4.6e+156)
		tmp = t_5;
	elseif (y1 <= -2.5e+136)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_6) + Float64(y1 * t_4)) + Float64(c * t_2)));
	elseif (y1 <= -0.0005)
		tmp = t_5;
	elseif (y1 <= -2.1e-160)
		tmp = Float64(Float64(t_4 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(Float64(t_6 * t_3) + t_1) + Float64(Float64(Float64(c * y4) - Float64(a * y5)) * t_2)));
	elseif (y1 <= -9.2e-201)
		tmp = t_7;
	elseif (y1 <= -2.5e-276)
		tmp = Float64(t * Float64(Float64(Float64(j * t_3) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y1 <= 4.7e-253)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * t_2)));
	elseif (y1 <= 2.9e-118)
		tmp = t_7;
	elseif (y1 <= 1.1e+35)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y3 * (z * ((a * y1) - (c * y0)));
	t_2 = (y * y3) - (t * y2);
	t_3 = (b * y4) - (i * y5);
	t_4 = (k * y2) - (j * y3);
	t_5 = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))));
	t_6 = (t * j) - (y * k);
	t_7 = b * (((a * ((x * y) - (z * t))) + (y4 * t_6)) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (y1 <= -1.36e+229)
		tmp = t_1;
	elseif (y1 <= -4.6e+156)
		tmp = t_5;
	elseif (y1 <= -2.5e+136)
		tmp = y4 * (((b * t_6) + (y1 * t_4)) + (c * t_2));
	elseif (y1 <= -0.0005)
		tmp = t_5;
	elseif (y1 <= -2.1e-160)
		tmp = (t_4 * ((y1 * y4) - (y0 * y5))) + (((t_6 * t_3) + t_1) + (((c * y4) - (a * y5)) * t_2));
	elseif (y1 <= -9.2e-201)
		tmp = t_7;
	elseif (y1 <= -2.5e-276)
		tmp = t * (((j * t_3) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (y1 <= 4.7e-253)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2));
	elseif (y1 <= 2.9e-118)
		tmp = t_7;
	elseif (y1 <= 1.1e+35)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y3 * N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * t$95$4), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.36e+229], t$95$1, If[LessEqual[y1, -4.6e+156], t$95$5, If[LessEqual[y1, -2.5e+136], N[(y4 * N[(N[(N[(b * t$95$6), $MachinePrecision] + N[(y1 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -0.0005], t$95$5, If[LessEqual[y1, -2.1e-160], N[(N[(t$95$4 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t$95$6 * t$95$3), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -9.2e-201], t$95$7, If[LessEqual[y1, -2.5e-276], N[(t * N[(N[(N[(j * t$95$3), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.7e-253], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.9e-118], t$95$7, If[LessEqual[y1, 1.1e+35], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y1 < -1.3599999999999999e229

   1. Initial program 17.2%

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

   3. Taylor expanded in y3 around -inf 28.1%

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

   4. Taylor expanded in z around inf 59.1%

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

   if -1.3599999999999999e229 < y1 < -4.5999999999999998e156 or -2.5000000000000001e136 < y1 < -5.0000000000000001e-4 or 1.0999999999999999e35 < y1

   1. Initial program 22.7%

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

   3. Taylor expanded in y1 around -inf 63.0%

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

      1. associate-*r* 63.0%

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

      2. neg-mul-1 63.0%

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

      3. +-commutative 63.0%

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

      4. mul-1-neg 63.0%

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

      5. unsub-neg 63.0%

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

      6. *-commutative 63.0%

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

      7. *-commutative 63.0%

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

      8. *-commutative 63.0%

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

      9. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   if -4.5999999999999998e156 < y1 < -2.5000000000000001e136

   1. Initial program 25.0%

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

   3. Taylor expanded in y4 around inf 87.8%

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

   if -5.0000000000000001e-4 < y1 < -2.1e-160

   1. Initial program 52.7%

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

   3. Taylor expanded in y3 around inf 62.7%

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

   if -2.1e-160 < y1 < -9.19999999999999943e-201 or 4.69999999999999981e-253 < y1 < 2.8999999999999998e-118

   1. Initial program 30.6%

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

   3. Taylor expanded in b around inf 64.4%

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

   if -9.19999999999999943e-201 < y1 < -2.49999999999999984e-276

   1. Initial program 42.5%

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

   3. Taylor expanded in t around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   if -2.49999999999999984e-276 < y1 < 4.69999999999999981e-253

   1. Initial program 33.6%

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

   3. Taylor expanded in c around inf 64.6%

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

      1. +-commutative 64.6%

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

      2. mul-1-neg 64.6%

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

      3. unsub-neg 64.6%

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

      4. *-commutative 64.6%

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

      5. *-commutative 64.6%

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

      6. *-commutative 64.6%

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

      7. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   if 2.8999999999999998e-118 < y1 < 1.0999999999999999e35

   1. Initial program 21.0%

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

   3. Taylor expanded in y3 around -inf 49.1%

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

   4. Taylor expanded in c around inf 63.1%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.36 \cdot 10^{+229}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -4.6 \cdot 10^{+156}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -2.5 \cdot 10^{+136}:\\ \;\;\;\;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}\;y1 \leq -0.0005:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -2.1 \cdot 10^{-160}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -9.2 \cdot 10^{-201}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq -2.5 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 4.7 \cdot 10^{-253}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.9 \cdot 10^{-118}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.1 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 53.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $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[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(b * N[(N[(N[(a * t$95$2), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $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 87.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around inf 42.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.6%

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

Alternative 3: 37.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot k - x \cdot j\\ t_2 := c \cdot i - a \cdot b\\ t_3 := b \cdot y4 - i \cdot y5\\ t_4 := y0 \cdot t\_1\\ t_5 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + t\_4\right)\\ \mathbf{if}\;y0 \leq -4.3 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;j \cdot \left(t \cdot t\_3\right)\\ \mathbf{elif}\;y0 \leq -1.85 \cdot 10^{+140}:\\ \;\;\;\;b \cdot t\_4\\ \mathbf{elif}\;y0 \leq -3.8 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot t\_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{-8}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y0 \leq -4.6 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t\_3 + z \cdot t\_2\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 7 \cdot 10^{-159}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 5.8 \cdot 10^{+59}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 3.55 \cdot 10^{+111}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{+184}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z k) (* x j)))
        (t_2 (- (* c i) (* a b)))
        (t_3 (- (* b y4) (* i y5)))
        (t_4 (* y0 t_1))
        (t_5
         (*
          b
          (+ (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k)))) t_4))))
   (if (<= y0 -4.3e+212)
     (* c (* y3 (- (* y y4) (* z y0))))
     (if (<= y0 -7.8e+180)
       (* j (* t t_3))
       (if (<= y0 -1.85e+140)
         (* b t_4)
         (if (<= y0 -3.8e+115)
           (*
            x
            (+
             (- (* y2 (- (* c y0) (* a y1))) (* y t_2))
             (* j (- (* i y1) (* b y0)))))
           (if (<= y0 -1.65e-8)
             t_5
             (if (<= y0 -4.6e-299)
               (* t (+ (+ (* j t_3) (* z t_2)) (* y2 (- (* a y5) (* c y4)))))
               (if (<= y0 7e-159)
                 (*
                  y3
                  (+
                   (* y (- (* c y4) (* a y5)))
                   (- (* a (* z y1)) (* j (* y1 y4)))))
                 (if (<= y0 1.5e+29)
                   (* x (* i (- (* j y1) (* y c))))
                   (if (<= y0 5.8e+59)
                     (* k (* y (- (* i y5) (* b y4))))
                     (if (<= y0 3.55e+111)
                       t_5
                       (if (<= y0 6e+184)
                         (* k (* y2 (- (* y1 y4) (* y0 y5))))
                         (*
                          y0
                          (+
                           (+
                            (* c (- (* x y2) (* z y3)))
                            (* y5 (- (* j y3) (* k y2))))
                           (* b 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 = (z * k) - (x * j);
	double t_2 = (c * i) - (a * b);
	double t_3 = (b * y4) - (i * y5);
	double t_4 = y0 * t_1;
	double t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_4);
	double tmp;
	if (y0 <= -4.3e+212) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y0 <= -7.8e+180) {
		tmp = j * (t * t_3);
	} else if (y0 <= -1.85e+140) {
		tmp = b * t_4;
	} else if (y0 <= -3.8e+115) {
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_2)) + (j * ((i * y1) - (b * y0))));
	} else if (y0 <= -1.65e-8) {
		tmp = t_5;
	} else if (y0 <= -4.6e-299) {
		tmp = t * (((j * t_3) + (z * t_2)) + (y2 * ((a * y5) - (c * y4))));
	} else if (y0 <= 7e-159) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y0 <= 1.5e+29) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y0 <= 5.8e+59) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y0 <= 3.55e+111) {
		tmp = t_5;
	} else if (y0 <= 6e+184) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (z * k) - (x * j)
    t_2 = (c * i) - (a * b)
    t_3 = (b * y4) - (i * y5)
    t_4 = y0 * t_1
    t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_4)
    if (y0 <= (-4.3d+212)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y0 <= (-7.8d+180)) then
        tmp = j * (t * t_3)
    else if (y0 <= (-1.85d+140)) then
        tmp = b * t_4
    else if (y0 <= (-3.8d+115)) then
        tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_2)) + (j * ((i * y1) - (b * y0))))
    else if (y0 <= (-1.65d-8)) then
        tmp = t_5
    else if (y0 <= (-4.6d-299)) then
        tmp = t * (((j * t_3) + (z * t_2)) + (y2 * ((a * y5) - (c * y4))))
    else if (y0 <= 7d-159) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
    else if (y0 <= 1.5d+29) then
        tmp = x * (i * ((j * y1) - (y * c)))
    else if (y0 <= 5.8d+59) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (y0 <= 3.55d+111) then
        tmp = t_5
    else if (y0 <= 6d+184) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * 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 = (z * k) - (x * j);
	double t_2 = (c * i) - (a * b);
	double t_3 = (b * y4) - (i * y5);
	double t_4 = y0 * t_1;
	double t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_4);
	double tmp;
	if (y0 <= -4.3e+212) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y0 <= -7.8e+180) {
		tmp = j * (t * t_3);
	} else if (y0 <= -1.85e+140) {
		tmp = b * t_4;
	} else if (y0 <= -3.8e+115) {
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_2)) + (j * ((i * y1) - (b * y0))));
	} else if (y0 <= -1.65e-8) {
		tmp = t_5;
	} else if (y0 <= -4.6e-299) {
		tmp = t * (((j * t_3) + (z * t_2)) + (y2 * ((a * y5) - (c * y4))));
	} else if (y0 <= 7e-159) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y0 <= 1.5e+29) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y0 <= 5.8e+59) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y0 <= 3.55e+111) {
		tmp = t_5;
	} else if (y0 <= 6e+184) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * 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 = (z * k) - (x * j)
	t_2 = (c * i) - (a * b)
	t_3 = (b * y4) - (i * y5)
	t_4 = y0 * t_1
	t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_4)
	tmp = 0
	if y0 <= -4.3e+212:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y0 <= -7.8e+180:
		tmp = j * (t * t_3)
	elif y0 <= -1.85e+140:
		tmp = b * t_4
	elif y0 <= -3.8e+115:
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_2)) + (j * ((i * y1) - (b * y0))))
	elif y0 <= -1.65e-8:
		tmp = t_5
	elif y0 <= -4.6e-299:
		tmp = t * (((j * t_3) + (z * t_2)) + (y2 * ((a * y5) - (c * y4))))
	elif y0 <= 7e-159:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
	elif y0 <= 1.5e+29:
		tmp = x * (i * ((j * y1) - (y * c)))
	elif y0 <= 5.8e+59:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif y0 <= 3.55e+111:
		tmp = t_5
	elif y0 <= 6e+184:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	else:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * 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(z * k) - Float64(x * j))
	t_2 = Float64(Float64(c * i) - Float64(a * b))
	t_3 = Float64(Float64(b * y4) - Float64(i * y5))
	t_4 = Float64(y0 * t_1)
	t_5 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + t_4))
	tmp = 0.0
	if (y0 <= -4.3e+212)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y0 <= -7.8e+180)
		tmp = Float64(j * Float64(t * t_3));
	elseif (y0 <= -1.85e+140)
		tmp = Float64(b * t_4);
	elseif (y0 <= -3.8e+115)
		tmp = Float64(x * Float64(Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(y * t_2)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y0 <= -1.65e-8)
		tmp = t_5;
	elseif (y0 <= -4.6e-299)
		tmp = Float64(t * Float64(Float64(Float64(j * t_3) + Float64(z * t_2)) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 7e-159)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(a * Float64(z * y1)) - Float64(j * Float64(y1 * y4)))));
	elseif (y0 <= 1.5e+29)
		tmp = Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (y0 <= 5.8e+59)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (y0 <= 3.55e+111)
		tmp = t_5;
	elseif (y0 <= 6e+184)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	else
		tmp = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * k) - (x * j);
	t_2 = (c * i) - (a * b);
	t_3 = (b * y4) - (i * y5);
	t_4 = y0 * t_1;
	t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_4);
	tmp = 0.0;
	if (y0 <= -4.3e+212)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y0 <= -7.8e+180)
		tmp = j * (t * t_3);
	elseif (y0 <= -1.85e+140)
		tmp = b * t_4;
	elseif (y0 <= -3.8e+115)
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_2)) + (j * ((i * y1) - (b * y0))));
	elseif (y0 <= -1.65e-8)
		tmp = t_5;
	elseif (y0 <= -4.6e-299)
		tmp = t * (((j * t_3) + (z * t_2)) + (y2 * ((a * y5) - (c * y4))));
	elseif (y0 <= 7e-159)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	elseif (y0 <= 1.5e+29)
		tmp = x * (i * ((j * y1) - (y * c)));
	elseif (y0 <= 5.8e+59)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (y0 <= 3.55e+111)
		tmp = t_5;
	elseif (y0 <= 6e+184)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	else
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * 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[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y0 * t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -4.3e+212], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -7.8e+180], N[(j * N[(t * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.85e+140], N[(b * t$95$4), $MachinePrecision], If[LessEqual[y0, -3.8e+115], N[(x * N[(N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.65e-8], t$95$5, If[LessEqual[y0, -4.6e-299], N[(t * N[(N[(N[(j * t$95$3), $MachinePrecision] + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7e-159], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(z * y1), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.5e+29], N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.8e+59], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.55e+111], t$95$5, If[LessEqual[y0, 6e+184], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y0 < -4.2999999999999996e212

   1. Initial program 13.6%

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

   3. Taylor expanded in y3 around -inf 50.3%

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

   4. Taylor expanded in c around inf 68.6%

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

   if -4.2999999999999996e212 < y0 < -7.8000000000000002e180

   1. Initial program 25.0%

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

   3. Taylor expanded in t around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in j around inf 59.1%

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

   if -7.8000000000000002e180 < y0 < -1.85000000000000001e140

   1. Initial program 28.6%

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

   3. Taylor expanded in b around inf 85.7%

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

   4. Taylor expanded in y0 around inf 100.0%

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

   if -1.85000000000000001e140 < y0 < -3.8000000000000001e115

   1. Initial program 0.9%

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

   3. Taylor expanded in x around inf 71.2%

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

   if -3.8000000000000001e115 < y0 < -1.64999999999999989e-8 or 5.79999999999999981e59 < y0 < 3.5500000000000002e111

   1. Initial program 34.3%

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

   3. Taylor expanded in b around inf 61.6%

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

   if -1.64999999999999989e-8 < y0 < -4.6000000000000001e-299

   1. Initial program 42.4%

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

   3. Taylor expanded in t around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

      4. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   if -4.6000000000000001e-299 < y0 < 7.00000000000000005e-159

   1. Initial program 40.0%

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

   3. Taylor expanded in y3 around -inf 64.4%

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

   4. Taylor expanded in y0 around 0 64.3%

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

   if 7.00000000000000005e-159 < y0 < 1.5e29

   1. Initial program 35.3%

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

   3. Taylor expanded in x around inf 53.7%

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

   4. Taylor expanded in i around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

   6. Simplified 57.0%

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

   if 1.5e29 < y0 < 5.79999999999999981e59

   1. Initial program 0.0%

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

   3. Taylor expanded in k around inf 33.3%

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

      1. +-commutative 33.3%

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

      2. mul-1-neg 33.3%

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

      3. unsub-neg 33.3%

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

      4. *-commutative 33.3%

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

      5. associate-*r* 33.3%

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

      6. neg-mul-1 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in y around inf 67.9%

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

   if 3.5500000000000002e111 < y0 < 5.99999999999999973e184

   1. Initial program 6.3%

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

   3. Taylor expanded in k around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

      5. associate-*r* 53.3%

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

      6. neg-mul-1 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in y2 around inf 71.1%

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

   if 5.99999999999999973e184 < y0

   1. Initial program 18.9%

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

   3. Taylor expanded in y0 around inf 74.9%

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

      1. +-commutative 74.9%

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

      2. mul-1-neg 74.9%

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

      3. unsub-neg 74.9%

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

      4. *-commutative 74.9%

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

      5. *-commutative 74.9%

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

      6. *-commutative 74.9%

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

      7. *-commutative 74.9%

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

   5. Simplified 74.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.3 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -7.8 \cdot 10^{+180}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -1.85 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -3.8 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot i - a \cdot b\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{-8}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -4.6 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 7 \cdot 10^{-159}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 5.8 \cdot 10^{+59}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 3.55 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{+184}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := z \cdot k - x \cdot j\\ t_3 := y0 \cdot t\_2\\ t_4 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t\_1\right) + t\_3\right)\\ t_5 := c \cdot i - a \cdot b\\ \mathbf{if}\;y0 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -3.7 \cdot 10^{+183}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -7.2 \cdot 10^{+140}:\\ \;\;\;\;b \cdot t\_3\\ \mathbf{elif}\;y0 \leq -4.4 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot t\_5\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -3.5 \cdot 10^{-10}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y0 \leq -1.8 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot t\_5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{-160}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 9.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.52 \cdot 10^{+64}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.08 \cdot 10^{+112}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{+184}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot t\_2\right)\\ \end{array} \end{array} \]

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 (- (* z k) (* x j)))
        (t_3 (* y0 t_2))
        (t_4 (* b (+ (+ (* a (- (* x y) (* z t))) (* y4 t_1)) t_3)))
        (t_5 (- (* c i) (* a b))))
   (if (<= y0 -2e+212)
     (* c (* y3 (- (* y y4) (* z y0))))
     (if (<= y0 -3.7e+183)
       (*
        y4
        (+
         (+ (* b t_1) (* y1 (- (* k y2) (* j y3))))
         (* c (- (* y y3) (* t y2)))))
       (if (<= y0 -7.2e+140)
         (* b t_3)
         (if (<= y0 -4.4e+114)
           (*
            x
            (+
             (- (* y2 (- (* c y0) (* a y1))) (* y t_5))
             (* j (- (* i y1) (* b y0)))))
           (if (<= y0 -3.5e-10)
             t_4
             (if (<= y0 -1.8e-299)
               (*
                t
                (+
                 (+ (* j (- (* b y4) (* i y5))) (* z t_5))
                 (* y2 (- (* a y5) (* c y4)))))
               (if (<= y0 4.8e-160)
                 (*
                  y3
                  (+
                   (* y (- (* c y4) (* a y5)))
                   (- (* a (* z y1)) (* j (* y1 y4)))))
                 (if (<= y0 9.2e+27)
                   (* x (* i (- (* j y1) (* y c))))
                   (if (<= y0 1.52e+64)
                     (* k (* y (- (* i y5) (* b y4))))
                     (if (<= y0 1.08e+112)
                       t_4
                       (if (<= y0 6e+184)
                         (* k (* y2 (- (* y1 y4) (* y0 y5))))
                         (*
                          y0
                          (+
                           (+
                            (* c (- (* x y2) (* z y3)))
                            (* y5 (- (* j y3) (* k y2))))
                           (* 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 = (t * j) - (y * k);
	double t_2 = (z * k) - (x * j);
	double t_3 = y0 * t_2;
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + t_3);
	double t_5 = (c * i) - (a * b);
	double tmp;
	if (y0 <= -2e+212) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y0 <= -3.7e+183) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y0 <= -7.2e+140) {
		tmp = b * t_3;
	} else if (y0 <= -4.4e+114) {
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_5)) + (j * ((i * y1) - (b * y0))));
	} else if (y0 <= -3.5e-10) {
		tmp = t_4;
	} else if (y0 <= -1.8e-299) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * t_5)) + (y2 * ((a * y5) - (c * y4))));
	} else if (y0 <= 4.8e-160) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y0 <= 9.2e+27) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y0 <= 1.52e+64) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y0 <= 1.08e+112) {
		tmp = t_4;
	} else if (y0 <= 6e+184) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = (z * k) - (x * j)
    t_3 = y0 * t_2
    t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + t_3)
    t_5 = (c * i) - (a * b)
    if (y0 <= (-2d+212)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y0 <= (-3.7d+183)) then
        tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (y0 <= (-7.2d+140)) then
        tmp = b * t_3
    else if (y0 <= (-4.4d+114)) then
        tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_5)) + (j * ((i * y1) - (b * y0))))
    else if (y0 <= (-3.5d-10)) then
        tmp = t_4
    else if (y0 <= (-1.8d-299)) then
        tmp = t * (((j * ((b * y4) - (i * y5))) + (z * t_5)) + (y2 * ((a * y5) - (c * y4))))
    else if (y0 <= 4.8d-160) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
    else if (y0 <= 9.2d+27) then
        tmp = x * (i * ((j * y1) - (y * c)))
    else if (y0 <= 1.52d+64) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (y0 <= 1.08d+112) then
        tmp = t_4
    else if (y0 <= 6d+184) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (z * k) - (x * j);
	double t_3 = y0 * t_2;
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + t_3);
	double t_5 = (c * i) - (a * b);
	double tmp;
	if (y0 <= -2e+212) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y0 <= -3.7e+183) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y0 <= -7.2e+140) {
		tmp = b * t_3;
	} else if (y0 <= -4.4e+114) {
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_5)) + (j * ((i * y1) - (b * y0))));
	} else if (y0 <= -3.5e-10) {
		tmp = t_4;
	} else if (y0 <= -1.8e-299) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * t_5)) + (y2 * ((a * y5) - (c * y4))));
	} else if (y0 <= 4.8e-160) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y0 <= 9.2e+27) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y0 <= 1.52e+64) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y0 <= 1.08e+112) {
		tmp = t_4;
	} else if (y0 <= 6e+184) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = (z * k) - (x * j)
	t_3 = y0 * t_2
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + t_3)
	t_5 = (c * i) - (a * b)
	tmp = 0
	if y0 <= -2e+212:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y0 <= -3.7e+183:
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif y0 <= -7.2e+140:
		tmp = b * t_3
	elif y0 <= -4.4e+114:
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_5)) + (j * ((i * y1) - (b * y0))))
	elif y0 <= -3.5e-10:
		tmp = t_4
	elif y0 <= -1.8e-299:
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * t_5)) + (y2 * ((a * y5) - (c * y4))))
	elif y0 <= 4.8e-160:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
	elif y0 <= 9.2e+27:
		tmp = x * (i * ((j * y1) - (y * c)))
	elif y0 <= 1.52e+64:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif y0 <= 1.08e+112:
		tmp = t_4
	elif y0 <= 6e+184:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	else:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * 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(t * j) - Float64(y * k))
	t_2 = Float64(Float64(z * k) - Float64(x * j))
	t_3 = Float64(y0 * t_2)
	t_4 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_1)) + t_3))
	t_5 = Float64(Float64(c * i) - Float64(a * b))
	tmp = 0.0
	if (y0 <= -2e+212)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y0 <= -3.7e+183)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y0 <= -7.2e+140)
		tmp = Float64(b * t_3);
	elseif (y0 <= -4.4e+114)
		tmp = Float64(x * Float64(Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(y * t_5)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y0 <= -3.5e-10)
		tmp = t_4;
	elseif (y0 <= -1.8e-299)
		tmp = Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(z * t_5)) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 4.8e-160)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(a * Float64(z * y1)) - Float64(j * Float64(y1 * y4)))));
	elseif (y0 <= 9.2e+27)
		tmp = Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (y0 <= 1.52e+64)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (y0 <= 1.08e+112)
		tmp = t_4;
	elseif (y0 <= 6e+184)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	else
		tmp = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * t_2)));
	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 = (z * k) - (x * j);
	t_3 = y0 * t_2;
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + t_3);
	t_5 = (c * i) - (a * b);
	tmp = 0.0;
	if (y0 <= -2e+212)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y0 <= -3.7e+183)
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (y0 <= -7.2e+140)
		tmp = b * t_3;
	elseif (y0 <= -4.4e+114)
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_5)) + (j * ((i * y1) - (b * y0))));
	elseif (y0 <= -3.5e-10)
		tmp = t_4;
	elseif (y0 <= -1.8e-299)
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * t_5)) + (y2 * ((a * y5) - (c * y4))));
	elseif (y0 <= 4.8e-160)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	elseif (y0 <= 9.2e+27)
		tmp = x * (i * ((j * y1) - (y * c)));
	elseif (y0 <= 1.52e+64)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (y0 <= 1.08e+112)
		tmp = t_4;
	elseif (y0 <= 6e+184)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	else
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y0 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -2e+212], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.7e+183], N[(y4 * N[(N[(N[(b * t$95$1), $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[y0, -7.2e+140], N[(b * t$95$3), $MachinePrecision], If[LessEqual[y0, -4.4e+114], N[(x * N[(N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.5e-10], t$95$4, If[LessEqual[y0, -1.8e-299], N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.8e-160], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(z * y1), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9.2e+27], N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.52e+64], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.08e+112], t$95$4, If[LessEqual[y0, 6e+184], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y0 < -1.9999999999999998e212

   1. Initial program 13.6%

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

   3. Taylor expanded in y3 around -inf 50.3%

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

   4. Taylor expanded in c around inf 68.6%

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

   if -1.9999999999999998e212 < y0 < -3.7000000000000001e183

   1. Initial program 25.0%

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

   3. Taylor expanded in y4 around inf 59.5%

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

   if -3.7000000000000001e183 < y0 < -7.1999999999999999e140

   1. Initial program 28.6%

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

   3. Taylor expanded in b around inf 85.7%

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

   4. Taylor expanded in y0 around inf 100.0%

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

   if -7.1999999999999999e140 < y0 < -4.4000000000000001e114

   1. Initial program 0.9%

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

   3. Taylor expanded in x around inf 71.2%

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

   if -4.4000000000000001e114 < y0 < -3.4999999999999998e-10 or 1.52e64 < y0 < 1.08e112

   1. Initial program 34.3%

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

   3. Taylor expanded in b around inf 61.6%

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

   if -3.4999999999999998e-10 < y0 < -1.8e-299

   1. Initial program 42.4%

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

   3. Taylor expanded in t around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

      4. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   if -1.8e-299 < y0 < 4.79999999999999982e-160

   1. Initial program 40.0%

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

   3. Taylor expanded in y3 around -inf 64.4%

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

   4. Taylor expanded in y0 around 0 64.3%

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

   if 4.79999999999999982e-160 < y0 < 9.2000000000000002e27

   1. Initial program 35.3%

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

   3. Taylor expanded in x around inf 53.7%

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

   4. Taylor expanded in i around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

   6. Simplified 57.0%

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

   if 9.2000000000000002e27 < y0 < 1.52e64

   1. Initial program 0.0%

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

   3. Taylor expanded in k around inf 33.3%

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

      1. +-commutative 33.3%

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

      2. mul-1-neg 33.3%

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

      3. unsub-neg 33.3%

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

      4. *-commutative 33.3%

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

      5. associate-*r* 33.3%

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

      6. neg-mul-1 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in y around inf 67.9%

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

   if 1.08e112 < y0 < 5.99999999999999973e184

   1. Initial program 6.3%

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

   3. Taylor expanded in k around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

      5. associate-*r* 53.3%

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

      6. neg-mul-1 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in y2 around inf 71.1%

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

   if 5.99999999999999973e184 < y0

   1. Initial program 18.9%

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

   3. Taylor expanded in y0 around inf 74.9%

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

      1. +-commutative 74.9%

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

      2. mul-1-neg 74.9%

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

      3. unsub-neg 74.9%

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

      4. *-commutative 74.9%

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

      5. *-commutative 74.9%

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

      6. *-commutative 74.9%

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

      7. *-commutative 74.9%

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

   5. Simplified 74.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -3.7 \cdot 10^{+183}:\\ \;\;\;\;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}\;y0 \leq -7.2 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -4.4 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot i - a \cdot b\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -3.5 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.8 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{-160}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 9.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.52 \cdot 10^{+64}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.08 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{+184}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 34.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot y4 - i \cdot y5\right)\\ t_2 := y0 \cdot \left(z \cdot k - x \cdot j\right)\\ t_3 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + t\_2\right)\\ \mathbf{if}\;y0 \leq -1.6 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -2.5 \cdot 10^{+184}:\\ \;\;\;\;j \cdot t\_1\\ \mathbf{elif}\;y0 \leq -4.6 \cdot 10^{+141}:\\ \;\;\;\;b \cdot t\_2\\ \mathbf{elif}\;y0 \leq -2.6 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -4.7 \cdot 10^{-48}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y0 \leq -5.4 \cdot 10^{-278}:\\ \;\;\;\;j \cdot \left(\left(t\_1 + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 8.5 \cdot 10^{-160}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.05 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 4.4 \cdot 10^{+62}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (- (* b y4) (* i y5))))
        (t_2 (* y0 (- (* z k) (* x j))))
        (t_3
         (*
          b
          (+ (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k)))) t_2))))
   (if (<= y0 -1.6e+212)
     (* c (* y3 (- (* y y4) (* z y0))))
     (if (<= y0 -2.5e+184)
       (* j t_1)
       (if (<= y0 -4.6e+141)
         (* b t_2)
         (if (<= y0 -2.6e+119)
           (* t (* y4 (- (* b j) (* c y2))))
           (if (<= y0 -4.7e-48)
             t_3
             (if (<= y0 -5.4e-278)
               (*
                j
                (-
                 (+ t_1 (* y3 (- (* y0 y5) (* y1 y4))))
                 (* x (- (* b y0) (* i y1)))))
               (if (<= y0 8.5e-160)
                 (*
                  y3
                  (+
                   (* y (- (* c y4) (* a y5)))
                   (- (* a (* z y1)) (* j (* y1 y4)))))
                 (if (<= y0 1.05e+27)
                   (* x (* i (- (* j y1) (* y c))))
                   (if (<= y0 4.4e+62)
                     (* k (* y (- (* i y5) (* b y4))))
                     (if (<= y0 1.5e+112)
                       t_3
                       (* k (* y2 (- (* y1 y4) (* y0 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 t_1 = t * ((b * y4) - (i * y5));
	double t_2 = y0 * ((z * k) - (x * j));
	double t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2);
	double tmp;
	if (y0 <= -1.6e+212) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y0 <= -2.5e+184) {
		tmp = j * t_1;
	} else if (y0 <= -4.6e+141) {
		tmp = b * t_2;
	} else if (y0 <= -2.6e+119) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y0 <= -4.7e-48) {
		tmp = t_3;
	} else if (y0 <= -5.4e-278) {
		tmp = j * ((t_1 + (y3 * ((y0 * y5) - (y1 * y4)))) - (x * ((b * y0) - (i * y1))));
	} else if (y0 <= 8.5e-160) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y0 <= 1.05e+27) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y0 <= 4.4e+62) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y0 <= 1.5e+112) {
		tmp = t_3;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((b * y4) - (i * y5))
    t_2 = y0 * ((z * k) - (x * j))
    t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2)
    if (y0 <= (-1.6d+212)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y0 <= (-2.5d+184)) then
        tmp = j * t_1
    else if (y0 <= (-4.6d+141)) then
        tmp = b * t_2
    else if (y0 <= (-2.6d+119)) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (y0 <= (-4.7d-48)) then
        tmp = t_3
    else if (y0 <= (-5.4d-278)) then
        tmp = j * ((t_1 + (y3 * ((y0 * y5) - (y1 * y4)))) - (x * ((b * y0) - (i * y1))))
    else if (y0 <= 8.5d-160) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
    else if (y0 <= 1.05d+27) then
        tmp = x * (i * ((j * y1) - (y * c)))
    else if (y0 <= 4.4d+62) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (y0 <= 1.5d+112) then
        tmp = t_3
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * 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 t_1 = t * ((b * y4) - (i * y5));
	double t_2 = y0 * ((z * k) - (x * j));
	double t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2);
	double tmp;
	if (y0 <= -1.6e+212) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y0 <= -2.5e+184) {
		tmp = j * t_1;
	} else if (y0 <= -4.6e+141) {
		tmp = b * t_2;
	} else if (y0 <= -2.6e+119) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y0 <= -4.7e-48) {
		tmp = t_3;
	} else if (y0 <= -5.4e-278) {
		tmp = j * ((t_1 + (y3 * ((y0 * y5) - (y1 * y4)))) - (x * ((b * y0) - (i * y1))));
	} else if (y0 <= 8.5e-160) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y0 <= 1.05e+27) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y0 <= 4.4e+62) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y0 <= 1.5e+112) {
		tmp = t_3;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * ((b * y4) - (i * y5))
	t_2 = y0 * ((z * k) - (x * j))
	t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2)
	tmp = 0
	if y0 <= -1.6e+212:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y0 <= -2.5e+184:
		tmp = j * t_1
	elif y0 <= -4.6e+141:
		tmp = b * t_2
	elif y0 <= -2.6e+119:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif y0 <= -4.7e-48:
		tmp = t_3
	elif y0 <= -5.4e-278:
		tmp = j * ((t_1 + (y3 * ((y0 * y5) - (y1 * y4)))) - (x * ((b * y0) - (i * y1))))
	elif y0 <= 8.5e-160:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
	elif y0 <= 1.05e+27:
		tmp = x * (i * ((j * y1) - (y * c)))
	elif y0 <= 4.4e+62:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif y0 <= 1.5e+112:
		tmp = t_3
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))
	t_2 = Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))
	t_3 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + t_2))
	tmp = 0.0
	if (y0 <= -1.6e+212)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y0 <= -2.5e+184)
		tmp = Float64(j * t_1);
	elseif (y0 <= -4.6e+141)
		tmp = Float64(b * t_2);
	elseif (y0 <= -2.6e+119)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y0 <= -4.7e-48)
		tmp = t_3;
	elseif (y0 <= -5.4e-278)
		tmp = Float64(j * Float64(Float64(t_1 + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) - Float64(x * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y0 <= 8.5e-160)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(a * Float64(z * y1)) - Float64(j * Float64(y1 * y4)))));
	elseif (y0 <= 1.05e+27)
		tmp = Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (y0 <= 4.4e+62)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (y0 <= 1.5e+112)
		tmp = t_3;
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * 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)
	t_1 = t * ((b * y4) - (i * y5));
	t_2 = y0 * ((z * k) - (x * j));
	t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2);
	tmp = 0.0;
	if (y0 <= -1.6e+212)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y0 <= -2.5e+184)
		tmp = j * t_1;
	elseif (y0 <= -4.6e+141)
		tmp = b * t_2;
	elseif (y0 <= -2.6e+119)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (y0 <= -4.7e-48)
		tmp = t_3;
	elseif (y0 <= -5.4e-278)
		tmp = j * ((t_1 + (y3 * ((y0 * y5) - (y1 * y4)))) - (x * ((b * y0) - (i * y1))));
	elseif (y0 <= 8.5e-160)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	elseif (y0 <= 1.05e+27)
		tmp = x * (i * ((j * y1) - (y * c)));
	elseif (y0 <= 4.4e+62)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (y0 <= 1.5e+112)
		tmp = t_3;
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.6e+212], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.5e+184], N[(j * t$95$1), $MachinePrecision], If[LessEqual[y0, -4.6e+141], N[(b * t$95$2), $MachinePrecision], If[LessEqual[y0, -2.6e+119], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4.7e-48], t$95$3, If[LessEqual[y0, -5.4e-278], N[(j * N[(N[(t$95$1 + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8.5e-160], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(z * y1), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.05e+27], N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.4e+62], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.5e+112], t$95$3, N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y0 < -1.5999999999999999e212

   1. Initial program 13.6%

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

   3. Taylor expanded in y3 around -inf 50.3%

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

   4. Taylor expanded in c around inf 68.6%

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

   if -1.5999999999999999e212 < y0 < -2.4999999999999999e184

   1. Initial program 25.0%

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

   3. Taylor expanded in t around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in j around inf 59.1%

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

   if -2.4999999999999999e184 < y0 < -4.6000000000000003e141

   1. Initial program 28.6%

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

   3. Taylor expanded in b around inf 85.7%

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

   4. Taylor expanded in y0 around inf 100.0%

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

   if -4.6000000000000003e141 < y0 < -2.6e119

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in y4 around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. *-commutative 60.9%

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

   8. Simplified 60.9%

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

   if -2.6e119 < y0 < -4.6999999999999998e-48 or 4.40000000000000029e62 < y0 < 1.4999999999999999e112

   1. Initial program 41.0%

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

   3. Taylor expanded in b around inf 58.3%

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

   if -4.6999999999999998e-48 < y0 < -5.4000000000000003e-278

   1. Initial program 30.8%

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

   3. Taylor expanded in j around inf 47.2%

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

      1. +-commutative 47.2%

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

      2. mul-1-neg 47.2%

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

      3. unsub-neg 47.2%

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

      4. *-commutative 47.2%

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

   5. Simplified 47.2%

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

   if -5.4000000000000003e-278 < y0 < 8.49999999999999959e-160

   1. Initial program 43.8%

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

   3. Taylor expanded in y3 around -inf 65.6%

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

   4. Taylor expanded in y0 around 0 65.5%

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

   if 8.49999999999999959e-160 < y0 < 1.04999999999999997e27

   1. Initial program 35.3%

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

   3. Taylor expanded in x around inf 53.7%

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

   4. Taylor expanded in i around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

   6. Simplified 57.0%

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

   if 1.04999999999999997e27 < y0 < 4.40000000000000029e62

   1. Initial program 0.0%

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

   3. Taylor expanded in k around inf 33.3%

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

      1. +-commutative 33.3%

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

      2. mul-1-neg 33.3%

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

      3. unsub-neg 33.3%

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

      4. *-commutative 33.3%

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

      5. associate-*r* 33.3%

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

      6. neg-mul-1 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in y around inf 67.9%

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

   if 1.4999999999999999e112 < y0

   1. Initial program 14.0%

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

   3. Taylor expanded in k around inf 41.2%

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

      1. +-commutative 41.2%

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

      2. mul-1-neg 41.2%

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

      3. unsub-neg 41.2%

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

      4. *-commutative 41.2%

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

      5. associate-*r* 41.2%

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

      6. neg-mul-1 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in y2 around inf 61.9%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.6 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -2.5 \cdot 10^{+184}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -4.6 \cdot 10^{+141}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -2.6 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -4.7 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5.4 \cdot 10^{-278}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 8.5 \cdot 10^{-160}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.05 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 4.4 \cdot 10^{+62}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := y0 \cdot \left(z \cdot k - x \cdot j\right)\\ t_3 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + t\_2\right)\\ \mathbf{if}\;y0 \leq -4.6 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -3.8 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(t \cdot t\_1\right)\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{+141}:\\ \;\;\;\;b \cdot t\_2\\ \mathbf{elif}\;y0 \leq -3.3 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.12 \cdot 10^{-7}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y0 \leq -1.05 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t\_1 + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{-159}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 6.4 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 9.6 \cdot 10^{+61}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{+112}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2 (* y0 (- (* z k) (* x j))))
        (t_3
         (*
          b
          (+ (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k)))) t_2))))
   (if (<= y0 -4.6e+212)
     (* c (* y3 (- (* y y4) (* z y0))))
     (if (<= y0 -3.8e+181)
       (* j (* t t_1))
       (if (<= y0 -1.15e+141)
         (* b t_2)
         (if (<= y0 -3.3e+121)
           (* t (* y4 (- (* b j) (* c y2))))
           (if (<= y0 -1.12e-7)
             t_3
             (if (<= y0 -1.05e-299)
               (*
                t
                (+
                 (+ (* j t_1) (* z (- (* c i) (* a b))))
                 (* y2 (- (* a y5) (* c y4)))))
               (if (<= y0 2.1e-159)
                 (*
                  y3
                  (+
                   (* y (- (* c y4) (* a y5)))
                   (- (* a (* z y1)) (* j (* y1 y4)))))
                 (if (<= y0 6.4e+30)
                   (* x (* i (- (* j y1) (* y c))))
                   (if (<= y0 9.6e+61)
                     (* k (* y (- (* i y5) (* b y4))))
                     (if (<= y0 1.7e+112)
                       t_3
                       (* k (* y2 (- (* y1 y4) (* y0 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 t_1 = (b * y4) - (i * y5);
	double t_2 = y0 * ((z * k) - (x * j));
	double t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2);
	double tmp;
	if (y0 <= -4.6e+212) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y0 <= -3.8e+181) {
		tmp = j * (t * t_1);
	} else if (y0 <= -1.15e+141) {
		tmp = b * t_2;
	} else if (y0 <= -3.3e+121) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y0 <= -1.12e-7) {
		tmp = t_3;
	} else if (y0 <= -1.05e-299) {
		tmp = t * (((j * t_1) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y0 <= 2.1e-159) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y0 <= 6.4e+30) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y0 <= 9.6e+61) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y0 <= 1.7e+112) {
		tmp = t_3;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * y4) - (i * y5)
    t_2 = y0 * ((z * k) - (x * j))
    t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2)
    if (y0 <= (-4.6d+212)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y0 <= (-3.8d+181)) then
        tmp = j * (t * t_1)
    else if (y0 <= (-1.15d+141)) then
        tmp = b * t_2
    else if (y0 <= (-3.3d+121)) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (y0 <= (-1.12d-7)) then
        tmp = t_3
    else if (y0 <= (-1.05d-299)) then
        tmp = t * (((j * t_1) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
    else if (y0 <= 2.1d-159) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
    else if (y0 <= 6.4d+30) then
        tmp = x * (i * ((j * y1) - (y * c)))
    else if (y0 <= 9.6d+61) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (y0 <= 1.7d+112) then
        tmp = t_3
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * 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 t_1 = (b * y4) - (i * y5);
	double t_2 = y0 * ((z * k) - (x * j));
	double t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2);
	double tmp;
	if (y0 <= -4.6e+212) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y0 <= -3.8e+181) {
		tmp = j * (t * t_1);
	} else if (y0 <= -1.15e+141) {
		tmp = b * t_2;
	} else if (y0 <= -3.3e+121) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y0 <= -1.12e-7) {
		tmp = t_3;
	} else if (y0 <= -1.05e-299) {
		tmp = t * (((j * t_1) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y0 <= 2.1e-159) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y0 <= 6.4e+30) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y0 <= 9.6e+61) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y0 <= 1.7e+112) {
		tmp = t_3;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	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 = y0 * ((z * k) - (x * j))
	t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2)
	tmp = 0
	if y0 <= -4.6e+212:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y0 <= -3.8e+181:
		tmp = j * (t * t_1)
	elif y0 <= -1.15e+141:
		tmp = b * t_2
	elif y0 <= -3.3e+121:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif y0 <= -1.12e-7:
		tmp = t_3
	elif y0 <= -1.05e-299:
		tmp = t * (((j * t_1) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
	elif y0 <= 2.1e-159:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
	elif y0 <= 6.4e+30:
		tmp = x * (i * ((j * y1) - (y * c)))
	elif y0 <= 9.6e+61:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif y0 <= 1.7e+112:
		tmp = t_3
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	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(y0 * Float64(Float64(z * k) - Float64(x * j)))
	t_3 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + t_2))
	tmp = 0.0
	if (y0 <= -4.6e+212)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y0 <= -3.8e+181)
		tmp = Float64(j * Float64(t * t_1));
	elseif (y0 <= -1.15e+141)
		tmp = Float64(b * t_2);
	elseif (y0 <= -3.3e+121)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y0 <= -1.12e-7)
		tmp = t_3;
	elseif (y0 <= -1.05e-299)
		tmp = Float64(t * Float64(Float64(Float64(j * t_1) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 2.1e-159)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(a * Float64(z * y1)) - Float64(j * Float64(y1 * y4)))));
	elseif (y0 <= 6.4e+30)
		tmp = Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (y0 <= 9.6e+61)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (y0 <= 1.7e+112)
		tmp = t_3;
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * 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)
	t_1 = (b * y4) - (i * y5);
	t_2 = y0 * ((z * k) - (x * j));
	t_3 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2);
	tmp = 0.0;
	if (y0 <= -4.6e+212)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y0 <= -3.8e+181)
		tmp = j * (t * t_1);
	elseif (y0 <= -1.15e+141)
		tmp = b * t_2;
	elseif (y0 <= -3.3e+121)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (y0 <= -1.12e-7)
		tmp = t_3;
	elseif (y0 <= -1.05e-299)
		tmp = t * (((j * t_1) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (y0 <= 2.1e-159)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	elseif (y0 <= 6.4e+30)
		tmp = x * (i * ((j * y1) - (y * c)));
	elseif (y0 <= 9.6e+61)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (y0 <= 1.7e+112)
		tmp = t_3;
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	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[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -4.6e+212], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.8e+181], N[(j * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.15e+141], N[(b * t$95$2), $MachinePrecision], If[LessEqual[y0, -3.3e+121], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.12e-7], t$95$3, If[LessEqual[y0, -1.05e-299], N[(t * N[(N[(N[(j * t$95$1), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.1e-159], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(z * y1), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.4e+30], N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9.6e+61], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.7e+112], t$95$3, N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y0 < -4.5999999999999997e212

   1. Initial program 13.6%

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

   3. Taylor expanded in y3 around -inf 50.3%

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

   4. Taylor expanded in c around inf 68.6%

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

   if -4.5999999999999997e212 < y0 < -3.8000000000000001e181

   1. Initial program 25.0%

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

   3. Taylor expanded in t around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in j around inf 59.1%

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

   if -3.8000000000000001e181 < y0 < -1.1500000000000001e141

   1. Initial program 28.6%

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

   3. Taylor expanded in b around inf 85.7%

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

   4. Taylor expanded in y0 around inf 100.0%

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

   if -1.1500000000000001e141 < y0 < -3.29999999999999979e121

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in y4 around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. *-commutative 60.9%

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

   8. Simplified 60.9%

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

   if -3.29999999999999979e121 < y0 < -1.12e-7 or 9.5999999999999995e61 < y0 < 1.69999999999999997e112

   1. Initial program 32.7%

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

   3. Taylor expanded in b around inf 61.1%

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

   if -1.12e-7 < y0 < -1.05000000000000005e-299

   1. Initial program 42.4%

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

   3. Taylor expanded in t around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

      4. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   if -1.05000000000000005e-299 < y0 < 2.0999999999999999e-159

   1. Initial program 40.0%

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

   3. Taylor expanded in y3 around -inf 64.4%

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

   4. Taylor expanded in y0 around 0 64.3%

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

   if 2.0999999999999999e-159 < y0 < 6.39999999999999945e30

   1. Initial program 35.3%

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

   3. Taylor expanded in x around inf 53.7%

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

   4. Taylor expanded in i around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

   6. Simplified 57.0%

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

   if 6.39999999999999945e30 < y0 < 9.5999999999999995e61

   1. Initial program 0.0%

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

   3. Taylor expanded in k around inf 33.3%

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

      1. +-commutative 33.3%

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

      2. mul-1-neg 33.3%

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

      3. unsub-neg 33.3%

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

      4. *-commutative 33.3%

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

      5. associate-*r* 33.3%

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

      6. neg-mul-1 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in y around inf 67.9%

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

   if 1.69999999999999997e112 < y0

   1. Initial program 14.0%

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

   3. Taylor expanded in k around inf 41.2%

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

      1. +-commutative 41.2%

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

      2. mul-1-neg 41.2%

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

      3. unsub-neg 41.2%

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

      4. *-commutative 41.2%

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

      5. associate-*r* 41.2%

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

      6. neg-mul-1 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in y2 around inf 61.9%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.6 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -3.8 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{+141}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -3.3 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.12 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.05 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{-159}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 6.4 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 9.6 \cdot 10^{+61}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i - a \cdot b\\ t_2 := b \cdot y4 - i \cdot y5\\ t_3 := y0 \cdot \left(z \cdot k - x \cdot j\right)\\ t_4 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + t\_3\right)\\ \mathbf{if}\;y0 \leq -1.7 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -2.7 \cdot 10^{+180}:\\ \;\;\;\;j \cdot \left(t \cdot t\_2\right)\\ \mathbf{elif}\;y0 \leq -4.4 \cdot 10^{+140}:\\ \;\;\;\;b \cdot t\_3\\ \mathbf{elif}\;y0 \leq -2.4 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot t\_1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -5.2 \cdot 10^{-9}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y0 \leq -1.95 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t\_2 + z \cdot t\_1\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 7.8 \cdot 10^{-162}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{+65}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 3.9 \cdot 10^{+111}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c i) (* a b)))
        (t_2 (- (* b y4) (* i y5)))
        (t_3 (* y0 (- (* z k) (* x j))))
        (t_4
         (*
          b
          (+ (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k)))) t_3))))
   (if (<= y0 -1.7e+212)
     (* c (* y3 (- (* y y4) (* z y0))))
     (if (<= y0 -2.7e+180)
       (* j (* t t_2))
       (if (<= y0 -4.4e+140)
         (* b t_3)
         (if (<= y0 -2.4e+115)
           (*
            x
            (+
             (- (* y2 (- (* c y0) (* a y1))) (* y t_1))
             (* j (- (* i y1) (* b y0)))))
           (if (<= y0 -5.2e-9)
             t_4
             (if (<= y0 -1.95e-299)
               (* t (+ (+ (* j t_2) (* z t_1)) (* y2 (- (* a y5) (* c y4)))))
               (if (<= y0 7.8e-162)
                 (*
                  y3
                  (+
                   (* y (- (* c y4) (* a y5)))
                   (- (* a (* z y1)) (* j (* y1 y4)))))
                 (if (<= y0 4.8e+29)
                   (* x (* i (- (* j y1) (* y c))))
                   (if (<= y0 9e+65)
                     (* k (* y (- (* i y5) (* b y4))))
                     (if (<= y0 3.9e+111)
                       t_4
                       (* k (* y2 (- (* y1 y4) (* y0 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 t_1 = (c * i) - (a * b);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = y0 * ((z * k) - (x * j));
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_3);
	double tmp;
	if (y0 <= -1.7e+212) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y0 <= -2.7e+180) {
		tmp = j * (t * t_2);
	} else if (y0 <= -4.4e+140) {
		tmp = b * t_3;
	} else if (y0 <= -2.4e+115) {
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_1)) + (j * ((i * y1) - (b * y0))));
	} else if (y0 <= -5.2e-9) {
		tmp = t_4;
	} else if (y0 <= -1.95e-299) {
		tmp = t * (((j * t_2) + (z * t_1)) + (y2 * ((a * y5) - (c * y4))));
	} else if (y0 <= 7.8e-162) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y0 <= 4.8e+29) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y0 <= 9e+65) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y0 <= 3.9e+111) {
		tmp = t_4;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (c * i) - (a * b)
    t_2 = (b * y4) - (i * y5)
    t_3 = y0 * ((z * k) - (x * j))
    t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_3)
    if (y0 <= (-1.7d+212)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y0 <= (-2.7d+180)) then
        tmp = j * (t * t_2)
    else if (y0 <= (-4.4d+140)) then
        tmp = b * t_3
    else if (y0 <= (-2.4d+115)) then
        tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_1)) + (j * ((i * y1) - (b * y0))))
    else if (y0 <= (-5.2d-9)) then
        tmp = t_4
    else if (y0 <= (-1.95d-299)) then
        tmp = t * (((j * t_2) + (z * t_1)) + (y2 * ((a * y5) - (c * y4))))
    else if (y0 <= 7.8d-162) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
    else if (y0 <= 4.8d+29) then
        tmp = x * (i * ((j * y1) - (y * c)))
    else if (y0 <= 9d+65) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (y0 <= 3.9d+111) then
        tmp = t_4
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * 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 t_1 = (c * i) - (a * b);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = y0 * ((z * k) - (x * j));
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_3);
	double tmp;
	if (y0 <= -1.7e+212) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y0 <= -2.7e+180) {
		tmp = j * (t * t_2);
	} else if (y0 <= -4.4e+140) {
		tmp = b * t_3;
	} else if (y0 <= -2.4e+115) {
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_1)) + (j * ((i * y1) - (b * y0))));
	} else if (y0 <= -5.2e-9) {
		tmp = t_4;
	} else if (y0 <= -1.95e-299) {
		tmp = t * (((j * t_2) + (z * t_1)) + (y2 * ((a * y5) - (c * y4))));
	} else if (y0 <= 7.8e-162) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y0 <= 4.8e+29) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y0 <= 9e+65) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y0 <= 3.9e+111) {
		tmp = t_4;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * i) - (a * b)
	t_2 = (b * y4) - (i * y5)
	t_3 = y0 * ((z * k) - (x * j))
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_3)
	tmp = 0
	if y0 <= -1.7e+212:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y0 <= -2.7e+180:
		tmp = j * (t * t_2)
	elif y0 <= -4.4e+140:
		tmp = b * t_3
	elif y0 <= -2.4e+115:
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_1)) + (j * ((i * y1) - (b * y0))))
	elif y0 <= -5.2e-9:
		tmp = t_4
	elif y0 <= -1.95e-299:
		tmp = t * (((j * t_2) + (z * t_1)) + (y2 * ((a * y5) - (c * y4))))
	elif y0 <= 7.8e-162:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
	elif y0 <= 4.8e+29:
		tmp = x * (i * ((j * y1) - (y * c)))
	elif y0 <= 9e+65:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif y0 <= 3.9e+111:
		tmp = t_4
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * i) - Float64(a * b))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	t_3 = Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))
	t_4 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + t_3))
	tmp = 0.0
	if (y0 <= -1.7e+212)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y0 <= -2.7e+180)
		tmp = Float64(j * Float64(t * t_2));
	elseif (y0 <= -4.4e+140)
		tmp = Float64(b * t_3);
	elseif (y0 <= -2.4e+115)
		tmp = Float64(x * Float64(Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(y * t_1)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y0 <= -5.2e-9)
		tmp = t_4;
	elseif (y0 <= -1.95e-299)
		tmp = Float64(t * Float64(Float64(Float64(j * t_2) + Float64(z * t_1)) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 7.8e-162)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(a * Float64(z * y1)) - Float64(j * Float64(y1 * y4)))));
	elseif (y0 <= 4.8e+29)
		tmp = Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (y0 <= 9e+65)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (y0 <= 3.9e+111)
		tmp = t_4;
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * 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)
	t_1 = (c * i) - (a * b);
	t_2 = (b * y4) - (i * y5);
	t_3 = y0 * ((z * k) - (x * j));
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_3);
	tmp = 0.0;
	if (y0 <= -1.7e+212)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y0 <= -2.7e+180)
		tmp = j * (t * t_2);
	elseif (y0 <= -4.4e+140)
		tmp = b * t_3;
	elseif (y0 <= -2.4e+115)
		tmp = x * (((y2 * ((c * y0) - (a * y1))) - (y * t_1)) + (j * ((i * y1) - (b * y0))));
	elseif (y0 <= -5.2e-9)
		tmp = t_4;
	elseif (y0 <= -1.95e-299)
		tmp = t * (((j * t_2) + (z * t_1)) + (y2 * ((a * y5) - (c * y4))));
	elseif (y0 <= 7.8e-162)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	elseif (y0 <= 4.8e+29)
		tmp = x * (i * ((j * y1) - (y * c)));
	elseif (y0 <= 9e+65)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (y0 <= 3.9e+111)
		tmp = t_4;
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.7e+212], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.7e+180], N[(j * N[(t * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4.4e+140], N[(b * t$95$3), $MachinePrecision], If[LessEqual[y0, -2.4e+115], N[(x * N[(N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5.2e-9], t$95$4, If[LessEqual[y0, -1.95e-299], N[(t * N[(N[(N[(j * t$95$2), $MachinePrecision] + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7.8e-162], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(z * y1), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.8e+29], N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9e+65], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.9e+111], t$95$4, N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y0 < -1.70000000000000018e212

   1. Initial program 13.6%

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

   3. Taylor expanded in y3 around -inf 50.3%

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

   4. Taylor expanded in c around inf 68.6%

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

   if -1.70000000000000018e212 < y0 < -2.70000000000000016e180

   1. Initial program 25.0%

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

   3. Taylor expanded in t around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in j around inf 59.1%

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

   if -2.70000000000000016e180 < y0 < -4.3999999999999997e140

   1. Initial program 28.6%

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

   3. Taylor expanded in b around inf 85.7%

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

   4. Taylor expanded in y0 around inf 100.0%

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

   if -4.3999999999999997e140 < y0 < -2.4e115

   1. Initial program 0.9%

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

   3. Taylor expanded in x around inf 71.2%

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

   if -2.4e115 < y0 < -5.2000000000000002e-9 or 9e65 < y0 < 3.89999999999999979e111

   1. Initial program 34.3%

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

   3. Taylor expanded in b around inf 61.6%

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

   if -5.2000000000000002e-9 < y0 < -1.9499999999999999e-299

   1. Initial program 42.4%

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

   3. Taylor expanded in t around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

      4. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   if -1.9499999999999999e-299 < y0 < 7.7999999999999999e-162

   1. Initial program 40.0%

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

   3. Taylor expanded in y3 around -inf 64.4%

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

   4. Taylor expanded in y0 around 0 64.3%

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

   if 7.7999999999999999e-162 < y0 < 4.8000000000000002e29

   1. Initial program 35.3%

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

   3. Taylor expanded in x around inf 53.7%

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

   4. Taylor expanded in i around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

   6. Simplified 57.0%

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

   if 4.8000000000000002e29 < y0 < 9e65

   1. Initial program 0.0%

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

   3. Taylor expanded in k around inf 33.3%

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

      1. +-commutative 33.3%

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

      2. mul-1-neg 33.3%

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

      3. unsub-neg 33.3%

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

      4. *-commutative 33.3%

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

      5. associate-*r* 33.3%

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

      6. neg-mul-1 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in y around inf 67.9%

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

   if 3.89999999999999979e111 < y0

   1. Initial program 14.0%

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

   3. Taylor expanded in k around inf 41.2%

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

      1. +-commutative 41.2%

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

      2. mul-1-neg 41.2%

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

      3. unsub-neg 41.2%

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

      4. *-commutative 41.2%

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

      5. associate-*r* 41.2%

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

      6. neg-mul-1 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in y2 around inf 61.9%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.7 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -2.7 \cdot 10^{+180}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -4.4 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -2.4 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot i - a \cdot b\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -5.2 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.95 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 7.8 \cdot 10^{-162}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{+65}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 3.9 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := z \cdot k - x \cdot j\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot t\_4 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ t_6 := t \cdot j - y \cdot k\\ t_7 := y4 \cdot \left(\left(b \cdot t\_6 + y1 \cdot t\_4\right) + c \cdot t\_1\right)\\ \mathbf{if}\;y1 \leq -2.05 \cdot 10^{+229}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -2.7 \cdot 10^{+158}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{+136}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;y1 \leq -4.1 \cdot 10^{-42}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y1 \leq -4.4 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 7.5 \cdot 10^{-253}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot t\_2 + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot t\_1\right)\\ \mathbf{elif}\;y1 \leq 4.6 \cdot 10^{-130}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t\_6\right) + y0 \cdot t\_3\right)\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{-55}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot t\_2 + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot t\_3\right)\\ \mathbf{elif}\;y1 \leq 2.1 \cdot 10^{+80}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{+126}:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y y3) (* t y2)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* z k) (* x j)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5
         (*
          y1
          (+
           (* i (- (* x j) (* z k)))
           (+ (* y4 t_4) (* a (- (* z y3) (* x y2)))))))
        (t_6 (- (* t j) (* y k)))
        (t_7 (* y4 (+ (+ (* b t_6) (* y1 t_4)) (* c t_1)))))
   (if (<= y1 -2.05e+229)
     (* y3 (* z (- (* a y1) (* c y0))))
     (if (<= y1 -2.7e+158)
       t_5
       (if (<= y1 -2.4e+136)
         t_7
         (if (<= y1 -4.1e-42)
           t_5
           (if (<= y1 -4.4e-276)
             (*
              t
              (+
               (+ (* j (- (* b y4) (* i y5))) (* z (- (* c i) (* a b))))
               (* y2 (- (* a y5) (* c y4)))))
             (if (<= y1 7.5e-253)
               (* c (+ (+ (* y0 t_2) (* i (- (* z t) (* x y)))) (* y4 t_1)))
               (if (<= y1 4.6e-130)
                 (* b (+ (+ (* a (- (* x y) (* z t))) (* y4 t_6)) (* y0 t_3)))
                 (if (<= y1 3.8e-55)
                   (*
                    y0
                    (+ (+ (* c t_2) (* y5 (- (* j y3) (* k y2)))) (* b t_3)))
                   (if (<= y1 2.1e+80)
                     (*
                      y3
                      (+
                       (* y (- (* c y4) (* a y5)))
                       (- (* a (* z y1)) (* j (* y1 y4)))))
                     (if (<= y1 3.2e+126) t_7 t_5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (z * k) - (x * j);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))));
	double t_6 = (t * j) - (y * k);
	double t_7 = y4 * (((b * t_6) + (y1 * t_4)) + (c * t_1));
	double tmp;
	if (y1 <= -2.05e+229) {
		tmp = y3 * (z * ((a * y1) - (c * y0)));
	} else if (y1 <= -2.7e+158) {
		tmp = t_5;
	} else if (y1 <= -2.4e+136) {
		tmp = t_7;
	} else if (y1 <= -4.1e-42) {
		tmp = t_5;
	} else if (y1 <= -4.4e-276) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y1 <= 7.5e-253) {
		tmp = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * t_1));
	} else if (y1 <= 4.6e-130) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_6)) + (y0 * t_3));
	} else if (y1 <= 3.8e-55) {
		tmp = y0 * (((c * t_2) + (y5 * ((j * y3) - (k * y2)))) + (b * t_3));
	} else if (y1 <= 2.1e+80) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y1 <= 3.2e+126) {
		tmp = t_7;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (y * y3) - (t * y2)
    t_2 = (x * y2) - (z * y3)
    t_3 = (z * k) - (x * j)
    t_4 = (k * y2) - (j * y3)
    t_5 = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))))
    t_6 = (t * j) - (y * k)
    t_7 = y4 * (((b * t_6) + (y1 * t_4)) + (c * t_1))
    if (y1 <= (-2.05d+229)) then
        tmp = y3 * (z * ((a * y1) - (c * y0)))
    else if (y1 <= (-2.7d+158)) then
        tmp = t_5
    else if (y1 <= (-2.4d+136)) then
        tmp = t_7
    else if (y1 <= (-4.1d-42)) then
        tmp = t_5
    else if (y1 <= (-4.4d-276)) then
        tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
    else if (y1 <= 7.5d-253) then
        tmp = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * t_1))
    else if (y1 <= 4.6d-130) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_6)) + (y0 * t_3))
    else if (y1 <= 3.8d-55) then
        tmp = y0 * (((c * t_2) + (y5 * ((j * y3) - (k * y2)))) + (b * t_3))
    else if (y1 <= 2.1d+80) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
    else if (y1 <= 3.2d+126) then
        tmp = t_7
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (z * k) - (x * j);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))));
	double t_6 = (t * j) - (y * k);
	double t_7 = y4 * (((b * t_6) + (y1 * t_4)) + (c * t_1));
	double tmp;
	if (y1 <= -2.05e+229) {
		tmp = y3 * (z * ((a * y1) - (c * y0)));
	} else if (y1 <= -2.7e+158) {
		tmp = t_5;
	} else if (y1 <= -2.4e+136) {
		tmp = t_7;
	} else if (y1 <= -4.1e-42) {
		tmp = t_5;
	} else if (y1 <= -4.4e-276) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y1 <= 7.5e-253) {
		tmp = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * t_1));
	} else if (y1 <= 4.6e-130) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_6)) + (y0 * t_3));
	} else if (y1 <= 3.8e-55) {
		tmp = y0 * (((c * t_2) + (y5 * ((j * y3) - (k * y2)))) + (b * t_3));
	} else if (y1 <= 2.1e+80) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y1 <= 3.2e+126) {
		tmp = t_7;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * y3) - (t * y2)
	t_2 = (x * y2) - (z * y3)
	t_3 = (z * k) - (x * j)
	t_4 = (k * y2) - (j * y3)
	t_5 = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))))
	t_6 = (t * j) - (y * k)
	t_7 = y4 * (((b * t_6) + (y1 * t_4)) + (c * t_1))
	tmp = 0
	if y1 <= -2.05e+229:
		tmp = y3 * (z * ((a * y1) - (c * y0)))
	elif y1 <= -2.7e+158:
		tmp = t_5
	elif y1 <= -2.4e+136:
		tmp = t_7
	elif y1 <= -4.1e-42:
		tmp = t_5
	elif y1 <= -4.4e-276:
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
	elif y1 <= 7.5e-253:
		tmp = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * t_1))
	elif y1 <= 4.6e-130:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_6)) + (y0 * t_3))
	elif y1 <= 3.8e-55:
		tmp = y0 * (((c * t_2) + (y5 * ((j * y3) - (k * y2)))) + (b * t_3))
	elif y1 <= 2.1e+80:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))))
	elif y1 <= 3.2e+126:
		tmp = t_7
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * y3) - Float64(t * y2))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(z * k) - Float64(x * j))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y4 * t_4) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))))
	t_6 = Float64(Float64(t * j) - Float64(y * k))
	t_7 = Float64(y4 * Float64(Float64(Float64(b * t_6) + Float64(y1 * t_4)) + Float64(c * t_1)))
	tmp = 0.0
	if (y1 <= -2.05e+229)
		tmp = Float64(y3 * Float64(z * Float64(Float64(a * y1) - Float64(c * y0))));
	elseif (y1 <= -2.7e+158)
		tmp = t_5;
	elseif (y1 <= -2.4e+136)
		tmp = t_7;
	elseif (y1 <= -4.1e-42)
		tmp = t_5;
	elseif (y1 <= -4.4e-276)
		tmp = Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y1 <= 7.5e-253)
		tmp = Float64(c * Float64(Float64(Float64(y0 * t_2) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * t_1)));
	elseif (y1 <= 4.6e-130)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_6)) + Float64(y0 * t_3)));
	elseif (y1 <= 3.8e-55)
		tmp = Float64(y0 * Float64(Float64(Float64(c * t_2) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * t_3)));
	elseif (y1 <= 2.1e+80)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(a * Float64(z * y1)) - Float64(j * Float64(y1 * y4)))));
	elseif (y1 <= 3.2e+126)
		tmp = t_7;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * y3) - (t * y2);
	t_2 = (x * y2) - (z * y3);
	t_3 = (z * k) - (x * j);
	t_4 = (k * y2) - (j * y3);
	t_5 = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))));
	t_6 = (t * j) - (y * k);
	t_7 = y4 * (((b * t_6) + (y1 * t_4)) + (c * t_1));
	tmp = 0.0;
	if (y1 <= -2.05e+229)
		tmp = y3 * (z * ((a * y1) - (c * y0)));
	elseif (y1 <= -2.7e+158)
		tmp = t_5;
	elseif (y1 <= -2.4e+136)
		tmp = t_7;
	elseif (y1 <= -4.1e-42)
		tmp = t_5;
	elseif (y1 <= -4.4e-276)
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (y1 <= 7.5e-253)
		tmp = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * t_1));
	elseif (y1 <= 4.6e-130)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_6)) + (y0 * t_3));
	elseif (y1 <= 3.8e-55)
		tmp = y0 * (((c * t_2) + (y5 * ((j * y3) - (k * y2)))) + (b * t_3));
	elseif (y1 <= 2.1e+80)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((a * (z * y1)) - (j * (y1 * y4))));
	elseif (y1 <= 3.2e+126)
		tmp = t_7;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * t$95$4), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y4 * N[(N[(N[(b * t$95$6), $MachinePrecision] + N[(y1 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -2.05e+229], N[(y3 * N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.7e+158], t$95$5, If[LessEqual[y1, -2.4e+136], t$95$7, If[LessEqual[y1, -4.1e-42], t$95$5, If[LessEqual[y1, -4.4e-276], N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7.5e-253], N[(c * N[(N[(N[(y0 * t$95$2), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.6e-130], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.8e-55], N[(y0 * N[(N[(N[(c * t$95$2), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.1e+80], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(z * y1), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.2e+126], t$95$7, t$95$5]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y1 < -2.0500000000000001e229

   1. Initial program 17.2%

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

   3. Taylor expanded in y3 around -inf 28.1%

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

   4. Taylor expanded in z around inf 59.1%

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

   if -2.0500000000000001e229 < y1 < -2.69999999999999979e158 or -2.4e136 < y1 < -4.1000000000000001e-42 or 3.1999999999999998e126 < y1

   1. Initial program 24.1%

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

   3. Taylor expanded in y1 around -inf 64.4%

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

      1. associate-*r* 64.4%

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

      2. neg-mul-1 64.4%

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

      3. +-commutative 64.4%

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

      4. mul-1-neg 64.4%

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

      5. unsub-neg 64.4%

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

      6. *-commutative 64.4%

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

      7. *-commutative 64.4%

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

      8. *-commutative 64.4%

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

      9. *-commutative 64.4%

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

   5. Simplified 64.4%

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

   if -2.69999999999999979e158 < y1 < -2.4e136 or 2.10000000000000001e80 < y1 < 3.1999999999999998e126

   1. Initial program 28.6%

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

   3. Taylor expanded in y4 around inf 93.0%

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

   if -4.1000000000000001e-42 < y1 < -4.39999999999999961e-276

   1. Initial program 41.3%

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

   3. Taylor expanded in t around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. mul-1-neg 62.0%

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

      3. unsub-neg 62.0%

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

      4. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   if -4.39999999999999961e-276 < y1 < 7.49999999999999987e-253

   1. Initial program 33.6%

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

   3. Taylor expanded in c around inf 64.6%

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

      1. +-commutative 64.6%

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

      2. mul-1-neg 64.6%

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

      3. unsub-neg 64.6%

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

      4. *-commutative 64.6%

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

      5. *-commutative 64.6%

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

      6. *-commutative 64.6%

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

      7. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   if 7.49999999999999987e-253 < y1 < 4.6000000000000002e-130

   1. Initial program 33.3%

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

   3. Taylor expanded in b around inf 60.0%

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

   if 4.6000000000000002e-130 < y1 < 3.7999999999999997e-55

   1. Initial program 33.9%

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

   3. Taylor expanded in y0 around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

      4. *-commutative 73.4%

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

      5. *-commutative 73.4%

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

      6. *-commutative 73.4%

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

      7. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if 3.7999999999999997e-55 < y1 < 2.10000000000000001e80

   1. Initial program 21.7%

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

   3. Taylor expanded in y3 around -inf 48.3%

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

   4. Taylor expanded in y0 around 0 57.2%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(\left(-1 \cdot \left(a \cdot \left(y1 \cdot z\right)\right) + j \cdot \left(y1 \cdot y4\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.05 \cdot 10^{+229}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -2.7 \cdot 10^{+158}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{+136}:\\ \;\;\;\;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}\;y1 \leq -4.1 \cdot 10^{-42}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -4.4 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 7.5 \cdot 10^{-253}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 4.6 \cdot 10^{-130}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{-55}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.1 \cdot 10^{+80}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{+126}:\\ \;\;\;\;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}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 32.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y4 \leq -1.15 \cdot 10^{+180}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -6.3 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -2.05 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -1.45 \cdot 10^{-232}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 1.45 \cdot 10^{-292}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 3.5 \cdot 10^{-221}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y4 \leq 6.4 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 1.32 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 7.2 \cdot 10^{+210}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* j (- (* i y1) (* b y0))))))
   (if (<= y4 -1.15e+180)
     (* b (* y4 (- (* t j) (* y k))))
     (if (<= y4 -6.3e+90)
       (* y2 (* y4 (- (* k y1) (* t c))))
       (if (<= y4 -2.05e-36)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y4 -1.45e-232)
           (* c (* y0 (- (* x y2) (* z y3))))
           (if (<= y4 1.45e-292)
             (* k (* z (- (* b y0) (* i y1))))
             (if (<= y4 3.5e-221)
               (* j (* t (- (* b y4) (* i y5))))
               (if (<= y4 6.5e-212)
                 (* a (* (* x y) b))
                 (if (<= y4 6.4e-99)
                   t_1
                   (if (<= y4 1.32e-29)
                     (* t (* a (- (* y2 y5) (* z b))))
                     (if (<= y4 7.5e+61)
                       t_1
                       (if (<= y4 7.2e+210)
                         (* c (* y4 (- (* y y3) (* t y2))))
                         (* y1 (* y4 (- (* k y2) (* j y3)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (j * ((i * y1) - (b * y0)));
	double tmp;
	if (y4 <= -1.15e+180) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -6.3e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -2.05e-36) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= -1.45e-232) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y4 <= 1.45e-292) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y4 <= 3.5e-221) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y4 <= 6.5e-212) {
		tmp = a * ((x * y) * b);
	} else if (y4 <= 6.4e-99) {
		tmp = t_1;
	} else if (y4 <= 1.32e-29) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (y4 <= 7.5e+61) {
		tmp = t_1;
	} else if (y4 <= 7.2e+210) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (j * ((i * y1) - (b * y0)))
    if (y4 <= (-1.15d+180)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y4 <= (-6.3d+90)) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y4 <= (-2.05d-36)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y4 <= (-1.45d-232)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y4 <= 1.45d-292) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (y4 <= 3.5d-221) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y4 <= 6.5d-212) then
        tmp = a * ((x * y) * b)
    else if (y4 <= 6.4d-99) then
        tmp = t_1
    else if (y4 <= 1.32d-29) then
        tmp = t * (a * ((y2 * y5) - (z * b)))
    else if (y4 <= 7.5d+61) then
        tmp = t_1
    else if (y4 <= 7.2d+210) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (j * ((i * y1) - (b * y0)));
	double tmp;
	if (y4 <= -1.15e+180) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -6.3e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -2.05e-36) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= -1.45e-232) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y4 <= 1.45e-292) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y4 <= 3.5e-221) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y4 <= 6.5e-212) {
		tmp = a * ((x * y) * b);
	} else if (y4 <= 6.4e-99) {
		tmp = t_1;
	} else if (y4 <= 1.32e-29) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (y4 <= 7.5e+61) {
		tmp = t_1;
	} else if (y4 <= 7.2e+210) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (j * ((i * y1) - (b * y0)))
	tmp = 0
	if y4 <= -1.15e+180:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y4 <= -6.3e+90:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y4 <= -2.05e-36:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y4 <= -1.45e-232:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y4 <= 1.45e-292:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif y4 <= 3.5e-221:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y4 <= 6.5e-212:
		tmp = a * ((x * y) * b)
	elif y4 <= 6.4e-99:
		tmp = t_1
	elif y4 <= 1.32e-29:
		tmp = t * (a * ((y2 * y5) - (z * b)))
	elif y4 <= 7.5e+61:
		tmp = t_1
	elif y4 <= 7.2e+210:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))))
	tmp = 0.0
	if (y4 <= -1.15e+180)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y4 <= -6.3e+90)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y4 <= -2.05e-36)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= -1.45e-232)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y4 <= 1.45e-292)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (y4 <= 3.5e-221)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y4 <= 6.5e-212)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y4 <= 6.4e-99)
		tmp = t_1;
	elseif (y4 <= 1.32e-29)
		tmp = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (y4 <= 7.5e+61)
		tmp = t_1;
	elseif (y4 <= 7.2e+210)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (j * ((i * y1) - (b * y0)));
	tmp = 0.0;
	if (y4 <= -1.15e+180)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y4 <= -6.3e+90)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y4 <= -2.05e-36)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y4 <= -1.45e-232)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y4 <= 1.45e-292)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (y4 <= 3.5e-221)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y4 <= 6.5e-212)
		tmp = a * ((x * y) * b);
	elseif (y4 <= 6.4e-99)
		tmp = t_1;
	elseif (y4 <= 1.32e-29)
		tmp = t * (a * ((y2 * y5) - (z * b)));
	elseif (y4 <= 7.5e+61)
		tmp = t_1;
	elseif (y4 <= 7.2e+210)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.15e+180], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -6.3e+90], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.05e-36], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.45e-232], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.45e-292], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.5e-221], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.5e-212], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.4e-99], t$95$1, If[LessEqual[y4, 1.32e-29], N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.5e+61], t$95$1, If[LessEqual[y4, 7.2e+210], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y4 < -1.1499999999999999e180

   1. Initial program 24.7%

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

   3. Taylor expanded in y4 around inf 62.7%

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

   4. Taylor expanded in b around inf 59.3%

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

   if -1.1499999999999999e180 < y4 < -6.3e90

   1. Initial program 28.6%

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

   3. Taylor expanded in y4 around inf 51.8%

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

   4. Taylor expanded in y2 around inf 72.3%

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

   if -6.3e90 < y4 < -2.05000000000000006e-36

   1. Initial program 25.0%

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

   3. Taylor expanded in b around inf 38.2%

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

   4. Taylor expanded in a around inf 57.2%

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

   if -2.05000000000000006e-36 < y4 < -1.45e-232

   1. Initial program 29.5%

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

   3. Taylor expanded in y0 around inf 44.6%

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

      1. +-commutative 44.6%

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

      2. mul-1-neg 44.6%

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

      3. unsub-neg 44.6%

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

      4. *-commutative 44.6%

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

      5. *-commutative 44.6%

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

      6. *-commutative 44.6%

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

      7. *-commutative 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in c around inf 38.7%

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

   if -1.45e-232 < y4 < 1.44999999999999996e-292

   1. Initial program 31.4%

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

   3. Taylor expanded in k around inf 49.0%

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

      1. +-commutative 49.0%

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

      2. mul-1-neg 49.0%

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

      3. unsub-neg 49.0%

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

      4. *-commutative 49.0%

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

      5. associate-*r* 49.0%

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

      6. neg-mul-1 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in z around inf 53.5%

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

   if 1.44999999999999996e-292 < y4 < 3.4999999999999999e-221

   1. Initial program 50.0%

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

   3. Taylor expanded in t around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. mul-1-neg 67.2%

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

      3. unsub-neg 67.2%

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

      4. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in j around inf 59.2%

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

   if 3.4999999999999999e-221 < y4 < 6.5e-212

   1. Initial program 0.0%

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

   3. Taylor expanded in b around inf 50.0%

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

   4. Taylor expanded in a around inf 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

   if 6.5e-212 < y4 < 6.4000000000000001e-99 or 1.3200000000000001e-29 < y4 < 7.5e61

   1. Initial program 32.1%

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

   3. Taylor expanded in x around inf 43.8%

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

   4. Taylor expanded in j around inf 44.2%

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

   if 6.4000000000000001e-99 < y4 < 1.3200000000000001e-29

   1. Initial program 20.0%

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

   3. Taylor expanded in t around inf 40.0%

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

      1. +-commutative 40.0%

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

      2. mul-1-neg 40.0%

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

      3. unsub-neg 40.0%

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

      4. *-commutative 40.0%

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

   5. Simplified 40.0%

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

   6. Taylor expanded in a around -inf 70.1%

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

      1. +-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

      4. *-commutative 70.1%

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

   8. Simplified 70.1%

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

   if 7.5e61 < y4 < 7.2000000000000005e210

   1. Initial program 28.9%

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

   3. Taylor expanded in y4 around inf 63.6%

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

   4. Taylor expanded in c around inf 58.2%

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

   if 7.2000000000000005e210 < y4

   1. Initial program 25.9%

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

   3. Taylor expanded in y4 around inf 77.7%

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

   4. Taylor expanded in y1 around inf 74.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.15 \cdot 10^{+180}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -6.3 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -2.05 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -1.45 \cdot 10^{-232}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 1.45 \cdot 10^{-292}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 3.5 \cdot 10^{-221}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y4 \leq 6.4 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.32 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 7.2 \cdot 10^{+210}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{if}\;y4 \leq -2.5 \cdot 10^{+177}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.8 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -4.5 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -2.4 \cdot 10^{-131}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.6 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -3.4 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 1.06 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y4 \leq 1.55 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 2 \cdot 10^{+31}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 1.7 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 8.2 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* z y3) (- (* a y1) (* c y0)))))
   (if (<= y4 -2.5e+177)
     (* b (* y4 (- (* t j) (* y k))))
     (if (<= y4 -1.8e+90)
       (* y2 (* y4 (- (* k y1) (* t c))))
       (if (<= y4 -4.5e-44)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y4 -2.4e-131)
           (* c (* y3 (- (* y y4) (* z y0))))
           (if (<= y4 -1.6e-175)
             (* x (* j (- (* i y1) (* b y0))))
             (if (<= y4 -3.4e-262)
               t_1
               (if (<= y4 1.06e-287)
                 (* b (* z (- (* k y0) (* t a))))
                 (if (<= y4 1.55e-89)
                   (* x (* i (- (* j y1) (* y c))))
                   (if (<= y4 2e+31)
                     (* k (* y0 (- (* z b) (* y2 y5))))
                     (if (<= y4 1.7e+152)
                       t_1
                       (if (<= y4 8.2e+212)
                         (* c (* y4 (- (* y y3) (* t y2))))
                         (* y3 (* y4 (- (* y c) (* j y1)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) * ((a * y1) - (c * y0));
	double tmp;
	if (y4 <= -2.5e+177) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.8e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -4.5e-44) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= -2.4e-131) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y4 <= -1.6e-175) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (y4 <= -3.4e-262) {
		tmp = t_1;
	} else if (y4 <= 1.06e-287) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y4 <= 1.55e-89) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y4 <= 2e+31) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (y4 <= 1.7e+152) {
		tmp = t_1;
	} else if (y4 <= 8.2e+212) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * y3) * ((a * y1) - (c * y0))
    if (y4 <= (-2.5d+177)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y4 <= (-1.8d+90)) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y4 <= (-4.5d-44)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y4 <= (-2.4d-131)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y4 <= (-1.6d-175)) then
        tmp = x * (j * ((i * y1) - (b * y0)))
    else if (y4 <= (-3.4d-262)) then
        tmp = t_1
    else if (y4 <= 1.06d-287) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (y4 <= 1.55d-89) then
        tmp = x * (i * ((j * y1) - (y * c)))
    else if (y4 <= 2d+31) then
        tmp = k * (y0 * ((z * b) - (y2 * y5)))
    else if (y4 <= 1.7d+152) then
        tmp = t_1
    else if (y4 <= 8.2d+212) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = y3 * (y4 * ((y * c) - (j * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) * ((a * y1) - (c * y0));
	double tmp;
	if (y4 <= -2.5e+177) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.8e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -4.5e-44) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= -2.4e-131) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y4 <= -1.6e-175) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (y4 <= -3.4e-262) {
		tmp = t_1;
	} else if (y4 <= 1.06e-287) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y4 <= 1.55e-89) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y4 <= 2e+31) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (y4 <= 1.7e+152) {
		tmp = t_1;
	} else if (y4 <= 8.2e+212) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (z * y3) * ((a * y1) - (c * y0))
	tmp = 0
	if y4 <= -2.5e+177:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y4 <= -1.8e+90:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y4 <= -4.5e-44:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y4 <= -2.4e-131:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y4 <= -1.6e-175:
		tmp = x * (j * ((i * y1) - (b * y0)))
	elif y4 <= -3.4e-262:
		tmp = t_1
	elif y4 <= 1.06e-287:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif y4 <= 1.55e-89:
		tmp = x * (i * ((j * y1) - (y * c)))
	elif y4 <= 2e+31:
		tmp = k * (y0 * ((z * b) - (y2 * y5)))
	elif y4 <= 1.7e+152:
		tmp = t_1
	elif y4 <= 8.2e+212:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = y3 * (y4 * ((y * c) - (j * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * y3) * Float64(Float64(a * y1) - Float64(c * y0)))
	tmp = 0.0
	if (y4 <= -2.5e+177)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y4 <= -1.8e+90)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y4 <= -4.5e-44)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= -2.4e-131)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y4 <= -1.6e-175)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y4 <= -3.4e-262)
		tmp = t_1;
	elseif (y4 <= 1.06e-287)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (y4 <= 1.55e-89)
		tmp = Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (y4 <= 2e+31)
		tmp = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (y4 <= 1.7e+152)
		tmp = t_1;
	elseif (y4 <= 8.2e+212)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(y3 * Float64(y4 * Float64(Float64(y * c) - Float64(j * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * y3) * ((a * y1) - (c * y0));
	tmp = 0.0;
	if (y4 <= -2.5e+177)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y4 <= -1.8e+90)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y4 <= -4.5e-44)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y4 <= -2.4e-131)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y4 <= -1.6e-175)
		tmp = x * (j * ((i * y1) - (b * y0)));
	elseif (y4 <= -3.4e-262)
		tmp = t_1;
	elseif (y4 <= 1.06e-287)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (y4 <= 1.55e-89)
		tmp = x * (i * ((j * y1) - (y * c)));
	elseif (y4 <= 2e+31)
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	elseif (y4 <= 1.7e+152)
		tmp = t_1;
	elseif (y4 <= 8.2e+212)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * y3), $MachinePrecision] * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.5e+177], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.8e+90], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -4.5e-44], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.4e-131], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.6e-175], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -3.4e-262], t$95$1, If[LessEqual[y4, 1.06e-287], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.55e-89], N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2e+31], N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.7e+152], t$95$1, If[LessEqual[y4, 8.2e+212], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(y4 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y4 < -2.5000000000000001e177

   1. Initial program 24.7%

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

   3. Taylor expanded in y4 around inf 62.7%

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

   4. Taylor expanded in b around inf 59.3%

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

   if -2.5000000000000001e177 < y4 < -1.8e90

   1. Initial program 28.6%

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

   3. Taylor expanded in y4 around inf 51.8%

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

   4. Taylor expanded in y2 around inf 72.3%

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

   if -1.8e90 < y4 < -4.4999999999999999e-44

   1. Initial program 25.0%

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

   3. Taylor expanded in b around inf 38.2%

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

   4. Taylor expanded in a around inf 57.2%

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

   if -4.4999999999999999e-44 < y4 < -2.4e-131

   1. Initial program 31.3%

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

   3. Taylor expanded in y3 around -inf 53.9%

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

   4. Taylor expanded in c around inf 47.8%

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

   if -2.4e-131 < y4 < -1.6e-175

   1. Initial program 11.8%

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

   3. Taylor expanded in x around inf 44.6%

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

   4. Taylor expanded in j around inf 66.9%

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

   if -1.6e-175 < y4 < -3.3999999999999999e-262 or 1.9999999999999999e31 < y4 < 1.7000000000000001e152

   1. Initial program 34.4%

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

   3. Taylor expanded in y3 around -inf 42.0%

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

   4. Taylor expanded in z around inf 52.6%

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

      1. associate-*r* 54.9%

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

   6. Simplified 54.9%

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

   if -3.3999999999999999e-262 < y4 < 1.0600000000000001e-287

   1. Initial program 33.1%

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

   3. Taylor expanded in b around inf 58.8%

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

   4. Taylor expanded in z around -inf 64.8%

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

      1. associate-*r* 64.8%

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

      2. neg-mul-1 64.8%

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

   6. Simplified 64.8%

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

   if 1.0600000000000001e-287 < y4 < 1.54999999999999998e-89

   1. Initial program 34.8%

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

   3. Taylor expanded in x around inf 37.5%

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

   4. Taylor expanded in i around -inf 46.6%

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

      1. mul-1-neg 46.6%

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

   6. Simplified 46.6%

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

   if 1.54999999999999998e-89 < y4 < 1.9999999999999999e31

   1. Initial program 27.7%

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

   3. Taylor expanded in k around inf 33.5%

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

      1. +-commutative 33.5%

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

      2. mul-1-neg 33.5%

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

      3. unsub-neg 33.5%

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

      4. *-commutative 33.5%

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

      5. associate-*r* 33.5%

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

      6. neg-mul-1 33.5%

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

   5. Simplified 33.5%

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

   6. Taylor expanded in y0 around -inf 55.9%

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

      1. associate-*r* 55.9%

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

      2. neg-mul-1 55.9%

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

   8. Simplified 55.9%

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

   if 1.7000000000000001e152 < y4 < 8.19999999999999978e212

   1. Initial program 25.2%

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

   3. Taylor expanded in y4 around inf 74.9%

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

   4. Taylor expanded in c around inf 70.3%

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

   if 8.19999999999999978e212 < y4

   1. Initial program 26.9%

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

   3. Taylor expanded in y4 around inf 76.9%

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

   4. Taylor expanded in y3 around -inf 77.2%

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

      1. mul-1-neg 77.2%

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

   6. Simplified 77.2%

      \[\leadsto \color{blue}{-y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.5 \cdot 10^{+177}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.8 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -4.5 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -2.4 \cdot 10^{-131}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.6 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -3.4 \cdot 10^{-262}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{elif}\;y4 \leq 1.06 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y4 \leq 1.55 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 2 \cdot 10^{+31}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 1.7 \cdot 10^{+152}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{elif}\;y4 \leq 8.2 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ t_3 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-209}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 5.7 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+124}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+181} \lor \neg \left(j \leq 2.55 \cdot 10^{+247}\right):\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t)))))
        (t_2 (* j (* t (- (* b y4) (* i y5)))))
        (t_3 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= j -1.5e+150)
     t_2
     (if (<= j -2.6e+42)
       (* k (* y1 (- (* y2 y4) (* z i))))
       (if (<= j -6e-25)
         t_2
         (if (<= j -1.4e-135)
           t_1
           (if (<= j -3.4e-209)
             t_3
             (if (<= j 5.7e-216)
               t_1
               (if (<= j 9.2e+44)
                 (* c (* y0 (- (* x y2) (* z y3))))
                 (if (<= j 3e+124)
                   t_3
                   (if (or (<= j 6.4e+181) (not (<= j 2.55e+247)))
                     (* b (* y0 (- (* z k) (* x j))))
                     (* 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 = a * (b * ((x * y) - (z * t)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double t_3 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (j <= -1.5e+150) {
		tmp = t_2;
	} else if (j <= -2.6e+42) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -6e-25) {
		tmp = t_2;
	} else if (j <= -1.4e-135) {
		tmp = t_1;
	} else if (j <= -3.4e-209) {
		tmp = t_3;
	} else if (j <= 5.7e-216) {
		tmp = t_1;
	} else if (j <= 9.2e+44) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 3e+124) {
		tmp = t_3;
	} else if ((j <= 6.4e+181) || !(j <= 2.55e+247)) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    t_2 = j * (t * ((b * y4) - (i * y5)))
    t_3 = c * (y4 * ((y * y3) - (t * y2)))
    if (j <= (-1.5d+150)) then
        tmp = t_2
    else if (j <= (-2.6d+42)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (j <= (-6d-25)) then
        tmp = t_2
    else if (j <= (-1.4d-135)) then
        tmp = t_1
    else if (j <= (-3.4d-209)) then
        tmp = t_3
    else if (j <= 5.7d-216) then
        tmp = t_1
    else if (j <= 9.2d+44) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (j <= 3d+124) then
        tmp = t_3
    else if ((j <= 6.4d+181) .or. (.not. (j <= 2.55d+247))) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    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 = a * (b * ((x * y) - (z * t)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double t_3 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (j <= -1.5e+150) {
		tmp = t_2;
	} else if (j <= -2.6e+42) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -6e-25) {
		tmp = t_2;
	} else if (j <= -1.4e-135) {
		tmp = t_1;
	} else if (j <= -3.4e-209) {
		tmp = t_3;
	} else if (j <= 5.7e-216) {
		tmp = t_1;
	} else if (j <= 9.2e+44) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 3e+124) {
		tmp = t_3;
	} else if ((j <= 6.4e+181) || !(j <= 2.55e+247)) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} 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 = a * (b * ((x * y) - (z * t)))
	t_2 = j * (t * ((b * y4) - (i * y5)))
	t_3 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if j <= -1.5e+150:
		tmp = t_2
	elif j <= -2.6e+42:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif j <= -6e-25:
		tmp = t_2
	elif j <= -1.4e-135:
		tmp = t_1
	elif j <= -3.4e-209:
		tmp = t_3
	elif j <= 5.7e-216:
		tmp = t_1
	elif j <= 9.2e+44:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif j <= 3e+124:
		tmp = t_3
	elif (j <= 6.4e+181) or not (j <= 2.55e+247):
		tmp = b * (y0 * ((z * k) - (x * j)))
	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(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	t_3 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (j <= -1.5e+150)
		tmp = t_2;
	elseif (j <= -2.6e+42)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (j <= -6e-25)
		tmp = t_2;
	elseif (j <= -1.4e-135)
		tmp = t_1;
	elseif (j <= -3.4e-209)
		tmp = t_3;
	elseif (j <= 5.7e-216)
		tmp = t_1;
	elseif (j <= 9.2e+44)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (j <= 3e+124)
		tmp = t_3;
	elseif ((j <= 6.4e+181) || !(j <= 2.55e+247))
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = Float64(t * Float64(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 = a * (b * ((x * y) - (z * t)));
	t_2 = j * (t * ((b * y4) - (i * y5)));
	t_3 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (j <= -1.5e+150)
		tmp = t_2;
	elseif (j <= -2.6e+42)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (j <= -6e-25)
		tmp = t_2;
	elseif (j <= -1.4e-135)
		tmp = t_1;
	elseif (j <= -3.4e-209)
		tmp = t_3;
	elseif (j <= 5.7e-216)
		tmp = t_1;
	elseif (j <= 9.2e+44)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (j <= 3e+124)
		tmp = t_3;
	elseif ((j <= 6.4e+181) || ~((j <= 2.55e+247)))
		tmp = b * (y0 * ((z * k) - (x * j)));
	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[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e+150], t$95$2, If[LessEqual[j, -2.6e+42], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-25], t$95$2, If[LessEqual[j, -1.4e-135], t$95$1, If[LessEqual[j, -3.4e-209], t$95$3, If[LessEqual[j, 5.7e-216], t$95$1, If[LessEqual[j, 9.2e+44], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e+124], t$95$3, If[Or[LessEqual[j, 6.4e+181], N[Not[LessEqual[j, 2.55e+247]], $MachinePrecision]], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.50000000000000006e150 or -2.5999999999999999e42 < j < -5.9999999999999995e-25

   1. Initial program 28.4%

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

   3. Taylor expanded in t around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in j around inf 53.4%

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

   if -1.50000000000000006e150 < j < -2.5999999999999999e42

   1. Initial program 24.1%

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

   3. Taylor expanded in k around inf 44.0%

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

      1. +-commutative 44.0%

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

      2. mul-1-neg 44.0%

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

      3. unsub-neg 44.0%

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

      4. *-commutative 44.0%

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

      5. associate-*r* 44.0%

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

      6. neg-mul-1 44.0%

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

   5. Simplified 44.0%

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

   6. Taylor expanded in y1 around inf 53.4%

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

   if -5.9999999999999995e-25 < j < -1.40000000000000012e-135 or -3.39999999999999988e-209 < j < 5.70000000000000004e-216

   1. Initial program 32.1%

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

   3. Taylor expanded in b around inf 45.5%

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

   4. Taylor expanded in a around inf 51.6%

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

   if -1.40000000000000012e-135 < j < -3.39999999999999988e-209 or 9.20000000000000018e44 < j < 3e124

   1. Initial program 22.4%

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

   3. Taylor expanded in y4 around inf 50.5%

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

   4. Taylor expanded in c around inf 51.1%

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

   if 5.70000000000000004e-216 < j < 9.20000000000000018e44

   1. Initial program 42.8%

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

   3. Taylor expanded in y0 around inf 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

      4. *-commutative 54.1%

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

      5. *-commutative 54.1%

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

      6. *-commutative 54.1%

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

      7. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in c around inf 45.6%

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

   if 3e124 < j < 6.4000000000000001e181 or 2.55000000000000001e247 < j

   1. Initial program 17.0%

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

   3. Taylor expanded in b around inf 44.9%

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

   4. Taylor expanded in y0 around inf 72.5%

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

   if 6.4000000000000001e181 < j < 2.55000000000000001e247

   1. Initial program 14.9%

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

   3. Taylor expanded in t around inf 43.4%

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

      1. +-commutative 43.4%

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

      2. mul-1-neg 43.4%

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

      3. unsub-neg 43.4%

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

      4. *-commutative 43.4%

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

   5. Simplified 43.4%

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

   6. Taylor expanded in y2 around inf 58.2%

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

      1. *-commutative 58.2%

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

      2. *-commutative 58.2%

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

   8. Simplified 58.2%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+150}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-25}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-209}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 5.7 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+124}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+181} \lor \neg \left(j \leq 2.55 \cdot 10^{+247}\right):\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 33.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y4 \leq -4.8 \cdot 10^{+173}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -6.8 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -7.5 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 2.4 \cdot 10^{-301}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 5.6 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 1.4 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 1.65 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 1.6 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 3.1 \cdot 10^{+250}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* j (- (* i y1) (* b y0))))))
   (if (<= y4 -4.8e+173)
     (* b (* y4 (- (* t j) (* y k))))
     (if (<= y4 -6.8e+90)
       (* y2 (* y4 (- (* k y1) (* t c))))
       (if (<= y4 -7.5e-43)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y4 2.4e-301)
           (* i (* k (- (* y y5) (* z y1))))
           (if (<= y4 6e-216)
             (* t (* z (- (* c i) (* a b))))
             (if (<= y4 5.6e-98)
               t_1
               (if (<= y4 1.4e-29)
                 (* t (* a (- (* y2 y5) (* z b))))
                 (if (<= y4 1.65e+63)
                   t_1
                   (if (<= y4 1.6e+212)
                     (* c (* y4 (- (* y y3) (* t y2))))
                     (if (<= y4 3.1e+250)
                       (* y1 (* y4 (- (* k y2) (* j y3))))
                       (* y3 (* y4 (- (* y c) (* j y1))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (j * ((i * y1) - (b * y0)));
	double tmp;
	if (y4 <= -4.8e+173) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -6.8e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -7.5e-43) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= 2.4e-301) {
		tmp = i * (k * ((y * y5) - (z * y1)));
	} else if (y4 <= 6e-216) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y4 <= 5.6e-98) {
		tmp = t_1;
	} else if (y4 <= 1.4e-29) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (y4 <= 1.65e+63) {
		tmp = t_1;
	} else if (y4 <= 1.6e+212) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y4 <= 3.1e+250) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (j * ((i * y1) - (b * y0)))
    if (y4 <= (-4.8d+173)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y4 <= (-6.8d+90)) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y4 <= (-7.5d-43)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y4 <= 2.4d-301) then
        tmp = i * (k * ((y * y5) - (z * y1)))
    else if (y4 <= 6d-216) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y4 <= 5.6d-98) then
        tmp = t_1
    else if (y4 <= 1.4d-29) then
        tmp = t * (a * ((y2 * y5) - (z * b)))
    else if (y4 <= 1.65d+63) then
        tmp = t_1
    else if (y4 <= 1.6d+212) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y4 <= 3.1d+250) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else
        tmp = y3 * (y4 * ((y * c) - (j * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (j * ((i * y1) - (b * y0)));
	double tmp;
	if (y4 <= -4.8e+173) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -6.8e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -7.5e-43) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= 2.4e-301) {
		tmp = i * (k * ((y * y5) - (z * y1)));
	} else if (y4 <= 6e-216) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y4 <= 5.6e-98) {
		tmp = t_1;
	} else if (y4 <= 1.4e-29) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (y4 <= 1.65e+63) {
		tmp = t_1;
	} else if (y4 <= 1.6e+212) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y4 <= 3.1e+250) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (j * ((i * y1) - (b * y0)))
	tmp = 0
	if y4 <= -4.8e+173:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y4 <= -6.8e+90:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y4 <= -7.5e-43:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y4 <= 2.4e-301:
		tmp = i * (k * ((y * y5) - (z * y1)))
	elif y4 <= 6e-216:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y4 <= 5.6e-98:
		tmp = t_1
	elif y4 <= 1.4e-29:
		tmp = t * (a * ((y2 * y5) - (z * b)))
	elif y4 <= 1.65e+63:
		tmp = t_1
	elif y4 <= 1.6e+212:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y4 <= 3.1e+250:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	else:
		tmp = y3 * (y4 * ((y * c) - (j * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))))
	tmp = 0.0
	if (y4 <= -4.8e+173)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y4 <= -6.8e+90)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y4 <= -7.5e-43)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= 2.4e-301)
		tmp = Float64(i * Float64(k * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (y4 <= 6e-216)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y4 <= 5.6e-98)
		tmp = t_1;
	elseif (y4 <= 1.4e-29)
		tmp = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (y4 <= 1.65e+63)
		tmp = t_1;
	elseif (y4 <= 1.6e+212)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y4 <= 3.1e+250)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	else
		tmp = Float64(y3 * Float64(y4 * Float64(Float64(y * c) - Float64(j * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (j * ((i * y1) - (b * y0)));
	tmp = 0.0;
	if (y4 <= -4.8e+173)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y4 <= -6.8e+90)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y4 <= -7.5e-43)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y4 <= 2.4e-301)
		tmp = i * (k * ((y * y5) - (z * y1)));
	elseif (y4 <= 6e-216)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y4 <= 5.6e-98)
		tmp = t_1;
	elseif (y4 <= 1.4e-29)
		tmp = t * (a * ((y2 * y5) - (z * b)));
	elseif (y4 <= 1.65e+63)
		tmp = t_1;
	elseif (y4 <= 1.6e+212)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y4 <= 3.1e+250)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	else
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4.8e+173], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -6.8e+90], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -7.5e-43], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.4e-301], N[(i * N[(k * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6e-216], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.6e-98], t$95$1, If[LessEqual[y4, 1.4e-29], N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.65e+63], t$95$1, If[LessEqual[y4, 1.6e+212], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.1e+250], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(y4 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y4 < -4.7999999999999998e173

   1. Initial program 24.7%

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

   3. Taylor expanded in y4 around inf 62.7%

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

   4. Taylor expanded in b around inf 59.3%

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

   if -4.7999999999999998e173 < y4 < -6.80000000000000036e90

   1. Initial program 28.6%

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

   3. Taylor expanded in y4 around inf 51.8%

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

   4. Taylor expanded in y2 around inf 72.3%

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

   if -6.80000000000000036e90 < y4 < -7.50000000000000068e-43

   1. Initial program 25.0%

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

   3. Taylor expanded in b around inf 38.2%

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

   4. Taylor expanded in a around inf 57.2%

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

   if -7.50000000000000068e-43 < y4 < 2.39999999999999991e-301

   1. Initial program 32.8%

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

   3. Taylor expanded in k around inf 37.7%

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

      1. +-commutative 37.7%

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

      2. mul-1-neg 37.7%

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

      3. unsub-neg 37.7%

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

      4. *-commutative 37.7%

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

      5. associate-*r* 37.7%

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

      6. neg-mul-1 37.7%

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

   5. Simplified 37.7%

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

   6. Taylor expanded in i around inf 39.4%

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

      1. mul-1-neg 39.4%

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

      2. +-commutative 39.4%

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

      3. mul-1-neg 39.4%

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

      4. sub-neg 39.4%

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

   8. Simplified 39.4%

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

   if 2.39999999999999991e-301 < y4 < 6.00000000000000025e-216

   1. Initial program 35.3%

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

   3. Taylor expanded in t around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in z around inf 57.3%

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

      1. *-commutative 57.3%

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

      2. *-commutative 57.3%

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

   8. Simplified 57.3%

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

   if 6.00000000000000025e-216 < y4 < 5.5999999999999998e-98 or 1.4000000000000001e-29 < y4 < 1.6500000000000001e63

   1. Initial program 31.4%

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

   3. Taylor expanded in x around inf 42.8%

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

   4. Taylor expanded in j around inf 43.2%

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

   if 5.5999999999999998e-98 < y4 < 1.4000000000000001e-29

   1. Initial program 20.0%

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

   3. Taylor expanded in t around inf 40.0%

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

      1. +-commutative 40.0%

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

      2. mul-1-neg 40.0%

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

      3. unsub-neg 40.0%

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

      4. *-commutative 40.0%

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

   5. Simplified 40.0%

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

   6. Taylor expanded in a around -inf 70.1%

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

      1. +-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

      4. *-commutative 70.1%

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

   8. Simplified 70.1%

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

   if 1.6500000000000001e63 < y4 < 1.5999999999999999e212

   1. Initial program 28.9%

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

   3. Taylor expanded in y4 around inf 63.6%

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

   4. Taylor expanded in c around inf 58.2%

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

   if 1.5999999999999999e212 < y4 < 3.1000000000000001e250

   1. Initial program 21.3%

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

   3. Taylor expanded in y4 around inf 71.3%

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

   4. Taylor expanded in y1 around inf 71.4%

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

   if 3.1000000000000001e250 < y4

   1. Initial program 30.8%

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

   3. Taylor expanded in y4 around inf 84.6%

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

   4. Taylor expanded in y3 around -inf 92.6%

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

      1. mul-1-neg 92.6%

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

   6. Simplified 92.6%

      \[\leadsto \color{blue}{-y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.8 \cdot 10^{+173}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -6.8 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -7.5 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 2.4 \cdot 10^{-301}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 5.6 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.4 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 1.65 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.6 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 3.1 \cdot 10^{+250}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{if}\;y4 \leq -4.4 \cdot 10^{+176}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -2.3 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -2.85 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -7 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 7.8 \cdot 10^{-290}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 2.2 \cdot 10^{+31}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 2 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 8.2 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* i (- (* j y1) (* y c))))))
   (if (<= y4 -4.4e+176)
     (* b (* y4 (- (* t j) (* y k))))
     (if (<= y4 -1.95e+90)
       (* y2 (* y4 (- (* k y1) (* t c))))
       (if (<= y4 -2.3e-41)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y4 -2.85e-132)
           (* c (* y3 (- (* y y4) (* z y0))))
           (if (<= y4 -7e-174)
             (* x (* j (- (* i y1) (* b y0))))
             (if (<= y4 7.8e-290)
               (* b (* z (- (* k y0) (* t a))))
               (if (<= y4 2.5e-86)
                 t_1
                 (if (<= y4 2.2e+31)
                   (* k (* y0 (- (* z b) (* y2 y5))))
                   (if (<= y4 2e+64)
                     t_1
                     (if (<= y4 8.2e+212)
                       (* c (* y4 (- (* y y3) (* t y2))))
                       (* y3 (* y4 (- (* y c) (* j y1))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (i * ((j * y1) - (y * c)));
	double tmp;
	if (y4 <= -4.4e+176) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.95e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -2.3e-41) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= -2.85e-132) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y4 <= -7e-174) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (y4 <= 7.8e-290) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y4 <= 2.5e-86) {
		tmp = t_1;
	} else if (y4 <= 2.2e+31) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (y4 <= 2e+64) {
		tmp = t_1;
	} else if (y4 <= 8.2e+212) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (i * ((j * y1) - (y * c)))
    if (y4 <= (-4.4d+176)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y4 <= (-1.95d+90)) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y4 <= (-2.3d-41)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y4 <= (-2.85d-132)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y4 <= (-7d-174)) then
        tmp = x * (j * ((i * y1) - (b * y0)))
    else if (y4 <= 7.8d-290) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (y4 <= 2.5d-86) then
        tmp = t_1
    else if (y4 <= 2.2d+31) then
        tmp = k * (y0 * ((z * b) - (y2 * y5)))
    else if (y4 <= 2d+64) then
        tmp = t_1
    else if (y4 <= 8.2d+212) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = y3 * (y4 * ((y * c) - (j * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (i * ((j * y1) - (y * c)));
	double tmp;
	if (y4 <= -4.4e+176) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.95e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -2.3e-41) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= -2.85e-132) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y4 <= -7e-174) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (y4 <= 7.8e-290) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y4 <= 2.5e-86) {
		tmp = t_1;
	} else if (y4 <= 2.2e+31) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (y4 <= 2e+64) {
		tmp = t_1;
	} else if (y4 <= 8.2e+212) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (i * ((j * y1) - (y * c)))
	tmp = 0
	if y4 <= -4.4e+176:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y4 <= -1.95e+90:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y4 <= -2.3e-41:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y4 <= -2.85e-132:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y4 <= -7e-174:
		tmp = x * (j * ((i * y1) - (b * y0)))
	elif y4 <= 7.8e-290:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif y4 <= 2.5e-86:
		tmp = t_1
	elif y4 <= 2.2e+31:
		tmp = k * (y0 * ((z * b) - (y2 * y5)))
	elif y4 <= 2e+64:
		tmp = t_1
	elif y4 <= 8.2e+212:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = y3 * (y4 * ((y * c) - (j * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c))))
	tmp = 0.0
	if (y4 <= -4.4e+176)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y4 <= -1.95e+90)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y4 <= -2.3e-41)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= -2.85e-132)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y4 <= -7e-174)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y4 <= 7.8e-290)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (y4 <= 2.5e-86)
		tmp = t_1;
	elseif (y4 <= 2.2e+31)
		tmp = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (y4 <= 2e+64)
		tmp = t_1;
	elseif (y4 <= 8.2e+212)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(y3 * Float64(y4 * Float64(Float64(y * c) - Float64(j * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (i * ((j * y1) - (y * c)));
	tmp = 0.0;
	if (y4 <= -4.4e+176)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y4 <= -1.95e+90)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y4 <= -2.3e-41)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y4 <= -2.85e-132)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y4 <= -7e-174)
		tmp = x * (j * ((i * y1) - (b * y0)));
	elseif (y4 <= 7.8e-290)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (y4 <= 2.5e-86)
		tmp = t_1;
	elseif (y4 <= 2.2e+31)
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	elseif (y4 <= 2e+64)
		tmp = t_1;
	elseif (y4 <= 8.2e+212)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4.4e+176], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.95e+90], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.3e-41], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.85e-132], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -7e-174], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.8e-290], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.5e-86], t$95$1, If[LessEqual[y4, 2.2e+31], N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2e+64], t$95$1, If[LessEqual[y4, 8.2e+212], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(y4 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y4 < -4.40000000000000015e176

   1. Initial program 24.7%

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

   3. Taylor expanded in y4 around inf 62.7%

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

   4. Taylor expanded in b around inf 59.3%

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

   if -4.40000000000000015e176 < y4 < -1.9500000000000001e90

   1. Initial program 28.6%

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

   3. Taylor expanded in y4 around inf 51.8%

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

   4. Taylor expanded in y2 around inf 72.3%

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

   if -1.9500000000000001e90 < y4 < -2.3000000000000001e-41

   1. Initial program 25.0%

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

   3. Taylor expanded in b around inf 38.2%

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

   4. Taylor expanded in a around inf 57.2%

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

   if -2.3000000000000001e-41 < y4 < -2.8500000000000001e-132

   1. Initial program 31.3%

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

   3. Taylor expanded in y3 around -inf 53.9%

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

   4. Taylor expanded in c around inf 47.8%

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

   if -2.8500000000000001e-132 < y4 < -6.99999999999999975e-174

   1. Initial program 11.8%

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

   3. Taylor expanded in x around inf 44.6%

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

   4. Taylor expanded in j around inf 66.9%

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

   if -6.99999999999999975e-174 < y4 < 7.79999999999999946e-290

   1. Initial program 38.6%

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

   3. Taylor expanded in b around inf 49.9%

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

   4. Taylor expanded in z around -inf 49.3%

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

      1. associate-*r* 49.3%

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

      2. neg-mul-1 49.3%

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

   6. Simplified 49.3%

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

   if 7.79999999999999946e-290 < y4 < 2.4999999999999999e-86 or 2.2000000000000001e31 < y4 < 2.00000000000000004e64

   1. Initial program 33.0%

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

   3. Taylor expanded in x around inf 41.1%

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

   4. Taylor expanded in i around -inf 49.8%

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

      1. mul-1-neg 49.8%

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

   6. Simplified 49.8%

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

   if 2.4999999999999999e-86 < y4 < 2.2000000000000001e31

   1. Initial program 27.7%

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

   3. Taylor expanded in k around inf 33.5%

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

      1. +-commutative 33.5%

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

      2. mul-1-neg 33.5%

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

      3. unsub-neg 33.5%

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

      4. *-commutative 33.5%

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

      5. associate-*r* 33.5%

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

      6. neg-mul-1 33.5%

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

   5. Simplified 33.5%

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

   6. Taylor expanded in y0 around -inf 55.9%

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

      1. associate-*r* 55.9%

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

      2. neg-mul-1 55.9%

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

   8. Simplified 55.9%

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

   if 2.00000000000000004e64 < y4 < 8.19999999999999978e212

   1. Initial program 28.1%

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

   3. Taylor expanded in y4 around inf 64.6%

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

   4. Taylor expanded in c around inf 56.8%

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

   if 8.19999999999999978e212 < y4

   1. Initial program 26.9%

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

   3. Taylor expanded in y4 around inf 76.9%

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

   4. Taylor expanded in y3 around -inf 77.2%

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

      1. mul-1-neg 77.2%

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

   6. Simplified 77.2%

      \[\leadsto \color{blue}{-y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.4 \cdot 10^{+176}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -2.3 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -2.85 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -7 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 7.8 \cdot 10^{-290}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 2.2 \cdot 10^{+31}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 2 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 8.2 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot y1 - c \cdot y0\right)\\ t_2 := y \cdot \left(c \cdot y4 - a \cdot y5\right)\\ \mathbf{if}\;y3 \leq -1.2 \cdot 10^{+102}:\\ \;\;\;\;y3 \cdot t\_1\\ \mathbf{elif}\;y3 \leq -1.8 \cdot 10^{-41}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -3.1 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq -3.8 \cdot 10^{-256}:\\ \;\;\;\;y3 \cdot \left(t\_2 + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -1.26 \cdot 10^{-297}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+194}:\\ \;\;\;\;y3 \cdot \left(t\_1 + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* z (- (* a y1) (* c y0)))) (t_2 (* y (- (* c y4) (* a y5)))))
   (if (<= y3 -1.2e+102)
     (* y3 t_1)
     (if (<= y3 -1.8e-41)
       (* j (* t (- (* b y4) (* i y5))))
       (if (<= y3 -3.1e-200)
         (*
          c
          (+
           (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
           (* y4 (- (* y y3) (* t y2)))))
         (if (<= y3 -3.8e-256)
           (* y3 (+ t_2 (- (* a (* z y1)) (* j (* y1 y4)))))
           (if (<= y3 -1.26e-297)
             (* t (* c (- (* z i) (* y2 y4))))
             (if (<= y3 2.05e+30)
               (*
                b
                (+
                 (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
                 (* y0 (- (* z k) (* x j)))))
               (if (<= y3 1.25e+194)
                 (* y3 (+ t_1 t_2))
                 (* y3 (* y4 (- (* y c) (* j y1)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((a * y1) - (c * y0));
	double t_2 = y * ((c * y4) - (a * y5));
	double tmp;
	if (y3 <= -1.2e+102) {
		tmp = y3 * t_1;
	} else if (y3 <= -1.8e-41) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y3 <= -3.1e-200) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y3 <= -3.8e-256) {
		tmp = y3 * (t_2 + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y3 <= -1.26e-297) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y3 <= 2.05e+30) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y3 <= 1.25e+194) {
		tmp = y3 * (t_1 + t_2);
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((a * y1) - (c * y0))
    t_2 = y * ((c * y4) - (a * y5))
    if (y3 <= (-1.2d+102)) then
        tmp = y3 * t_1
    else if (y3 <= (-1.8d-41)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y3 <= (-3.1d-200)) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y3 <= (-3.8d-256)) then
        tmp = y3 * (t_2 + ((a * (z * y1)) - (j * (y1 * y4))))
    else if (y3 <= (-1.26d-297)) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (y3 <= 2.05d+30) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y3 <= 1.25d+194) then
        tmp = y3 * (t_1 + t_2)
    else
        tmp = y3 * (y4 * ((y * c) - (j * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((a * y1) - (c * y0));
	double t_2 = y * ((c * y4) - (a * y5));
	double tmp;
	if (y3 <= -1.2e+102) {
		tmp = y3 * t_1;
	} else if (y3 <= -1.8e-41) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y3 <= -3.1e-200) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y3 <= -3.8e-256) {
		tmp = y3 * (t_2 + ((a * (z * y1)) - (j * (y1 * y4))));
	} else if (y3 <= -1.26e-297) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (y3 <= 2.05e+30) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y3 <= 1.25e+194) {
		tmp = y3 * (t_1 + t_2);
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = z * ((a * y1) - (c * y0))
	t_2 = y * ((c * y4) - (a * y5))
	tmp = 0
	if y3 <= -1.2e+102:
		tmp = y3 * t_1
	elif y3 <= -1.8e-41:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y3 <= -3.1e-200:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	elif y3 <= -3.8e-256:
		tmp = y3 * (t_2 + ((a * (z * y1)) - (j * (y1 * y4))))
	elif y3 <= -1.26e-297:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif y3 <= 2.05e+30:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y3 <= 1.25e+194:
		tmp = y3 * (t_1 + t_2)
	else:
		tmp = y3 * (y4 * ((y * c) - (j * 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(z * Float64(Float64(a * y1) - Float64(c * y0)))
	t_2 = Float64(y * Float64(Float64(c * y4) - Float64(a * y5)))
	tmp = 0.0
	if (y3 <= -1.2e+102)
		tmp = Float64(y3 * t_1);
	elseif (y3 <= -1.8e-41)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y3 <= -3.1e-200)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y3 <= -3.8e-256)
		tmp = Float64(y3 * Float64(t_2 + Float64(Float64(a * Float64(z * y1)) - Float64(j * Float64(y1 * y4)))));
	elseif (y3 <= -1.26e-297)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y3 <= 2.05e+30)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y3 <= 1.25e+194)
		tmp = Float64(y3 * Float64(t_1 + t_2));
	else
		tmp = Float64(y3 * Float64(y4 * Float64(Float64(y * c) - Float64(j * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = z * ((a * y1) - (c * y0));
	t_2 = y * ((c * y4) - (a * y5));
	tmp = 0.0;
	if (y3 <= -1.2e+102)
		tmp = y3 * t_1;
	elseif (y3 <= -1.8e-41)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y3 <= -3.1e-200)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y3 <= -3.8e-256)
		tmp = y3 * (t_2 + ((a * (z * y1)) - (j * (y1 * y4))));
	elseif (y3 <= -1.26e-297)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (y3 <= 2.05e+30)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y3 <= 1.25e+194)
		tmp = y3 * (t_1 + t_2);
	else
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.2e+102], N[(y3 * t$95$1), $MachinePrecision], If[LessEqual[y3, -1.8e-41], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -3.1e-200], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -3.8e-256], N[(y3 * N[(t$95$2 + N[(N[(a * N[(z * y1), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.26e-297], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.05e+30], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.25e+194], N[(y3 * N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(y4 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y3 < -1.19999999999999997e102

   1. Initial program 32.8%

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

   3. Taylor expanded in y3 around -inf 53.8%

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

   4. Taylor expanded in z around inf 56.4%

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

   if -1.19999999999999997e102 < y3 < -1.8e-41

   1. Initial program 17.4%

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

   3. Taylor expanded in t around inf 34.8%

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

      1. +-commutative 34.8%

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

      2. mul-1-neg 34.8%

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

      3. unsub-neg 34.8%

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

      4. *-commutative 34.8%

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

   5. Simplified 34.8%

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

   6. Taylor expanded in j around inf 56.4%

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

   if -1.8e-41 < y3 < -3.0999999999999999e-200

   1. Initial program 44.9%

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

   3. Taylor expanded in c around inf 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

      4. *-commutative 48.2%

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

      5. *-commutative 48.2%

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

      6. *-commutative 48.2%

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

      7. *-commutative 48.2%

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

   5. Simplified 48.2%

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

   if -3.0999999999999999e-200 < y3 < -3.79999999999999977e-256

   1. Initial program 15.4%

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

   3. Taylor expanded in y3 around -inf 39.6%

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

   4. Taylor expanded in y0 around 0 62.6%

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

   if -3.79999999999999977e-256 < y3 < -1.2599999999999999e-297

   1. Initial program 40.0%

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

   3. Taylor expanded in t around inf 40.7%

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

      1. +-commutative 40.7%

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

      2. mul-1-neg 40.7%

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

      3. unsub-neg 40.7%

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

      4. *-commutative 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in c around -inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

      4. *-commutative 70.8%

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

   8. Simplified 70.8%

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

   if -1.2599999999999999e-297 < y3 < 2.05000000000000003e30

   1. Initial program 28.1%

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

   3. Taylor expanded in b around inf 49.8%

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

   if 2.05000000000000003e30 < y3 < 1.24999999999999997e194

   1. Initial program 30.7%

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

   3. Taylor expanded in y3 around -inf 58.9%

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

   4. Taylor expanded in j around 0 58.7%

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

   if 1.24999999999999997e194 < y3

   1. Initial program 10.0%

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

   3. Taylor expanded in y4 around inf 55.0%

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

   4. Taylor expanded in y3 around -inf 60.5%

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

      1. mul-1-neg 60.5%

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

   6. Simplified 60.5%

      \[\leadsto \color{blue}{-y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.2 \cdot 10^{+102}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.8 \cdot 10^{-41}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -3.1 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq -3.8 \cdot 10^{-256}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(a \cdot \left(z \cdot y1\right) - j \cdot \left(y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -1.26 \cdot 10^{-297}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+194}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y4 - a \cdot y5\\ t_2 := y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + y \cdot t\_1\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.45 \cdot 10^{-99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-139}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-180}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-272}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-226}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+159}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4\right) - \left(y2 \cdot t\_1 + a \cdot \left(z \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y4) (* a y5)))
        (t_2 (* y3 (+ (* z (- (* a y1) (* c y0))) (* y t_1)))))
   (if (<= x -7.8e+105)
     (* a (* b (- (* x y) (* z t))))
     (if (<= x -3.45e-99)
       t_2
       (if (<= x -1.35e-139)
         (* i (* k (- (* y y5) (* z y1))))
         (if (<= x -6.3e-180)
           (* y3 (* y4 (- (* y c) (* j y1))))
           (if (<= x -5.4e-272)
             (* k (* y1 (- (* y2 y4) (* z i))))
             (if (<= x 8.6e-226)
               t_2
               (if (<= x 3.3e+159)
                 (* t (- (* b (* j y4)) (+ (* y2 t_1) (* a (* z b)))))
                 (* x (* i (- (* j y1) (* y c)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) - (a * y5);
	double t_2 = y3 * ((z * ((a * y1) - (c * y0))) + (y * t_1));
	double tmp;
	if (x <= -7.8e+105) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -3.45e-99) {
		tmp = t_2;
	} else if (x <= -1.35e-139) {
		tmp = i * (k * ((y * y5) - (z * y1)));
	} else if (x <= -6.3e-180) {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	} else if (x <= -5.4e-272) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (x <= 8.6e-226) {
		tmp = t_2;
	} else if (x <= 3.3e+159) {
		tmp = t * ((b * (j * y4)) - ((y2 * t_1) + (a * (z * b))));
	} else {
		tmp = x * (i * ((j * y1) - (y * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * y4) - (a * y5)
    t_2 = y3 * ((z * ((a * y1) - (c * y0))) + (y * t_1))
    if (x <= (-7.8d+105)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (x <= (-3.45d-99)) then
        tmp = t_2
    else if (x <= (-1.35d-139)) then
        tmp = i * (k * ((y * y5) - (z * y1)))
    else if (x <= (-6.3d-180)) then
        tmp = y3 * (y4 * ((y * c) - (j * y1)))
    else if (x <= (-5.4d-272)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (x <= 8.6d-226) then
        tmp = t_2
    else if (x <= 3.3d+159) then
        tmp = t * ((b * (j * y4)) - ((y2 * t_1) + (a * (z * b))))
    else
        tmp = x * (i * ((j * y1) - (y * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) - (a * y5);
	double t_2 = y3 * ((z * ((a * y1) - (c * y0))) + (y * t_1));
	double tmp;
	if (x <= -7.8e+105) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -3.45e-99) {
		tmp = t_2;
	} else if (x <= -1.35e-139) {
		tmp = i * (k * ((y * y5) - (z * y1)));
	} else if (x <= -6.3e-180) {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	} else if (x <= -5.4e-272) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (x <= 8.6e-226) {
		tmp = t_2;
	} else if (x <= 3.3e+159) {
		tmp = t * ((b * (j * y4)) - ((y2 * t_1) + (a * (z * b))));
	} else {
		tmp = x * (i * ((j * y1) - (y * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y4) - (a * y5)
	t_2 = y3 * ((z * ((a * y1) - (c * y0))) + (y * t_1))
	tmp = 0
	if x <= -7.8e+105:
		tmp = a * (b * ((x * y) - (z * t)))
	elif x <= -3.45e-99:
		tmp = t_2
	elif x <= -1.35e-139:
		tmp = i * (k * ((y * y5) - (z * y1)))
	elif x <= -6.3e-180:
		tmp = y3 * (y4 * ((y * c) - (j * y1)))
	elif x <= -5.4e-272:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif x <= 8.6e-226:
		tmp = t_2
	elif x <= 3.3e+159:
		tmp = t * ((b * (j * y4)) - ((y2 * t_1) + (a * (z * b))))
	else:
		tmp = x * (i * ((j * y1) - (y * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y4) - Float64(a * y5))
	t_2 = Float64(y3 * Float64(Float64(z * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(y * t_1)))
	tmp = 0.0
	if (x <= -7.8e+105)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (x <= -3.45e-99)
		tmp = t_2;
	elseif (x <= -1.35e-139)
		tmp = Float64(i * Float64(k * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (x <= -6.3e-180)
		tmp = Float64(y3 * Float64(y4 * Float64(Float64(y * c) - Float64(j * y1))));
	elseif (x <= -5.4e-272)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (x <= 8.6e-226)
		tmp = t_2;
	elseif (x <= 3.3e+159)
		tmp = Float64(t * Float64(Float64(b * Float64(j * y4)) - Float64(Float64(y2 * t_1) + Float64(a * Float64(z * b)))));
	else
		tmp = Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y4) - (a * y5);
	t_2 = y3 * ((z * ((a * y1) - (c * y0))) + (y * t_1));
	tmp = 0.0;
	if (x <= -7.8e+105)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (x <= -3.45e-99)
		tmp = t_2;
	elseif (x <= -1.35e-139)
		tmp = i * (k * ((y * y5) - (z * y1)));
	elseif (x <= -6.3e-180)
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	elseif (x <= -5.4e-272)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (x <= 8.6e-226)
		tmp = t_2;
	elseif (x <= 3.3e+159)
		tmp = t * ((b * (j * y4)) - ((y2 * t_1) + (a * (z * b))));
	else
		tmp = x * (i * ((j * y1) - (y * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y3 * N[(N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e+105], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.45e-99], t$95$2, If[LessEqual[x, -1.35e-139], N[(i * N[(k * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.3e-180], N[(y3 * N[(y4 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.4e-272], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.6e-226], t$95$2, If[LessEqual[x, 3.3e+159], N[(t * N[(N[(b * N[(j * y4), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * t$95$1), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -7.79999999999999957e105

   1. Initial program 19.4%

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

   3. Taylor expanded in b around inf 55.4%

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

   4. Taylor expanded in a around inf 59.0%

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

   if -7.79999999999999957e105 < x < -3.4500000000000002e-99 or -5.39999999999999985e-272 < x < 8.60000000000000049e-226

   1. Initial program 38.0%

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

   3. Taylor expanded in y3 around -inf 50.7%

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

   4. Taylor expanded in j around 0 53.7%

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

   if -3.4500000000000002e-99 < x < -1.3499999999999999e-139

   1. Initial program 42.9%

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

   3. Taylor expanded in k around inf 57.1%

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

      1. +-commutative 57.1%

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

      2. mul-1-neg 57.1%

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

      3. unsub-neg 57.1%

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

      4. *-commutative 57.1%

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

      5. associate-*r* 57.1%

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

      6. neg-mul-1 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in i around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. +-commutative 71.4%

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

      3. mul-1-neg 71.4%

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

      4. sub-neg 71.4%

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

   8. Simplified 71.4%

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

   if -1.3499999999999999e-139 < x < -6.2999999999999996e-180

   1. Initial program 30.1%

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

   3. Taylor expanded in y4 around inf 58.7%

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

   4. Taylor expanded in y3 around -inf 73.0%

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

      1. mul-1-neg 73.0%

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

   6. Simplified 73.0%

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

   if -6.2999999999999996e-180 < x < -5.39999999999999985e-272

   1. Initial program 25.2%

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

   3. Taylor expanded in k around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

      5. associate-*r* 60.6%

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

      6. neg-mul-1 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in y1 around inf 56.1%

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

   if 8.60000000000000049e-226 < x < 3.2999999999999999e159

   1. Initial program 28.9%

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

   3. Taylor expanded in t around inf 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

      4. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in i around 0 48.9%

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

   if 3.2999999999999999e159 < x

   1. Initial program 18.2%

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

   3. Taylor expanded in x around inf 54.5%

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

   4. Taylor expanded in i around -inf 55.4%

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

      1. mul-1-neg 55.4%

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

   6. Simplified 55.4%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.45 \cdot 10^{-99}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-139}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-180}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-272}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-226}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+159}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4\right) - \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right) + a \cdot \left(z \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y4 \leq -3.2 \cdot 10^{+176}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.6 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -8.4 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 2.8 \cdot 10^{-299}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 8.5 \cdot 10^{-217}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 8.2 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 6.2 \cdot 10^{+209}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* j (- (* i y1) (* b y0))))))
   (if (<= y4 -3.2e+176)
     (* b (* y4 (- (* t j) (* y k))))
     (if (<= y4 -1.6e+90)
       (* y2 (* y4 (- (* k y1) (* t c))))
       (if (<= y4 -8.4e-44)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y4 2.8e-299)
           (* i (* k (- (* y y5) (* z y1))))
           (if (<= y4 8.5e-217)
             (* t (* z (- (* c i) (* a b))))
             (if (<= y4 5.2e-95)
               t_1
               (if (<= y4 8.2e-26)
                 (* t (* a (- (* y2 y5) (* z b))))
                 (if (<= y4 3.5e+63)
                   t_1
                   (if (<= y4 6.2e+209)
                     (* c (* y4 (- (* y y3) (* t y2))))
                     (* y1 (* y4 (- (* k y2) (* j y3)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (j * ((i * y1) - (b * y0)));
	double tmp;
	if (y4 <= -3.2e+176) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.6e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -8.4e-44) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= 2.8e-299) {
		tmp = i * (k * ((y * y5) - (z * y1)));
	} else if (y4 <= 8.5e-217) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y4 <= 5.2e-95) {
		tmp = t_1;
	} else if (y4 <= 8.2e-26) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (y4 <= 3.5e+63) {
		tmp = t_1;
	} else if (y4 <= 6.2e+209) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (j * ((i * y1) - (b * y0)))
    if (y4 <= (-3.2d+176)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y4 <= (-1.6d+90)) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y4 <= (-8.4d-44)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y4 <= 2.8d-299) then
        tmp = i * (k * ((y * y5) - (z * y1)))
    else if (y4 <= 8.5d-217) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y4 <= 5.2d-95) then
        tmp = t_1
    else if (y4 <= 8.2d-26) then
        tmp = t * (a * ((y2 * y5) - (z * b)))
    else if (y4 <= 3.5d+63) then
        tmp = t_1
    else if (y4 <= 6.2d+209) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (j * ((i * y1) - (b * y0)));
	double tmp;
	if (y4 <= -3.2e+176) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.6e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -8.4e-44) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= 2.8e-299) {
		tmp = i * (k * ((y * y5) - (z * y1)));
	} else if (y4 <= 8.5e-217) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y4 <= 5.2e-95) {
		tmp = t_1;
	} else if (y4 <= 8.2e-26) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (y4 <= 3.5e+63) {
		tmp = t_1;
	} else if (y4 <= 6.2e+209) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (j * ((i * y1) - (b * y0)))
	tmp = 0
	if y4 <= -3.2e+176:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y4 <= -1.6e+90:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y4 <= -8.4e-44:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y4 <= 2.8e-299:
		tmp = i * (k * ((y * y5) - (z * y1)))
	elif y4 <= 8.5e-217:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y4 <= 5.2e-95:
		tmp = t_1
	elif y4 <= 8.2e-26:
		tmp = t * (a * ((y2 * y5) - (z * b)))
	elif y4 <= 3.5e+63:
		tmp = t_1
	elif y4 <= 6.2e+209:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))))
	tmp = 0.0
	if (y4 <= -3.2e+176)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y4 <= -1.6e+90)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y4 <= -8.4e-44)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= 2.8e-299)
		tmp = Float64(i * Float64(k * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (y4 <= 8.5e-217)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y4 <= 5.2e-95)
		tmp = t_1;
	elseif (y4 <= 8.2e-26)
		tmp = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (y4 <= 3.5e+63)
		tmp = t_1;
	elseif (y4 <= 6.2e+209)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (j * ((i * y1) - (b * y0)));
	tmp = 0.0;
	if (y4 <= -3.2e+176)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y4 <= -1.6e+90)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y4 <= -8.4e-44)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y4 <= 2.8e-299)
		tmp = i * (k * ((y * y5) - (z * y1)));
	elseif (y4 <= 8.5e-217)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y4 <= 5.2e-95)
		tmp = t_1;
	elseif (y4 <= 8.2e-26)
		tmp = t * (a * ((y2 * y5) - (z * b)));
	elseif (y4 <= 3.5e+63)
		tmp = t_1;
	elseif (y4 <= 6.2e+209)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -3.2e+176], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.6e+90], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -8.4e-44], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.8e-299], N[(i * N[(k * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 8.5e-217], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.2e-95], t$95$1, If[LessEqual[y4, 8.2e-26], N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.5e+63], t$95$1, If[LessEqual[y4, 6.2e+209], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y4 < -3.1999999999999998e176

   1. Initial program 24.7%

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

   3. Taylor expanded in y4 around inf 62.7%

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

   4. Taylor expanded in b around inf 59.3%

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

   if -3.1999999999999998e176 < y4 < -1.59999999999999999e90

   1. Initial program 28.6%

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

   3. Taylor expanded in y4 around inf 51.8%

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

   4. Taylor expanded in y2 around inf 72.3%

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

   if -1.59999999999999999e90 < y4 < -8.40000000000000005e-44

   1. Initial program 25.0%

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

   3. Taylor expanded in b around inf 38.2%

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

   4. Taylor expanded in a around inf 57.2%

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

   if -8.40000000000000005e-44 < y4 < 2.8000000000000001e-299

   1. Initial program 32.8%

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

   3. Taylor expanded in k around inf 37.7%

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

      1. +-commutative 37.7%

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

      2. mul-1-neg 37.7%

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

      3. unsub-neg 37.7%

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

      4. *-commutative 37.7%

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

      5. associate-*r* 37.7%

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

      6. neg-mul-1 37.7%

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

   5. Simplified 37.7%

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

   6. Taylor expanded in i around inf 39.4%

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

      1. mul-1-neg 39.4%

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

      2. +-commutative 39.4%

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

      3. mul-1-neg 39.4%

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

      4. sub-neg 39.4%

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

   8. Simplified 39.4%

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

   if 2.8000000000000001e-299 < y4 < 8.4999999999999994e-217

   1. Initial program 35.3%

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

   3. Taylor expanded in t around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 71.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 71.0%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 71.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in z around inf 57.3%

      \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 57.3%

         \[\leadsto t \cdot \left(z \cdot \left(\color{blue}{i \cdot c} - a \cdot b\right)\right) \]

      2. *-commutative 57.3%

         \[\leadsto t \cdot \left(z \cdot \left(i \cdot c - \color{blue}{b \cdot a}\right)\right) \]

   8. Simplified 57.3%

      \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(i \cdot c - b \cdot a\right)\right)} \]

   if 8.4999999999999994e-217 < y4 < 5.20000000000000001e-95 or 8.1999999999999997e-26 < y4 < 3.50000000000000029e63

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 42.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 43.2%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 5.20000000000000001e-95 < y4 < 8.1999999999999997e-26

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 40.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 40.0%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 40.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 40.0%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 40.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in a around -inf 70.1%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 70.1%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 70.1%

         \[\leadsto t \cdot \left(a \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. unsub-neg 70.1%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

      4. *-commutative 70.1%

         \[\leadsto t \cdot \left(a \cdot \left(\color{blue}{y5 \cdot y2} - b \cdot z\right)\right) \]

   8. Simplified 70.1%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y5 \cdot y2 - b \cdot z\right)\right)} \]

   if 3.50000000000000029e63 < y4 < 6.2000000000000002e209

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 63.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 58.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 6.2000000000000002e209 < y4

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 77.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in y1 around inf 74.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3.2 \cdot 10^{+176}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.6 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -8.4 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 2.8 \cdot 10^{-299}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 8.5 \cdot 10^{-217}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 8.2 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 6.2 \cdot 10^{+209}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1 \cdot 10^{+176}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -5.9 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 1.8 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y4 \leq 2.05 \cdot 10^{-226}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y4 \leq 9 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.8 \cdot 10^{+211}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 3.4 \cdot 10^{+250}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1e+176)
   (* b (* y4 (- (* t j) (* y k))))
   (if (<= y4 -5.9e+90)
     (* y2 (* y4 (- (* k y1) (* t c))))
     (if (<= y4 -1.02e-41)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y4 1.8e-287)
         (* b (* z (- (* k y0) (* t a))))
         (if (<= y4 2.05e-226)
           (* j (* t (- (* b y4) (* i y5))))
           (if (<= y4 4e-212)
             (* a (* (* x y) b))
             (if (<= y4 9e+60)
               (* x (* j (- (* i y1) (* b y0))))
               (if (<= y4 1.8e+211)
                 (* c (* y4 (- (* y y3) (* t y2))))
                 (if (<= y4 3.4e+250)
                   (* y1 (* y4 (- (* k y2) (* j y3))))
                   (* y3 (* y4 (- (* y c) (* j y1))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1e+176) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -5.9e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -1.02e-41) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= 1.8e-287) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y4 <= 2.05e-226) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y4 <= 4e-212) {
		tmp = a * ((x * y) * b);
	} else if (y4 <= 9e+60) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (y4 <= 1.8e+211) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y4 <= 3.4e+250) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1d+176)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y4 <= (-5.9d+90)) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y4 <= (-1.02d-41)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y4 <= 1.8d-287) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (y4 <= 2.05d-226) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y4 <= 4d-212) then
        tmp = a * ((x * y) * b)
    else if (y4 <= 9d+60) then
        tmp = x * (j * ((i * y1) - (b * y0)))
    else if (y4 <= 1.8d+211) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y4 <= 3.4d+250) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else
        tmp = y3 * (y4 * ((y * c) - (j * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1e+176) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -5.9e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -1.02e-41) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= 1.8e-287) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y4 <= 2.05e-226) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y4 <= 4e-212) {
		tmp = a * ((x * y) * b);
	} else if (y4 <= 9e+60) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (y4 <= 1.8e+211) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y4 <= 3.4e+250) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1e+176:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y4 <= -5.9e+90:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y4 <= -1.02e-41:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y4 <= 1.8e-287:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif y4 <= 2.05e-226:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y4 <= 4e-212:
		tmp = a * ((x * y) * b)
	elif y4 <= 9e+60:
		tmp = x * (j * ((i * y1) - (b * y0)))
	elif y4 <= 1.8e+211:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y4 <= 3.4e+250:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	else:
		tmp = y3 * (y4 * ((y * c) - (j * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1e+176)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y4 <= -5.9e+90)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y4 <= -1.02e-41)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= 1.8e-287)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (y4 <= 2.05e-226)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y4 <= 4e-212)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y4 <= 9e+60)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y4 <= 1.8e+211)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y4 <= 3.4e+250)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	else
		tmp = Float64(y3 * Float64(y4 * Float64(Float64(y * c) - Float64(j * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1e+176)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y4 <= -5.9e+90)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y4 <= -1.02e-41)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y4 <= 1.8e-287)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (y4 <= 2.05e-226)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y4 <= 4e-212)
		tmp = a * ((x * y) * b);
	elseif (y4 <= 9e+60)
		tmp = x * (j * ((i * y1) - (b * y0)));
	elseif (y4 <= 1.8e+211)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y4 <= 3.4e+250)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	else
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1e+176], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -5.9e+90], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.02e-41], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.8e-287], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.05e-226], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4e-212], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 9e+60], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.8e+211], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.4e+250], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(y4 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y4 < -1e176

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 62.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in b around inf 59.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -1e176 < y4 < -5.90000000000000038e90

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 51.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in y2 around inf 72.3%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   if -5.90000000000000038e90 < y4 < -1.02e-41

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 57.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.02e-41 < y4 < 1.8000000000000001e-287

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in z around -inf 40.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 40.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot z\right) \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

      2. neg-mul-1 40.6%

         \[\leadsto b \cdot \left(\color{blue}{\left(-z\right)} \cdot \left(a \cdot t - k \cdot y0\right)\right) \]

   6. Simplified 40.6%

      \[\leadsto b \cdot \color{blue}{\left(\left(-z\right) \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

   if 1.8000000000000001e-287 < y4 < 2.05000000000000019e-226

   1. Initial program 45.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 64.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 64.4%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 64.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 64.4%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in j around inf 64.1%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if 2.05000000000000019e-226 < y4 < 3.99999999999999982e-212

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if 3.99999999999999982e-212 < y4 < 9.00000000000000026e60

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 37.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 40.0%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 9.00000000000000026e60 < y4 < 1.80000000000000001e211

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 63.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 58.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 1.80000000000000001e211 < y4 < 3.39999999999999973e250

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 71.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in y1 around inf 71.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   if 3.39999999999999973e250 < y4

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 84.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in y3 around -inf 92.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 92.6%

         \[\leadsto \color{blue}{-y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]

   6. Simplified 92.6%

      \[\leadsto \color{blue}{-y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1 \cdot 10^{+176}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -5.9 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 1.8 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y4 \leq 2.05 \cdot 10^{-226}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y4 \leq 9 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.8 \cdot 10^{+211}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 3.4 \cdot 10^{+250}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -5.6 \cdot 10^{+174}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.62 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -3.65 \cdot 10^{-131}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.55 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -7.4 \cdot 10^{-261}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-288}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y4 \leq 4.6 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 2.65 \cdot 10^{+213}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -5.6e+174)
   (* b (* y4 (- (* t j) (* y k))))
   (if (<= y4 -1.62e+90)
     (* y2 (* y4 (- (* k y1) (* t c))))
     (if (<= y4 -1.02e-41)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y4 -3.65e-131)
         (* c (* y3 (- (* y y4) (* z y0))))
         (if (<= y4 -1.55e-173)
           (* x (* j (- (* i y1) (* b y0))))
           (if (<= y4 -7.4e-261)
             (* y3 (* z (- (* a y1) (* c y0))))
             (if (<= y4 6.5e-288)
               (* b (* z (- (* k y0) (* t a))))
               (if (<= y4 4.6e+62)
                 (* x (* i (- (* j y1) (* y c))))
                 (if (<= y4 2.65e+213)
                   (* c (* y4 (- (* y y3) (* t y2))))
                   (* y3 (* y4 (- (* y c) (* j y1))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -5.6e+174) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.62e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -1.02e-41) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= -3.65e-131) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y4 <= -1.55e-173) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (y4 <= -7.4e-261) {
		tmp = y3 * (z * ((a * y1) - (c * y0)));
	} else if (y4 <= 6.5e-288) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y4 <= 4.6e+62) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y4 <= 2.65e+213) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-5.6d+174)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y4 <= (-1.62d+90)) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y4 <= (-1.02d-41)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y4 <= (-3.65d-131)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y4 <= (-1.55d-173)) then
        tmp = x * (j * ((i * y1) - (b * y0)))
    else if (y4 <= (-7.4d-261)) then
        tmp = y3 * (z * ((a * y1) - (c * y0)))
    else if (y4 <= 6.5d-288) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (y4 <= 4.6d+62) then
        tmp = x * (i * ((j * y1) - (y * c)))
    else if (y4 <= 2.65d+213) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = y3 * (y4 * ((y * c) - (j * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -5.6e+174) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.62e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -1.02e-41) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= -3.65e-131) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y4 <= -1.55e-173) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (y4 <= -7.4e-261) {
		tmp = y3 * (z * ((a * y1) - (c * y0)));
	} else if (y4 <= 6.5e-288) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y4 <= 4.6e+62) {
		tmp = x * (i * ((j * y1) - (y * c)));
	} else if (y4 <= 2.65e+213) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -5.6e+174:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y4 <= -1.62e+90:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y4 <= -1.02e-41:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y4 <= -3.65e-131:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y4 <= -1.55e-173:
		tmp = x * (j * ((i * y1) - (b * y0)))
	elif y4 <= -7.4e-261:
		tmp = y3 * (z * ((a * y1) - (c * y0)))
	elif y4 <= 6.5e-288:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif y4 <= 4.6e+62:
		tmp = x * (i * ((j * y1) - (y * c)))
	elif y4 <= 2.65e+213:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = y3 * (y4 * ((y * c) - (j * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -5.6e+174)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y4 <= -1.62e+90)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y4 <= -1.02e-41)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= -3.65e-131)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y4 <= -1.55e-173)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y4 <= -7.4e-261)
		tmp = Float64(y3 * Float64(z * Float64(Float64(a * y1) - Float64(c * y0))));
	elseif (y4 <= 6.5e-288)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (y4 <= 4.6e+62)
		tmp = Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (y4 <= 2.65e+213)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(y3 * Float64(y4 * Float64(Float64(y * c) - Float64(j * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -5.6e+174)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y4 <= -1.62e+90)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y4 <= -1.02e-41)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y4 <= -3.65e-131)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y4 <= -1.55e-173)
		tmp = x * (j * ((i * y1) - (b * y0)));
	elseif (y4 <= -7.4e-261)
		tmp = y3 * (z * ((a * y1) - (c * y0)));
	elseif (y4 <= 6.5e-288)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (y4 <= 4.6e+62)
		tmp = x * (i * ((j * y1) - (y * c)));
	elseif (y4 <= 2.65e+213)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -5.6e+174], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.62e+90], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.02e-41], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -3.65e-131], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.55e-173], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -7.4e-261], N[(y3 * N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.5e-288], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4.6e+62], N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.65e+213], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(y4 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y4 < -5.5999999999999999e174

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 62.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in b around inf 59.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -5.5999999999999999e174 < y4 < -1.62e90

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 51.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in y2 around inf 72.3%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   if -1.62e90 < y4 < -1.02e-41

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 57.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.02e-41 < y4 < -3.6500000000000001e-131

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 53.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in c around inf 47.8%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   if -3.6500000000000001e-131 < y4 < -1.55000000000000003e-173

   1. Initial program 11.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 44.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 66.9%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -1.55000000000000003e-173 < y4 < -7.4000000000000004e-261

   1. Initial program 46.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 37.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in z around inf 55.9%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)} \]

   if -7.4000000000000004e-261 < y4 < 6.4999999999999999e-288

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 58.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in z around -inf 64.8%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 64.8%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot z\right) \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

      2. neg-mul-1 64.8%

         \[\leadsto b \cdot \left(\color{blue}{\left(-z\right)} \cdot \left(a \cdot t - k \cdot y0\right)\right) \]

   6. Simplified 64.8%

      \[\leadsto b \cdot \color{blue}{\left(\left(-z\right) \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

   if 6.4999999999999999e-288 < y4 < 4.59999999999999968e62

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 39.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in i around -inf 41.2%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.2%

         \[\leadsto x \cdot \color{blue}{\left(-i \cdot \left(c \cdot y - j \cdot y1\right)\right)} \]

   6. Simplified 41.2%

      \[\leadsto x \cdot \color{blue}{\left(-i \cdot \left(c \cdot y - j \cdot y1\right)\right)} \]

   if 4.59999999999999968e62 < y4 < 2.6499999999999999e213

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 64.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 56.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 2.6499999999999999e213 < y4

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 76.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in y3 around -inf 77.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 77.2%

         \[\leadsto \color{blue}{-y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]

   6. Simplified 77.2%

      \[\leadsto \color{blue}{-y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -5.6 \cdot 10^{+174}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.62 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -3.65 \cdot 10^{-131}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.55 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -7.4 \cdot 10^{-261}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-288}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y4 \leq 4.6 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 2.65 \cdot 10^{+213}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y1 - c \cdot y0\\ t_2 := z \cdot t\_1\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-185}:\\ \;\;\;\;y3 \cdot t\_2\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-269}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-186}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-62}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 6.769 \cdot 10^{+199}:\\ \;\;\;\;y3 \cdot \left(t\_2 + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y1) (* c y0))) (t_2 (* z t_1)))
   (if (<= y -1.25e+38)
     (* c (* y3 (- (* y y4) (* z y0))))
     (if (<= y -1.18e-29)
       (* t (* y4 (- (* b j) (* c y2))))
       (if (<= y -1.55e-185)
         (* y3 t_2)
         (if (<= y -8.2e-269)
           (* y1 (* y4 (- (* k y2) (* j y3))))
           (if (<= y 1.2e-186)
             (* (* z y3) t_1)
             (if (<= y 3.5e-62)
               (* j (* t (- (* b y4) (* i y5))))
               (if (<= y 6.769e+199)
                 (* y3 (+ t_2 (* y (- (* c y4) (* a y5)))))
                 (* k (* y (- (* i y5) (* b y4)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y1) - (c * y0);
	double t_2 = z * t_1;
	double tmp;
	if (y <= -1.25e+38) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y <= -1.18e-29) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y <= -1.55e-185) {
		tmp = y3 * t_2;
	} else if (y <= -8.2e-269) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (y <= 1.2e-186) {
		tmp = (z * y3) * t_1;
	} else if (y <= 3.5e-62) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y <= 6.769e+199) {
		tmp = y3 * (t_2 + (y * ((c * y4) - (a * y5))));
	} else {
		tmp = k * (y * ((i * y5) - (b * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * y1) - (c * y0)
    t_2 = z * t_1
    if (y <= (-1.25d+38)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (y <= (-1.18d-29)) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (y <= (-1.55d-185)) then
        tmp = y3 * t_2
    else if (y <= (-8.2d-269)) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (y <= 1.2d-186) then
        tmp = (z * y3) * t_1
    else if (y <= 3.5d-62) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y <= 6.769d+199) then
        tmp = y3 * (t_2 + (y * ((c * y4) - (a * y5))))
    else
        tmp = k * (y * ((i * y5) - (b * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y1) - (c * y0);
	double t_2 = z * t_1;
	double tmp;
	if (y <= -1.25e+38) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (y <= -1.18e-29) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y <= -1.55e-185) {
		tmp = y3 * t_2;
	} else if (y <= -8.2e-269) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (y <= 1.2e-186) {
		tmp = (z * y3) * t_1;
	} else if (y <= 3.5e-62) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y <= 6.769e+199) {
		tmp = y3 * (t_2 + (y * ((c * y4) - (a * y5))));
	} else {
		tmp = k * (y * ((i * y5) - (b * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y1) - (c * y0)
	t_2 = z * t_1
	tmp = 0
	if y <= -1.25e+38:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif y <= -1.18e-29:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif y <= -1.55e-185:
		tmp = y3 * t_2
	elif y <= -8.2e-269:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif y <= 1.2e-186:
		tmp = (z * y3) * t_1
	elif y <= 3.5e-62:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y <= 6.769e+199:
		tmp = y3 * (t_2 + (y * ((c * y4) - (a * y5))))
	else:
		tmp = k * (y * ((i * y5) - (b * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y1) - Float64(c * y0))
	t_2 = Float64(z * t_1)
	tmp = 0.0
	if (y <= -1.25e+38)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (y <= -1.18e-29)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y <= -1.55e-185)
		tmp = Float64(y3 * t_2);
	elseif (y <= -8.2e-269)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y <= 1.2e-186)
		tmp = Float64(Float64(z * y3) * t_1);
	elseif (y <= 3.5e-62)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y <= 6.769e+199)
		tmp = Float64(y3 * Float64(t_2 + Float64(y * Float64(Float64(c * y4) - Float64(a * y5)))));
	else
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y1) - (c * y0);
	t_2 = z * t_1;
	tmp = 0.0;
	if (y <= -1.25e+38)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (y <= -1.18e-29)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (y <= -1.55e-185)
		tmp = y3 * t_2;
	elseif (y <= -8.2e-269)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (y <= 1.2e-186)
		tmp = (z * y3) * t_1;
	elseif (y <= 3.5e-62)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y <= 6.769e+199)
		tmp = y3 * (t_2 + (y * ((c * y4) - (a * y5))));
	else
		tmp = k * (y * ((i * y5) - (b * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * t$95$1), $MachinePrecision]}, If[LessEqual[y, -1.25e+38], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.18e-29], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.55e-185], N[(y3 * t$95$2), $MachinePrecision], If[LessEqual[y, -8.2e-269], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-186], N[(N[(z * y3), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y, 3.5e-62], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.769e+199], N[(y3 * N[(t$95$2 + N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -1.24999999999999992e38

   1. Initial program 11.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 32.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in c around inf 54.6%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]

   if -1.24999999999999992e38 < y < -1.17999999999999996e-29

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 46.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 46.1%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 46.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 46.1%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 46.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in y4 around inf 64.6%

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 64.6%

         \[\leadsto t \cdot \left(y4 \cdot \left(\color{blue}{j \cdot b} - c \cdot y2\right)\right) \]

      2. *-commutative 64.6%

         \[\leadsto t \cdot \left(y4 \cdot \left(j \cdot b - \color{blue}{y2 \cdot c}\right)\right) \]

   8. Simplified 64.6%

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(j \cdot b - y2 \cdot c\right)\right)} \]

   if -1.17999999999999996e-29 < y < -1.5499999999999998e-185

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 32.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in z around inf 54.3%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)} \]

   if -1.5499999999999998e-185 < y < -8.2000000000000006e-269

   1. Initial program 47.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 53.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in y1 around inf 53.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   if -8.2000000000000006e-269 < y < 1.20000000000000002e-186

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 37.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in z around inf 55.5%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 58.3%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   6. Simplified 58.3%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   if 1.20000000000000002e-186 < y < 3.5000000000000001e-62

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 33.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 33.2%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 33.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 33.2%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 33.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in j around inf 41.4%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if 3.5000000000000001e-62 < y < 6.7690000000000003e199

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 54.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in j around 0 52.7%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if 6.7690000000000003e199 < y

   1. Initial program 14.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 33.9%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.9%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 33.9%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 33.9%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 33.9%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 33.9%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 33.9%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 33.9%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 53.0%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-185}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-269}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-186}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-62}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 6.769 \cdot 10^{+199}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ t_3 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.22 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-209}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+124}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t)))))
        (t_2 (* j (* t (- (* b y4) (* i y5)))))
        (t_3 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= j -2.9e+150)
     t_2
     (if (<= j -3.4e+42)
       (* k (* y1 (- (* y2 y4) (* z i))))
       (if (<= j -1e-22)
         t_2
         (if (<= j -1.22e-135)
           t_1
           (if (<= j -4.1e-209)
             t_3
             (if (<= j 6.4e-215)
               t_1
               (if (<= j 7e+44)
                 (* c (* y0 (- (* x y2) (* z y3))))
                 (if (<= j 3.7e+124)
                   t_3
                   (* b (* y0 (- (* z k) (* x j))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double t_3 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (j <= -2.9e+150) {
		tmp = t_2;
	} else if (j <= -3.4e+42) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -1e-22) {
		tmp = t_2;
	} else if (j <= -1.22e-135) {
		tmp = t_1;
	} else if (j <= -4.1e-209) {
		tmp = t_3;
	} else if (j <= 6.4e-215) {
		tmp = t_1;
	} else if (j <= 7e+44) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 3.7e+124) {
		tmp = t_3;
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    t_2 = j * (t * ((b * y4) - (i * y5)))
    t_3 = c * (y4 * ((y * y3) - (t * y2)))
    if (j <= (-2.9d+150)) then
        tmp = t_2
    else if (j <= (-3.4d+42)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (j <= (-1d-22)) then
        tmp = t_2
    else if (j <= (-1.22d-135)) then
        tmp = t_1
    else if (j <= (-4.1d-209)) then
        tmp = t_3
    else if (j <= 6.4d-215) then
        tmp = t_1
    else if (j <= 7d+44) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (j <= 3.7d+124) then
        tmp = t_3
    else
        tmp = b * (y0 * ((z * k) - (x * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double t_3 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (j <= -2.9e+150) {
		tmp = t_2;
	} else if (j <= -3.4e+42) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -1e-22) {
		tmp = t_2;
	} else if (j <= -1.22e-135) {
		tmp = t_1;
	} else if (j <= -4.1e-209) {
		tmp = t_3;
	} else if (j <= 6.4e-215) {
		tmp = t_1;
	} else if (j <= 7e+44) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 3.7e+124) {
		tmp = t_3;
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	t_2 = j * (t * ((b * y4) - (i * y5)))
	t_3 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if j <= -2.9e+150:
		tmp = t_2
	elif j <= -3.4e+42:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif j <= -1e-22:
		tmp = t_2
	elif j <= -1.22e-135:
		tmp = t_1
	elif j <= -4.1e-209:
		tmp = t_3
	elif j <= 6.4e-215:
		tmp = t_1
	elif j <= 7e+44:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif j <= 3.7e+124:
		tmp = t_3
	else:
		tmp = b * (y0 * ((z * k) - (x * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	t_3 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (j <= -2.9e+150)
		tmp = t_2;
	elseif (j <= -3.4e+42)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (j <= -1e-22)
		tmp = t_2;
	elseif (j <= -1.22e-135)
		tmp = t_1;
	elseif (j <= -4.1e-209)
		tmp = t_3;
	elseif (j <= 6.4e-215)
		tmp = t_1;
	elseif (j <= 7e+44)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (j <= 3.7e+124)
		tmp = t_3;
	else
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	t_2 = j * (t * ((b * y4) - (i * y5)));
	t_3 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (j <= -2.9e+150)
		tmp = t_2;
	elseif (j <= -3.4e+42)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (j <= -1e-22)
		tmp = t_2;
	elseif (j <= -1.22e-135)
		tmp = t_1;
	elseif (j <= -4.1e-209)
		tmp = t_3;
	elseif (j <= 6.4e-215)
		tmp = t_1;
	elseif (j <= 7e+44)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (j <= 3.7e+124)
		tmp = t_3;
	else
		tmp = b * (y0 * ((z * k) - (x * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.9e+150], t$95$2, If[LessEqual[j, -3.4e+42], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1e-22], t$95$2, If[LessEqual[j, -1.22e-135], t$95$1, If[LessEqual[j, -4.1e-209], t$95$3, If[LessEqual[j, 6.4e-215], t$95$1, If[LessEqual[j, 7e+44], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e+124], t$95$3, N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.90000000000000011e150 or -3.39999999999999975e42 < j < -1e-22

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 50.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 50.4%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 50.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 50.4%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 50.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in j around inf 53.4%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -2.90000000000000011e150 < j < -3.39999999999999975e42

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 44.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 44.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 44.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y1 around inf 53.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   if -1e-22 < j < -1.22e-135 or -4.09999999999999977e-209 < j < 6.4000000000000003e-215

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 51.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.22e-135 < j < -4.09999999999999977e-209 or 6.9999999999999998e44 < j < 3.70000000000000008e124

   1. Initial program 22.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 50.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 51.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 6.4000000000000003e-215 < j < 6.9999999999999998e44

   1. Initial program 42.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 45.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 3.70000000000000008e124 < j

   1. Initial program 15.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 49.1%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.22 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-209}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+124}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ t_3 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -5.5 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{+40}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.62 \cdot 10^{-208}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+122}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t)))))
        (t_2 (* j (* t (- (* b y4) (* i y5)))))
        (t_3 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= j -5.5e+151)
     t_2
     (if (<= j -1.1e+40)
       (* k (* y1 (- (* y2 y4) (* z i))))
       (if (<= j -8.5e-23)
         t_2
         (if (<= j -1.25e-135)
           t_1
           (if (<= j -1.62e-208)
             t_3
             (if (<= j 3e-215)
               t_1
               (if (<= j 7.6e+38)
                 (* c (* y0 (- (* x y2) (* z y3))))
                 (if (<= j 2.3e+122)
                   t_3
                   (* x (* j (- (* i y1) (* b y0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double t_3 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (j <= -5.5e+151) {
		tmp = t_2;
	} else if (j <= -1.1e+40) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -8.5e-23) {
		tmp = t_2;
	} else if (j <= -1.25e-135) {
		tmp = t_1;
	} else if (j <= -1.62e-208) {
		tmp = t_3;
	} else if (j <= 3e-215) {
		tmp = t_1;
	} else if (j <= 7.6e+38) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 2.3e+122) {
		tmp = t_3;
	} else {
		tmp = x * (j * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    t_2 = j * (t * ((b * y4) - (i * y5)))
    t_3 = c * (y4 * ((y * y3) - (t * y2)))
    if (j <= (-5.5d+151)) then
        tmp = t_2
    else if (j <= (-1.1d+40)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (j <= (-8.5d-23)) then
        tmp = t_2
    else if (j <= (-1.25d-135)) then
        tmp = t_1
    else if (j <= (-1.62d-208)) then
        tmp = t_3
    else if (j <= 3d-215) then
        tmp = t_1
    else if (j <= 7.6d+38) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (j <= 2.3d+122) then
        tmp = t_3
    else
        tmp = x * (j * ((i * y1) - (b * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double t_3 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (j <= -5.5e+151) {
		tmp = t_2;
	} else if (j <= -1.1e+40) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -8.5e-23) {
		tmp = t_2;
	} else if (j <= -1.25e-135) {
		tmp = t_1;
	} else if (j <= -1.62e-208) {
		tmp = t_3;
	} else if (j <= 3e-215) {
		tmp = t_1;
	} else if (j <= 7.6e+38) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 2.3e+122) {
		tmp = t_3;
	} else {
		tmp = x * (j * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	t_2 = j * (t * ((b * y4) - (i * y5)))
	t_3 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if j <= -5.5e+151:
		tmp = t_2
	elif j <= -1.1e+40:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif j <= -8.5e-23:
		tmp = t_2
	elif j <= -1.25e-135:
		tmp = t_1
	elif j <= -1.62e-208:
		tmp = t_3
	elif j <= 3e-215:
		tmp = t_1
	elif j <= 7.6e+38:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif j <= 2.3e+122:
		tmp = t_3
	else:
		tmp = x * (j * ((i * y1) - (b * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	t_3 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (j <= -5.5e+151)
		tmp = t_2;
	elseif (j <= -1.1e+40)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (j <= -8.5e-23)
		tmp = t_2;
	elseif (j <= -1.25e-135)
		tmp = t_1;
	elseif (j <= -1.62e-208)
		tmp = t_3;
	elseif (j <= 3e-215)
		tmp = t_1;
	elseif (j <= 7.6e+38)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (j <= 2.3e+122)
		tmp = t_3;
	else
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	t_2 = j * (t * ((b * y4) - (i * y5)));
	t_3 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (j <= -5.5e+151)
		tmp = t_2;
	elseif (j <= -1.1e+40)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (j <= -8.5e-23)
		tmp = t_2;
	elseif (j <= -1.25e-135)
		tmp = t_1;
	elseif (j <= -1.62e-208)
		tmp = t_3;
	elseif (j <= 3e-215)
		tmp = t_1;
	elseif (j <= 7.6e+38)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (j <= 2.3e+122)
		tmp = t_3;
	else
		tmp = x * (j * ((i * y1) - (b * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.5e+151], t$95$2, If[LessEqual[j, -1.1e+40], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e-23], t$95$2, If[LessEqual[j, -1.25e-135], t$95$1, If[LessEqual[j, -1.62e-208], t$95$3, If[LessEqual[j, 3e-215], t$95$1, If[LessEqual[j, 7.6e+38], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e+122], t$95$3, N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -5.4999999999999994e151 or -1.0999999999999999e40 < j < -8.4999999999999996e-23

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 50.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 50.4%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 50.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 50.4%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 50.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in j around inf 53.4%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -5.4999999999999994e151 < j < -1.0999999999999999e40

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 44.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 44.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 44.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y1 around inf 53.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   if -8.4999999999999996e-23 < j < -1.25000000000000005e-135 or -1.6200000000000001e-208 < j < 3.00000000000000025e-215

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 51.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.25000000000000005e-135 < j < -1.6200000000000001e-208 or 7.5999999999999996e38 < j < 2.3000000000000001e122

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 53.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 51.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 3.00000000000000025e-215 < j < 7.5999999999999996e38

   1. Initial program 42.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 45.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 2.3000000000000001e122 < j

   1. Initial program 15.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 54.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 54.2%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.5 \cdot 10^{+151}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{+40}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-23}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -1.62 \cdot 10^{-208}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -2.2 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+42}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -2.75 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -1.66 \cdot 10^{-209}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* t (- (* b y4) (* i y5))))))
   (if (<= j -2.2e+151)
     t_1
     (if (<= j -3.2e+42)
       (* k (* y1 (- (* y2 y4) (* z i))))
       (if (<= j -2.75e-40)
         t_1
         (if (<= j -3.5e-185)
           (* x (* y (- (* a b) (* c i))))
           (if (<= j -1.66e-209)
             (* t (* c (- (* z i) (* y2 y4))))
             (if (<= j 7.5e-216)
               (* a (* b (- (* x y) (* z t))))
               (if (<= j 1.15e+40)
                 (* c (* y0 (- (* x y2) (* z y3))))
                 (if (<= j 2.3e+122)
                   (* c (* y4 (- (* y y3) (* t y2))))
                   (* x (* j (- (* i y1) (* b y0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (j <= -2.2e+151) {
		tmp = t_1;
	} else if (j <= -3.2e+42) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -2.75e-40) {
		tmp = t_1;
	} else if (j <= -3.5e-185) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (j <= -1.66e-209) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (j <= 7.5e-216) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (j <= 1.15e+40) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 2.3e+122) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = x * (j * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * ((b * y4) - (i * y5)))
    if (j <= (-2.2d+151)) then
        tmp = t_1
    else if (j <= (-3.2d+42)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (j <= (-2.75d-40)) then
        tmp = t_1
    else if (j <= (-3.5d-185)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (j <= (-1.66d-209)) then
        tmp = t * (c * ((z * i) - (y2 * y4)))
    else if (j <= 7.5d-216) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (j <= 1.15d+40) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (j <= 2.3d+122) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = x * (j * ((i * y1) - (b * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (j <= -2.2e+151) {
		tmp = t_1;
	} else if (j <= -3.2e+42) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -2.75e-40) {
		tmp = t_1;
	} else if (j <= -3.5e-185) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (j <= -1.66e-209) {
		tmp = t * (c * ((z * i) - (y2 * y4)));
	} else if (j <= 7.5e-216) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (j <= 1.15e+40) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 2.3e+122) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = x * (j * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (t * ((b * y4) - (i * y5)))
	tmp = 0
	if j <= -2.2e+151:
		tmp = t_1
	elif j <= -3.2e+42:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif j <= -2.75e-40:
		tmp = t_1
	elif j <= -3.5e-185:
		tmp = x * (y * ((a * b) - (c * i)))
	elif j <= -1.66e-209:
		tmp = t * (c * ((z * i) - (y2 * y4)))
	elif j <= 7.5e-216:
		tmp = a * (b * ((x * y) - (z * t)))
	elif j <= 1.15e+40:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif j <= 2.3e+122:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = x * (j * ((i * y1) - (b * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	tmp = 0.0
	if (j <= -2.2e+151)
		tmp = t_1;
	elseif (j <= -3.2e+42)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (j <= -2.75e-40)
		tmp = t_1;
	elseif (j <= -3.5e-185)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (j <= -1.66e-209)
		tmp = Float64(t * Float64(c * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (j <= 7.5e-216)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (j <= 1.15e+40)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (j <= 2.3e+122)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (t * ((b * y4) - (i * y5)));
	tmp = 0.0;
	if (j <= -2.2e+151)
		tmp = t_1;
	elseif (j <= -3.2e+42)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (j <= -2.75e-40)
		tmp = t_1;
	elseif (j <= -3.5e-185)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (j <= -1.66e-209)
		tmp = t * (c * ((z * i) - (y2 * y4)));
	elseif (j <= 7.5e-216)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (j <= 1.15e+40)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (j <= 2.3e+122)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = x * (j * ((i * y1) - (b * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.2e+151], t$95$1, If[LessEqual[j, -3.2e+42], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.75e-40], t$95$1, If[LessEqual[j, -3.5e-185], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.66e-209], N[(t * N[(c * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e-216], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.15e+40], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e+122], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -2.20000000000000007e151 or -3.20000000000000002e42 < j < -2.75000000000000001e-40

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 51.4%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 51.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 51.4%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in j around inf 52.2%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -2.20000000000000007e151 < j < -3.20000000000000002e42

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 44.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 44.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 44.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 44.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y1 around inf 53.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   if -2.75000000000000001e-40 < j < -3.4999999999999998e-185

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 24.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 47.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if -3.4999999999999998e-185 < j < -1.66e-209

   1. Initial program 66.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 35.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 35.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 35.1%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 35.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 35.1%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 35.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 83.7%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 83.7%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 83.7%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 83.7%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 83.7%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 83.7%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   if -1.66e-209 < j < 7.50000000000000064e-216

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 7.50000000000000064e-216 < j < 1.14999999999999997e40

   1. Initial program 42.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 45.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 1.14999999999999997e40 < j < 2.3000000000000001e122

   1. Initial program 17.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 47.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 59.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 2.3000000000000001e122 < j

   1. Initial program 15.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 54.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 54.2%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.2 \cdot 10^{+151}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+42}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -2.75 \cdot 10^{-40}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -1.66 \cdot 10^{-209}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 32.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{if}\;y4 \leq -4.8 \cdot 10^{+178}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -2.4 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -3 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 1.8 \cdot 10^{-290}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 5.4 \cdot 10^{+31}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 1.6 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 2.1 \cdot 10^{+213}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* i (- (* j y1) (* y c))))))
   (if (<= y4 -4.8e+178)
     (* b (* y4 (- (* t j) (* y k))))
     (if (<= y4 -2.4e+90)
       (* y2 (* y4 (- (* k y1) (* t c))))
       (if (<= y4 -3e-41)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y4 1.8e-290)
           (* b (* z (- (* k y0) (* t a))))
           (if (<= y4 7.5e-86)
             t_1
             (if (<= y4 5.4e+31)
               (* k (* y0 (- (* z b) (* y2 y5))))
               (if (<= y4 1.6e+63)
                 t_1
                 (if (<= y4 2.1e+213)
                   (* c (* y4 (- (* y y3) (* t y2))))
                   (* y3 (* y4 (- (* y c) (* j y1))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (i * ((j * y1) - (y * c)));
	double tmp;
	if (y4 <= -4.8e+178) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -2.4e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -3e-41) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= 1.8e-290) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y4 <= 7.5e-86) {
		tmp = t_1;
	} else if (y4 <= 5.4e+31) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (y4 <= 1.6e+63) {
		tmp = t_1;
	} else if (y4 <= 2.1e+213) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (i * ((j * y1) - (y * c)))
    if (y4 <= (-4.8d+178)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y4 <= (-2.4d+90)) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y4 <= (-3d-41)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y4 <= 1.8d-290) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (y4 <= 7.5d-86) then
        tmp = t_1
    else if (y4 <= 5.4d+31) then
        tmp = k * (y0 * ((z * b) - (y2 * y5)))
    else if (y4 <= 1.6d+63) then
        tmp = t_1
    else if (y4 <= 2.1d+213) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = y3 * (y4 * ((y * c) - (j * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (i * ((j * y1) - (y * c)));
	double tmp;
	if (y4 <= -4.8e+178) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -2.4e+90) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y4 <= -3e-41) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= 1.8e-290) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y4 <= 7.5e-86) {
		tmp = t_1;
	} else if (y4 <= 5.4e+31) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (y4 <= 1.6e+63) {
		tmp = t_1;
	} else if (y4 <= 2.1e+213) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (i * ((j * y1) - (y * c)))
	tmp = 0
	if y4 <= -4.8e+178:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y4 <= -2.4e+90:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y4 <= -3e-41:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y4 <= 1.8e-290:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif y4 <= 7.5e-86:
		tmp = t_1
	elif y4 <= 5.4e+31:
		tmp = k * (y0 * ((z * b) - (y2 * y5)))
	elif y4 <= 1.6e+63:
		tmp = t_1
	elif y4 <= 2.1e+213:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = y3 * (y4 * ((y * c) - (j * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c))))
	tmp = 0.0
	if (y4 <= -4.8e+178)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y4 <= -2.4e+90)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y4 <= -3e-41)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= 1.8e-290)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (y4 <= 7.5e-86)
		tmp = t_1;
	elseif (y4 <= 5.4e+31)
		tmp = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (y4 <= 1.6e+63)
		tmp = t_1;
	elseif (y4 <= 2.1e+213)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(y3 * Float64(y4 * Float64(Float64(y * c) - Float64(j * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (i * ((j * y1) - (y * c)));
	tmp = 0.0;
	if (y4 <= -4.8e+178)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y4 <= -2.4e+90)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y4 <= -3e-41)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y4 <= 1.8e-290)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (y4 <= 7.5e-86)
		tmp = t_1;
	elseif (y4 <= 5.4e+31)
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	elseif (y4 <= 1.6e+63)
		tmp = t_1;
	elseif (y4 <= 2.1e+213)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4.8e+178], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.4e+90], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -3e-41], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.8e-290], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.5e-86], t$95$1, If[LessEqual[y4, 5.4e+31], N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.6e+63], t$95$1, If[LessEqual[y4, 2.1e+213], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(y4 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y4 < -4.8e178

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 62.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in b around inf 59.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -4.8e178 < y4 < -2.4000000000000001e90

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 51.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in y2 around inf 72.3%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   if -2.4000000000000001e90 < y4 < -2.99999999999999989e-41

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 57.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -2.99999999999999989e-41 < y4 < 1.7999999999999999e-290

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in z around -inf 40.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 40.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot z\right) \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

      2. neg-mul-1 40.6%

         \[\leadsto b \cdot \left(\color{blue}{\left(-z\right)} \cdot \left(a \cdot t - k \cdot y0\right)\right) \]

   6. Simplified 40.6%

      \[\leadsto b \cdot \color{blue}{\left(\left(-z\right) \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

   if 1.7999999999999999e-290 < y4 < 7.50000000000000055e-86 or 5.39999999999999971e31 < y4 < 1.60000000000000006e63

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 41.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in i around -inf 49.8%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.8%

         \[\leadsto x \cdot \color{blue}{\left(-i \cdot \left(c \cdot y - j \cdot y1\right)\right)} \]

   6. Simplified 49.8%

      \[\leadsto x \cdot \color{blue}{\left(-i \cdot \left(c \cdot y - j \cdot y1\right)\right)} \]

   if 7.50000000000000055e-86 < y4 < 5.39999999999999971e31

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 33.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 33.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 33.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 33.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 33.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 33.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 33.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y0 around -inf 55.9%

      \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 55.9%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

      2. neg-mul-1 55.9%

         \[\leadsto k \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(y2 \cdot y5 - b \cdot z\right)\right) \]

   8. Simplified 55.9%

      \[\leadsto k \cdot \color{blue}{\left(\left(-y0\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   if 1.60000000000000006e63 < y4 < 2.1000000000000001e213

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 64.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 56.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 2.1000000000000001e213 < y4

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 76.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in y3 around -inf 77.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 77.2%

         \[\leadsto \color{blue}{-y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]

   6. Simplified 77.2%

      \[\leadsto \color{blue}{-y3 \cdot \left(y4 \cdot \left(j \cdot y1 - c \cdot y\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.8 \cdot 10^{+178}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -2.4 \cdot 10^{+90}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq -3 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 1.8 \cdot 10^{-290}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 5.4 \cdot 10^{+31}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 1.6 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 2.1 \cdot 10^{+213}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 35.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := c \cdot y4 - a \cdot y5\\ t_3 := y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + y \cdot t\_2\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \left(b \cdot t\_1\right)\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-101}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-290}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_1 + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{-226}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4\right) - \left(y2 \cdot t\_2 + a \cdot \left(z \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t)))
        (t_2 (- (* c y4) (* a y5)))
        (t_3 (* y3 (+ (* z (- (* a y1) (* c y0))) (* y t_2)))))
   (if (<= x -4.8e+109)
     (* a (* b t_1))
     (if (<= x -2.75e-101)
       t_3
       (if (<= x 4.4e-290)
         (*
          b
          (+
           (+ (* a t_1) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))
         (if (<= x 3.15e-226)
           t_3
           (if (<= x 4e+158)
             (* t (- (* b (* j y4)) (+ (* y2 t_2) (* a (* z b)))))
             (* x (* i (- (* j y1) (* y c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (z * t);
	double t_2 = (c * y4) - (a * y5);
	double t_3 = y3 * ((z * ((a * y1) - (c * y0))) + (y * t_2));
	double tmp;
	if (x <= -4.8e+109) {
		tmp = a * (b * t_1);
	} else if (x <= -2.75e-101) {
		tmp = t_3;
	} else if (x <= 4.4e-290) {
		tmp = b * (((a * t_1) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (x <= 3.15e-226) {
		tmp = t_3;
	} else if (x <= 4e+158) {
		tmp = t * ((b * (j * y4)) - ((y2 * t_2) + (a * (z * b))));
	} else {
		tmp = x * (i * ((j * y1) - (y * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    t_2 = (c * y4) - (a * y5)
    t_3 = y3 * ((z * ((a * y1) - (c * y0))) + (y * t_2))
    if (x <= (-4.8d+109)) then
        tmp = a * (b * t_1)
    else if (x <= (-2.75d-101)) then
        tmp = t_3
    else if (x <= 4.4d-290) then
        tmp = b * (((a * t_1) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (x <= 3.15d-226) then
        tmp = t_3
    else if (x <= 4d+158) then
        tmp = t * ((b * (j * y4)) - ((y2 * t_2) + (a * (z * b))))
    else
        tmp = x * (i * ((j * y1) - (y * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (z * t);
	double t_2 = (c * y4) - (a * y5);
	double t_3 = y3 * ((z * ((a * y1) - (c * y0))) + (y * t_2));
	double tmp;
	if (x <= -4.8e+109) {
		tmp = a * (b * t_1);
	} else if (x <= -2.75e-101) {
		tmp = t_3;
	} else if (x <= 4.4e-290) {
		tmp = b * (((a * t_1) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (x <= 3.15e-226) {
		tmp = t_3;
	} else if (x <= 4e+158) {
		tmp = t * ((b * (j * y4)) - ((y2 * t_2) + (a * (z * b))));
	} else {
		tmp = x * (i * ((j * y1) - (y * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y) - (z * t)
	t_2 = (c * y4) - (a * y5)
	t_3 = y3 * ((z * ((a * y1) - (c * y0))) + (y * t_2))
	tmp = 0
	if x <= -4.8e+109:
		tmp = a * (b * t_1)
	elif x <= -2.75e-101:
		tmp = t_3
	elif x <= 4.4e-290:
		tmp = b * (((a * t_1) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif x <= 3.15e-226:
		tmp = t_3
	elif x <= 4e+158:
		tmp = t * ((b * (j * y4)) - ((y2 * t_2) + (a * (z * b))))
	else:
		tmp = x * (i * ((j * y1) - (y * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	t_2 = Float64(Float64(c * y4) - Float64(a * y5))
	t_3 = Float64(y3 * Float64(Float64(z * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(y * t_2)))
	tmp = 0.0
	if (x <= -4.8e+109)
		tmp = Float64(a * Float64(b * t_1));
	elseif (x <= -2.75e-101)
		tmp = t_3;
	elseif (x <= 4.4e-290)
		tmp = Float64(b * Float64(Float64(Float64(a * t_1) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (x <= 3.15e-226)
		tmp = t_3;
	elseif (x <= 4e+158)
		tmp = Float64(t * Float64(Float64(b * Float64(j * y4)) - Float64(Float64(y2 * t_2) + Float64(a * Float64(z * b)))));
	else
		tmp = Float64(x * Float64(i * Float64(Float64(j * y1) - Float64(y * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y) - (z * t);
	t_2 = (c * y4) - (a * y5);
	t_3 = y3 * ((z * ((a * y1) - (c * y0))) + (y * t_2));
	tmp = 0.0;
	if (x <= -4.8e+109)
		tmp = a * (b * t_1);
	elseif (x <= -2.75e-101)
		tmp = t_3;
	elseif (x <= 4.4e-290)
		tmp = b * (((a * t_1) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (x <= 3.15e-226)
		tmp = t_3;
	elseif (x <= 4e+158)
		tmp = t * ((b * (j * y4)) - ((y2 * t_2) + (a * (z * b))));
	else
		tmp = x * (i * ((j * y1) - (y * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y3 * N[(N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+109], N[(a * N[(b * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.75e-101], t$95$3, If[LessEqual[x, 4.4e-290], N[(b * N[(N[(N[(a * t$95$1), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.15e-226], t$95$3, If[LessEqual[x, 4e+158], N[(t * N[(N[(b * N[(j * y4), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * t$95$2), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(i * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.79999999999999975e109

   1. Initial program 19.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 55.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 59.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -4.79999999999999975e109 < x < -2.74999999999999986e-101 or 4.4000000000000002e-290 < x < 3.1499999999999999e-226

   1. Initial program 39.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 50.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in j around 0 54.4%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if -2.74999999999999986e-101 < x < 4.4000000000000002e-290

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 48.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 3.1499999999999999e-226 < x < 3.99999999999999981e158

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 50.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 50.7%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 50.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 50.7%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 50.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in i around 0 48.9%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot \left(j \cdot y4\right) - \left(a \cdot \left(b \cdot z\right) + y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if 3.99999999999999981e158 < x

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 54.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in i around -inf 55.4%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.4%

         \[\leadsto x \cdot \color{blue}{\left(-i \cdot \left(c \cdot y - j \cdot y1\right)\right)} \]

   6. Simplified 55.4%

      \[\leadsto x \cdot \color{blue}{\left(-i \cdot \left(c \cdot y - j \cdot y1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-101}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-290}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{-226}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4\right) - \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right) + a \cdot \left(z \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 31.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -2.1 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+124}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t)))))
        (t_2 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= j -2.1e+85)
     (* b (* y4 (- (* t j) (* y k))))
     (if (<= j -1.55e-135)
       t_1
       (if (<= j -7.5e-209)
         t_2
         (if (<= j 1.05e-215)
           t_1
           (if (<= j 3.6e+44)
             (* c (* y0 (- (* x y2) (* z y3))))
             (if (<= j 5e+124) t_2 (* b (* y0 (- (* z k) (* x j))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (j <= -2.1e+85) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (j <= -1.55e-135) {
		tmp = t_1;
	} else if (j <= -7.5e-209) {
		tmp = t_2;
	} else if (j <= 1.05e-215) {
		tmp = t_1;
	} else if (j <= 3.6e+44) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 5e+124) {
		tmp = t_2;
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    t_2 = c * (y4 * ((y * y3) - (t * y2)))
    if (j <= (-2.1d+85)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (j <= (-1.55d-135)) then
        tmp = t_1
    else if (j <= (-7.5d-209)) then
        tmp = t_2
    else if (j <= 1.05d-215) then
        tmp = t_1
    else if (j <= 3.6d+44) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (j <= 5d+124) then
        tmp = t_2
    else
        tmp = b * (y0 * ((z * k) - (x * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (j <= -2.1e+85) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (j <= -1.55e-135) {
		tmp = t_1;
	} else if (j <= -7.5e-209) {
		tmp = t_2;
	} else if (j <= 1.05e-215) {
		tmp = t_1;
	} else if (j <= 3.6e+44) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 5e+124) {
		tmp = t_2;
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	t_2 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if j <= -2.1e+85:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif j <= -1.55e-135:
		tmp = t_1
	elif j <= -7.5e-209:
		tmp = t_2
	elif j <= 1.05e-215:
		tmp = t_1
	elif j <= 3.6e+44:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif j <= 5e+124:
		tmp = t_2
	else:
		tmp = b * (y0 * ((z * k) - (x * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (j <= -2.1e+85)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (j <= -1.55e-135)
		tmp = t_1;
	elseif (j <= -7.5e-209)
		tmp = t_2;
	elseif (j <= 1.05e-215)
		tmp = t_1;
	elseif (j <= 3.6e+44)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (j <= 5e+124)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	t_2 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (j <= -2.1e+85)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (j <= -1.55e-135)
		tmp = t_1;
	elseif (j <= -7.5e-209)
		tmp = t_2;
	elseif (j <= 1.05e-215)
		tmp = t_1;
	elseif (j <= 3.6e+44)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (j <= 5e+124)
		tmp = t_2;
	else
		tmp = b * (y0 * ((z * k) - (x * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.1e+85], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.55e-135], t$95$1, If[LessEqual[j, -7.5e-209], t$95$2, If[LessEqual[j, 1.05e-215], t$95$1, If[LessEqual[j, 3.6e+44], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e+124], t$95$2, N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.1000000000000001e85

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 42.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in b around inf 47.8%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -2.1000000000000001e85 < j < -1.55e-135 or -7.49999999999999965e-209 < j < 1.05e-215

   1. Initial program 33.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 47.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.55e-135 < j < -7.49999999999999965e-209 or 3.6e44 < j < 4.9999999999999996e124

   1. Initial program 22.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 50.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 51.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 1.05e-215 < j < 3.6e44

   1. Initial program 42.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 45.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 4.9999999999999996e124 < j

   1. Initial program 15.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 49.1%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-209}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+124}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 31.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -7.4 \cdot 10^{-25}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2.25 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.75 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+45}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t)))))
        (t_2 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= j -7.4e-25)
     (* j (* t (- (* b y4) (* i y5))))
     (if (<= j -1.5e-135)
       t_1
       (if (<= j -2.25e-209)
         t_2
         (if (<= j 2.75e-216)
           t_1
           (if (<= j 6.8e+45)
             (* c (* y0 (- (* x y2) (* z y3))))
             (if (<= j 3.7e+126) t_2 (* b (* y0 (- (* z k) (* x j))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (j <= -7.4e-25) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (j <= -1.5e-135) {
		tmp = t_1;
	} else if (j <= -2.25e-209) {
		tmp = t_2;
	} else if (j <= 2.75e-216) {
		tmp = t_1;
	} else if (j <= 6.8e+45) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 3.7e+126) {
		tmp = t_2;
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    t_2 = c * (y4 * ((y * y3) - (t * y2)))
    if (j <= (-7.4d-25)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (j <= (-1.5d-135)) then
        tmp = t_1
    else if (j <= (-2.25d-209)) then
        tmp = t_2
    else if (j <= 2.75d-216) then
        tmp = t_1
    else if (j <= 6.8d+45) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (j <= 3.7d+126) then
        tmp = t_2
    else
        tmp = b * (y0 * ((z * k) - (x * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (j <= -7.4e-25) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (j <= -1.5e-135) {
		tmp = t_1;
	} else if (j <= -2.25e-209) {
		tmp = t_2;
	} else if (j <= 2.75e-216) {
		tmp = t_1;
	} else if (j <= 6.8e+45) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (j <= 3.7e+126) {
		tmp = t_2;
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	t_2 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if j <= -7.4e-25:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif j <= -1.5e-135:
		tmp = t_1
	elif j <= -2.25e-209:
		tmp = t_2
	elif j <= 2.75e-216:
		tmp = t_1
	elif j <= 6.8e+45:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif j <= 3.7e+126:
		tmp = t_2
	else:
		tmp = b * (y0 * ((z * k) - (x * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (j <= -7.4e-25)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (j <= -1.5e-135)
		tmp = t_1;
	elseif (j <= -2.25e-209)
		tmp = t_2;
	elseif (j <= 2.75e-216)
		tmp = t_1;
	elseif (j <= 6.8e+45)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (j <= 3.7e+126)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	t_2 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (j <= -7.4e-25)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (j <= -1.5e-135)
		tmp = t_1;
	elseif (j <= -2.25e-209)
		tmp = t_2;
	elseif (j <= 2.75e-216)
		tmp = t_1;
	elseif (j <= 6.8e+45)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (j <= 3.7e+126)
		tmp = t_2;
	else
		tmp = b * (y0 * ((z * k) - (x * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.4e-25], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.5e-135], t$95$1, If[LessEqual[j, -2.25e-209], t$95$2, If[LessEqual[j, 2.75e-216], t$95$1, If[LessEqual[j, 6.8e+45], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e+126], t$95$2, N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -7.40000000000000017e-25

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 48.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 48.3%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 48.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 48.3%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 48.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in j around inf 46.1%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -7.40000000000000017e-25 < j < -1.50000000000000006e-135 or -2.2499999999999999e-209 < j < 2.74999999999999995e-216

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 51.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.50000000000000006e-135 < j < -2.2499999999999999e-209 or 6.8e45 < j < 3.6999999999999998e126

   1. Initial program 22.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 50.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 51.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 2.74999999999999995e-216 < j < 6.8e45

   1. Initial program 42.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 45.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 3.6999999999999998e126 < j

   1. Initial program 15.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 49.1%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.4 \cdot 10^{-25}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -2.25 \cdot 10^{-209}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2.75 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+45}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+126}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 28.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y4 \leq -2.5 \cdot 10^{+264}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -6.6 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -4.2 \cdot 10^{-307}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 5.8 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 4.2 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= y4 -2.5e+264)
     (* c (* y (* y3 y4)))
     (if (<= y4 -6.6e-197)
       t_1
       (if (<= y4 -4.2e-307)
         (* k (* y0 (* z b)))
         (if (<= y4 5.8e-208)
           t_1
           (if (<= y4 4.2e+111)
             (* b (* y0 (- (* z k) (* x j))))
             (* y3 (* y (* 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 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y4 <= -2.5e+264) {
		tmp = c * (y * (y3 * y4));
	} else if (y4 <= -6.6e-197) {
		tmp = t_1;
	} else if (y4 <= -4.2e-307) {
		tmp = k * (y0 * (z * b));
	} else if (y4 <= 5.8e-208) {
		tmp = t_1;
	} else if (y4 <= 4.2e+111) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = y3 * (y * (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) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (y4 <= (-2.5d+264)) then
        tmp = c * (y * (y3 * y4))
    else if (y4 <= (-6.6d-197)) then
        tmp = t_1
    else if (y4 <= (-4.2d-307)) then
        tmp = k * (y0 * (z * b))
    else if (y4 <= 5.8d-208) then
        tmp = t_1
    else if (y4 <= 4.2d+111) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else
        tmp = y3 * (y * (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 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y4 <= -2.5e+264) {
		tmp = c * (y * (y3 * y4));
	} else if (y4 <= -6.6e-197) {
		tmp = t_1;
	} else if (y4 <= -4.2e-307) {
		tmp = k * (y0 * (z * b));
	} else if (y4 <= 5.8e-208) {
		tmp = t_1;
	} else if (y4 <= 4.2e+111) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = y3 * (y * (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 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y4 <= -2.5e+264:
		tmp = c * (y * (y3 * y4))
	elif y4 <= -6.6e-197:
		tmp = t_1
	elif y4 <= -4.2e-307:
		tmp = k * (y0 * (z * b))
	elif y4 <= 5.8e-208:
		tmp = t_1
	elif y4 <= 4.2e+111:
		tmp = b * (y0 * ((z * k) - (x * j)))
	else:
		tmp = y3 * (y * (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(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y4 <= -2.5e+264)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y4 <= -6.6e-197)
		tmp = t_1;
	elseif (y4 <= -4.2e-307)
		tmp = Float64(k * Float64(y0 * Float64(z * b)));
	elseif (y4 <= 5.8e-208)
		tmp = t_1;
	elseif (y4 <= 4.2e+111)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = Float64(y3 * Float64(y * 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 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y4 <= -2.5e+264)
		tmp = c * (y * (y3 * y4));
	elseif (y4 <= -6.6e-197)
		tmp = t_1;
	elseif (y4 <= -4.2e-307)
		tmp = k * (y0 * (z * b));
	elseif (y4 <= 5.8e-208)
		tmp = t_1;
	elseif (y4 <= 4.2e+111)
		tmp = b * (y0 * ((z * k) - (x * j)));
	else
		tmp = y3 * (y * (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[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.5e+264], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -6.6e-197], t$95$1, If[LessEqual[y4, -4.2e-307], N[(k * N[(y0 * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.8e-208], t$95$1, If[LessEqual[y4, 4.2e+111], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(y * N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -2.50000000000000017e264

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 42.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y around inf 75.8%

      \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(y \cdot \left(a \cdot y5 - c \cdot y4\right)\right)}\right) \]

   5. Taylor expanded in a around 0 75.9%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 75.9%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right)} \]

      2. neg-mul-1 75.9%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\right) \]

      3. *-commutative 75.9%

         \[\leadsto -1 \cdot \left(\left(-c\right) \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3\right)}\right)\right) \]

   7. Simplified 75.9%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(y \cdot \left(y4 \cdot y3\right)\right)\right)} \]

   if -2.50000000000000017e264 < y4 < -6.5999999999999995e-197 or -4.2000000000000002e-307 < y4 < 5.7999999999999999e-208

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 41.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -6.5999999999999995e-197 < y4 < -4.2000000000000002e-307

   1. Initial program 47.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 42.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 42.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 42.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 42.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 42.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 42.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 42.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y0 around -inf 48.2%

      \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 48.2%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

      2. neg-mul-1 48.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(y2 \cdot y5 - b \cdot z\right)\right) \]

   8. Simplified 48.2%

      \[\leadsto k \cdot \color{blue}{\left(\left(-y0\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around 0 48.0%

      \[\leadsto k \cdot \left(\left(-y0\right) \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 48.0%

          \[\leadsto k \cdot \left(\left(-y0\right) \cdot \color{blue}{\left(-b \cdot z\right)}\right) \]

       2. distribute-lft-neg-out 48.0%

          \[\leadsto k \cdot \left(\left(-y0\right) \cdot \color{blue}{\left(\left(-b\right) \cdot z\right)}\right) \]

       3. *-commutative 48.0%

          \[\leadsto k \cdot \left(\left(-y0\right) \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)}\right) \]

   11. Simplified 48.0%

       \[\leadsto k \cdot \left(\left(-y0\right) \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)}\right) \]

   if 5.7999999999999999e-208 < y4 < 4.1999999999999999e111

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 33.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 32.6%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 4.1999999999999999e111 < y4

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 42.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y around inf 44.6%

      \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(y \cdot \left(a \cdot y5 - c \cdot y4\right)\right)}\right) \]

   5. Taylor expanded in a around 0 44.6%

      \[\leadsto -1 \cdot \left(y3 \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(c \cdot y4\right)\right)}\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto -1 \cdot \left(y3 \cdot \left(y \cdot \color{blue}{\left(-c \cdot y4\right)}\right)\right) \]

      2. distribute-lft-neg-out 44.6%

         \[\leadsto -1 \cdot \left(y3 \cdot \left(y \cdot \color{blue}{\left(\left(-c\right) \cdot y4\right)}\right)\right) \]

      3. *-commutative 44.6%

         \[\leadsto -1 \cdot \left(y3 \cdot \left(y \cdot \color{blue}{\left(y4 \cdot \left(-c\right)\right)}\right)\right) \]

   7. Simplified 44.6%

      \[\leadsto -1 \cdot \left(y3 \cdot \left(y \cdot \color{blue}{\left(y4 \cdot \left(-c\right)\right)}\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.5 \cdot 10^{+264}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -6.6 \cdot 10^{-197}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -4.2 \cdot 10^{-307}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 5.8 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 4.2 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 30.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;j \leq -3.3 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-208}:\\ \;\;\;\;t \cdot \left(c \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= j -3.3e+85)
     (* b (* y4 (- (* t j) (* y k))))
     (if (<= j -5.2e-174)
       t_1
       (if (<= j -1.1e-208)
         (* t (* c (* y2 (- y4))))
         (if (<= j 4.4e-215)
           t_1
           (if (<= j 1.75e+44)
             (* c (* y0 (- (* x y2) (* z y3))))
             (* b (* y0 (- (* z k) (* x j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (j <= -3.3e+85) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (j <= -5.2e-174) {
		tmp = t_1;
	} else if (j <= -1.1e-208) {
		tmp = t * (c * (y2 * -y4));
	} else if (j <= 4.4e-215) {
		tmp = t_1;
	} else if (j <= 1.75e+44) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (j <= (-3.3d+85)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (j <= (-5.2d-174)) then
        tmp = t_1
    else if (j <= (-1.1d-208)) then
        tmp = t * (c * (y2 * -y4))
    else if (j <= 4.4d-215) then
        tmp = t_1
    else if (j <= 1.75d+44) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else
        tmp = b * (y0 * ((z * k) - (x * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (j <= -3.3e+85) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (j <= -5.2e-174) {
		tmp = t_1;
	} else if (j <= -1.1e-208) {
		tmp = t * (c * (y2 * -y4));
	} else if (j <= 4.4e-215) {
		tmp = t_1;
	} else if (j <= 1.75e+44) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if j <= -3.3e+85:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif j <= -5.2e-174:
		tmp = t_1
	elif j <= -1.1e-208:
		tmp = t * (c * (y2 * -y4))
	elif j <= 4.4e-215:
		tmp = t_1
	elif j <= 1.75e+44:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	else:
		tmp = b * (y0 * ((z * k) - (x * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (j <= -3.3e+85)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (j <= -5.2e-174)
		tmp = t_1;
	elseif (j <= -1.1e-208)
		tmp = Float64(t * Float64(c * Float64(y2 * Float64(-y4))));
	elseif (j <= 4.4e-215)
		tmp = t_1;
	elseif (j <= 1.75e+44)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	else
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (j <= -3.3e+85)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (j <= -5.2e-174)
		tmp = t_1;
	elseif (j <= -1.1e-208)
		tmp = t * (c * (y2 * -y4));
	elseif (j <= 4.4e-215)
		tmp = t_1;
	elseif (j <= 1.75e+44)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	else
		tmp = b * (y0 * ((z * k) - (x * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.3e+85], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.2e-174], t$95$1, If[LessEqual[j, -1.1e-208], N[(t * N[(c * N[(y2 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-215], t$95$1, If[LessEqual[j, 1.75e+44], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -3.2999999999999999e85

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 42.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in b around inf 47.8%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -3.2999999999999999e85 < j < -5.2000000000000004e-174 or -1.1e-208 < j < 4.39999999999999993e-215

   1. Initial program 32.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 45.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -5.2000000000000004e-174 < j < -1.1e-208

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 28.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 28.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 28.3%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 28.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 28.3%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 28.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 55.4%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 55.4%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 55.4%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 55.4%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 55.4%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 55.4%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   9. Taylor expanded in i around 0 46.5%

      \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(-1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

       1. neg-mul-1 46.5%

          \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(-y2 \cdot y4\right)}\right) \]

       2. distribute-lft-neg-in 46.5%

          \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(\left(-y2\right) \cdot y4\right)}\right) \]

   11. Simplified 46.5%

       \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(\left(-y2\right) \cdot y4\right)}\right) \]

   if 4.39999999999999993e-215 < j < 1.75e44

   1. Initial program 42.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 54.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 54.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 45.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 1.75e44 < j

   1. Initial program 15.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 42.1%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.3 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-174}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-208}:\\ \;\;\;\;t \cdot \left(c \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 21.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-93}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-288}:\\ \;\;\;\;k \cdot \left(z \cdot \left(i \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-64}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-13}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+20}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -1.4e-93)
   (* y3 (* y (* c y4)))
   (if (<= y -4e-288)
     (* k (* z (* i (- y1))))
     (if (<= y 1.3e-64)
       (* k (* y0 (* y2 (- y5))))
       (if (<= y 6.5e-13)
         (* k (* z (* b y0)))
         (if (<= y 3.5e+20) (* c (* t (* y2 (- y4)))) (* a (* (* x y) b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -1.4e-93) {
		tmp = y3 * (y * (c * y4));
	} else if (y <= -4e-288) {
		tmp = k * (z * (i * -y1));
	} else if (y <= 1.3e-64) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y <= 6.5e-13) {
		tmp = k * (z * (b * y0));
	} else if (y <= 3.5e+20) {
		tmp = c * (t * (y2 * -y4));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-1.4d-93)) then
        tmp = y3 * (y * (c * y4))
    else if (y <= (-4d-288)) then
        tmp = k * (z * (i * -y1))
    else if (y <= 1.3d-64) then
        tmp = k * (y0 * (y2 * -y5))
    else if (y <= 6.5d-13) then
        tmp = k * (z * (b * y0))
    else if (y <= 3.5d+20) then
        tmp = c * (t * (y2 * -y4))
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -1.4e-93) {
		tmp = y3 * (y * (c * y4));
	} else if (y <= -4e-288) {
		tmp = k * (z * (i * -y1));
	} else if (y <= 1.3e-64) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y <= 6.5e-13) {
		tmp = k * (z * (b * y0));
	} else if (y <= 3.5e+20) {
		tmp = c * (t * (y2 * -y4));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -1.4e-93:
		tmp = y3 * (y * (c * y4))
	elif y <= -4e-288:
		tmp = k * (z * (i * -y1))
	elif y <= 1.3e-64:
		tmp = k * (y0 * (y2 * -y5))
	elif y <= 6.5e-13:
		tmp = k * (z * (b * y0))
	elif y <= 3.5e+20:
		tmp = c * (t * (y2 * -y4))
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -1.4e-93)
		tmp = Float64(y3 * Float64(y * Float64(c * y4)));
	elseif (y <= -4e-288)
		tmp = Float64(k * Float64(z * Float64(i * Float64(-y1))));
	elseif (y <= 1.3e-64)
		tmp = Float64(k * Float64(y0 * Float64(y2 * Float64(-y5))));
	elseif (y <= 6.5e-13)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (y <= 3.5e+20)
		tmp = Float64(c * Float64(t * Float64(y2 * Float64(-y4))));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -1.4e-93)
		tmp = y3 * (y * (c * y4));
	elseif (y <= -4e-288)
		tmp = k * (z * (i * -y1));
	elseif (y <= 1.3e-64)
		tmp = k * (y0 * (y2 * -y5));
	elseif (y <= 6.5e-13)
		tmp = k * (z * (b * y0));
	elseif (y <= 3.5e+20)
		tmp = c * (t * (y2 * -y4));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -1.4e-93], N[(y3 * N[(y * N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4e-288], N[(k * N[(z * N[(i * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-64], N[(k * N[(y0 * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-13], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+20], N[(c * N[(t * N[(y2 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.39999999999999999e-93

   1. Initial program 22.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 36.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y around inf 40.2%

      \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(y \cdot \left(a \cdot y5 - c \cdot y4\right)\right)}\right) \]

   5. Taylor expanded in a around 0 41.7%

      \[\leadsto -1 \cdot \left(y3 \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(c \cdot y4\right)\right)}\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 41.7%

         \[\leadsto -1 \cdot \left(y3 \cdot \left(y \cdot \color{blue}{\left(-c \cdot y4\right)}\right)\right) \]

      2. distribute-lft-neg-out 41.7%

         \[\leadsto -1 \cdot \left(y3 \cdot \left(y \cdot \color{blue}{\left(\left(-c\right) \cdot y4\right)}\right)\right) \]

      3. *-commutative 41.7%

         \[\leadsto -1 \cdot \left(y3 \cdot \left(y \cdot \color{blue}{\left(y4 \cdot \left(-c\right)\right)}\right)\right) \]

   7. Simplified 41.7%

      \[\leadsto -1 \cdot \left(y3 \cdot \left(y \cdot \color{blue}{\left(y4 \cdot \left(-c\right)\right)}\right)\right) \]

   if -1.39999999999999999e-93 < y < -4.00000000000000023e-288

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 36.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 36.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 36.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 36.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 36.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 36.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 36.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 36.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 36.7%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   7. Taylor expanded in b around 0 29.7%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y1\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 29.7%

         \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-i \cdot y1\right)}\right) \]

      2. distribute-rgt-neg-in 29.7%

         \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(i \cdot \left(-y1\right)\right)}\right) \]

   9. Simplified 29.7%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(i \cdot \left(-y1\right)\right)}\right) \]

   if -4.00000000000000023e-288 < y < 1.3e-64

   1. Initial program 36.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 34.7%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 34.7%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 34.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 34.7%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 34.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 34.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 34.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 34.7%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y0 around -inf 37.8%

      \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 37.8%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

      2. neg-mul-1 37.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(y2 \cdot y5 - b \cdot z\right)\right) \]

   8. Simplified 37.8%

      \[\leadsto k \cdot \color{blue}{\left(\left(-y0\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around inf 30.7%

      \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 30.7%

          \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(y2 \cdot y5\right)\right)} \]

       2. neg-mul-1 30.7%

          \[\leadsto k \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(y2 \cdot y5\right)\right) \]

   11. Simplified 30.7%

       \[\leadsto k \cdot \color{blue}{\left(\left(-y0\right) \cdot \left(y2 \cdot y5\right)\right)} \]

   if 1.3e-64 < y < 6.49999999999999957e-13

   1. Initial program 8.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 42.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 42.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 42.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 42.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 42.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 42.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 42.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 50.4%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   7. Taylor expanded in b around inf 51.1%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(b \cdot y0\right)}\right) \]

   if 6.49999999999999957e-13 < y < 3.5e20

   1. Initial program 66.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 37.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 37.1%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 37.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 37.1%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 37.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 35.6%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 35.6%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 35.6%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 35.6%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 35.6%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 35.6%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   9. Taylor expanded in i around 0 35.6%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 35.6%

          \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   11. Simplified 35.6%

       \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   if 3.5e20 < y

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 35.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 43.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 38.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-93}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-288}:\\ \;\;\;\;k \cdot \left(z \cdot \left(i \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-64}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-13}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+20}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 26.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ t_2 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-255}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-67}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{+213}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* c (* z i)))) (t_2 (* a (* b (- (* x y) (* z t))))))
   (if (<= i -5.2e+44)
     t_1
     (if (<= i 2.6e-255)
       t_2
       (if (<= i 5e-67)
         (* c (* t (* y2 (- y4))))
         (if (<= i 2.8e+213) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * (z * i));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (i <= -5.2e+44) {
		tmp = t_1;
	} else if (i <= 2.6e-255) {
		tmp = t_2;
	} else if (i <= 5e-67) {
		tmp = c * (t * (y2 * -y4));
	} else if (i <= 2.8e+213) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (c * (z * i))
    t_2 = a * (b * ((x * y) - (z * t)))
    if (i <= (-5.2d+44)) then
        tmp = t_1
    else if (i <= 2.6d-255) then
        tmp = t_2
    else if (i <= 5d-67) then
        tmp = c * (t * (y2 * -y4))
    else if (i <= 2.8d+213) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * (z * i));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (i <= -5.2e+44) {
		tmp = t_1;
	} else if (i <= 2.6e-255) {
		tmp = t_2;
	} else if (i <= 5e-67) {
		tmp = c * (t * (y2 * -y4));
	} else if (i <= 2.8e+213) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (c * (z * i))
	t_2 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if i <= -5.2e+44:
		tmp = t_1
	elif i <= 2.6e-255:
		tmp = t_2
	elif i <= 5e-67:
		tmp = c * (t * (y2 * -y4))
	elif i <= 2.8e+213:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(c * Float64(z * i)))
	t_2 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (i <= -5.2e+44)
		tmp = t_1;
	elseif (i <= 2.6e-255)
		tmp = t_2;
	elseif (i <= 5e-67)
		tmp = Float64(c * Float64(t * Float64(y2 * Float64(-y4))));
	elseif (i <= 2.8e+213)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (c * (z * i));
	t_2 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (i <= -5.2e+44)
		tmp = t_1;
	elseif (i <= 2.6e-255)
		tmp = t_2;
	elseif (i <= 5e-67)
		tmp = c * (t * (y2 * -y4));
	elseif (i <= 2.8e+213)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.2e+44], t$95$1, If[LessEqual[i, 2.6e-255], t$95$2, If[LessEqual[i, 5e-67], N[(c * N[(t * N[(y2 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.8e+213], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -5.1999999999999998e44 or 2.7999999999999999e213 < i

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 48.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 48.9%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 48.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 48.9%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 48.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 50.8%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 50.8%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.8%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.8%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 50.8%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 50.8%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   9. Taylor expanded in i around inf 45.3%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 45.3%

          \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(z \cdot i\right)}\right) \]

   11. Simplified 45.3%

       \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(z \cdot i\right)\right)} \]

   if -5.1999999999999998e44 < i < 2.60000000000000021e-255 or 4.9999999999999999e-67 < i < 2.7999999999999999e213

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 38.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 2.60000000000000021e-255 < i < 4.9999999999999999e-67

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 38.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 38.3%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 38.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 38.3%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 38.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 36.5%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 36.5%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 36.5%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 36.5%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 36.5%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 36.5%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   9. Taylor expanded in i around 0 36.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 36.4%

          \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   11. Simplified 36.4%

       \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-67}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{+213}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 27.1% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y2 \leq -1.05 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -4.4 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{-187}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 4 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= y2 -1.05e+79)
     t_1
     (if (<= y2 -4.4e-200)
       (* b (* y4 (- (* t j) (* y k))))
       (if (<= y2 3.4e-187)
         (* b (* y0 (- (* z k) (* x j))))
         (if (<= y2 4e+99) t_1 (* t (* c (* y2 (- y4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y2 <= -1.05e+79) {
		tmp = t_1;
	} else if (y2 <= -4.4e-200) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 3.4e-187) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= 4e+99) {
		tmp = t_1;
	} else {
		tmp = t * (c * (y2 * -y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (y2 <= (-1.05d+79)) then
        tmp = t_1
    else if (y2 <= (-4.4d-200)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y2 <= 3.4d-187) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y2 <= 4d+99) then
        tmp = t_1
    else
        tmp = t * (c * (y2 * -y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y2 <= -1.05e+79) {
		tmp = t_1;
	} else if (y2 <= -4.4e-200) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 3.4e-187) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= 4e+99) {
		tmp = t_1;
	} else {
		tmp = t * (c * (y2 * -y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y2 <= -1.05e+79:
		tmp = t_1
	elif y2 <= -4.4e-200:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y2 <= 3.4e-187:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y2 <= 4e+99:
		tmp = t_1
	else:
		tmp = t * (c * (y2 * -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(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y2 <= -1.05e+79)
		tmp = t_1;
	elseif (y2 <= -4.4e-200)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y2 <= 3.4e-187)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y2 <= 4e+99)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(c * Float64(y2 * Float64(-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 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y2 <= -1.05e+79)
		tmp = t_1;
	elseif (y2 <= -4.4e-200)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y2 <= 3.4e-187)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y2 <= 4e+99)
		tmp = t_1;
	else
		tmp = t * (c * (y2 * -y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.05e+79], t$95$1, If[LessEqual[y2, -4.4e-200], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.4e-187], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4e+99], t$95$1, N[(t * N[(c * N[(y2 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.05000000000000004e79 or 3.4000000000000001e-187 < y2 < 3.9999999999999999e99

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 39.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.05000000000000004e79 < y2 < -4.40000000000000027e-200

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 41.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in b around inf 38.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -4.40000000000000027e-200 < y2 < 3.4000000000000001e-187

   1. Initial program 36.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 38.1%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 3.9999999999999999e99 < y2

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 48.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 48.1%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 48.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 48.1%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 48.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 63.6%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 63.6%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 63.6%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 63.6%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 63.6%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 63.6%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   9. Taylor expanded in i around 0 55.9%

      \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(-1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

       1. neg-mul-1 55.9%

          \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(-y2 \cdot y4\right)}\right) \]

       2. distribute-lft-neg-in 55.9%

          \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(\left(-y2\right) \cdot y4\right)}\right) \]

   11. Simplified 55.9%

       \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(\left(-y2\right) \cdot y4\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.05 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq -4.4 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{-187}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 4 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 21.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{if}\;i \leq -4000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-307}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-64}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* c (* z i)))))
   (if (<= i -4000000.0)
     t_1
     (if (<= i 1.85e-307)
       (* a (* (* x y) b))
       (if (<= i 2.15e-64)
         (* c (* t (* y2 (- y4))))
         (if (<= i 1.1e+210) (* a (* y (* x b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * (z * i));
	double tmp;
	if (i <= -4000000.0) {
		tmp = t_1;
	} else if (i <= 1.85e-307) {
		tmp = a * ((x * y) * b);
	} else if (i <= 2.15e-64) {
		tmp = c * (t * (y2 * -y4));
	} else if (i <= 1.1e+210) {
		tmp = a * (y * (x * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * (z * i))
    if (i <= (-4000000.0d0)) then
        tmp = t_1
    else if (i <= 1.85d-307) then
        tmp = a * ((x * y) * b)
    else if (i <= 2.15d-64) then
        tmp = c * (t * (y2 * -y4))
    else if (i <= 1.1d+210) then
        tmp = a * (y * (x * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (c * (z * i));
	double tmp;
	if (i <= -4000000.0) {
		tmp = t_1;
	} else if (i <= 1.85e-307) {
		tmp = a * ((x * y) * b);
	} else if (i <= 2.15e-64) {
		tmp = c * (t * (y2 * -y4));
	} else if (i <= 1.1e+210) {
		tmp = a * (y * (x * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (c * (z * i))
	tmp = 0
	if i <= -4000000.0:
		tmp = t_1
	elif i <= 1.85e-307:
		tmp = a * ((x * y) * b)
	elif i <= 2.15e-64:
		tmp = c * (t * (y2 * -y4))
	elif i <= 1.1e+210:
		tmp = a * (y * (x * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(c * Float64(z * i)))
	tmp = 0.0
	if (i <= -4000000.0)
		tmp = t_1;
	elseif (i <= 1.85e-307)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (i <= 2.15e-64)
		tmp = Float64(c * Float64(t * Float64(y2 * Float64(-y4))));
	elseif (i <= 1.1e+210)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (c * (z * i));
	tmp = 0.0;
	if (i <= -4000000.0)
		tmp = t_1;
	elseif (i <= 1.85e-307)
		tmp = a * ((x * y) * b);
	elseif (i <= 2.15e-64)
		tmp = c * (t * (y2 * -y4));
	elseif (i <= 1.1e+210)
		tmp = a * (y * (x * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4000000.0], t$95$1, If[LessEqual[i, 1.85e-307], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.15e-64], N[(c * N[(t * N[(y2 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e+210], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4e6 or 1.09999999999999993e210 < i

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 48.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 48.3%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 48.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 48.3%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 48.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 50.3%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 50.3%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.3%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.3%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 50.3%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 50.3%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   9. Taylor expanded in i around inf 43.7%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 43.7%

          \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(z \cdot i\right)}\right) \]

   11. Simplified 43.7%

       \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(z \cdot i\right)\right)} \]

   if -4e6 < i < 1.85e-307

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 47.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 28.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if 1.85e-307 < i < 2.14999999999999987e-64

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 38.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 38.4%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 38.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 38.4%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 38.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 34.1%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 34.1%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 34.1%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 34.1%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 34.1%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 34.1%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   9. Taylor expanded in i around 0 32.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 32.5%

          \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   11. Simplified 32.5%

       \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   if 2.14999999999999987e-64 < i < 1.09999999999999993e210

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 34.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 25.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 27.0%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

   7. Simplified 27.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot x\right) \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4000000:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-307}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-64}:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 22.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3000000:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;i \leq 6.3 \cdot 10^{-307}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;i \leq 125000000:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(i \cdot \left(-y1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= i -3000000.0)
   (* t (* c (* z i)))
   (if (<= i 6.3e-307)
     (* a (* (* x y) b))
     (if (<= i 125000000.0)
       (* c (* t (* y2 (- y4))))
       (* k (* z (* i (- 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 (i <= -3000000.0) {
		tmp = t * (c * (z * i));
	} else if (i <= 6.3e-307) {
		tmp = a * ((x * y) * b);
	} else if (i <= 125000000.0) {
		tmp = c * (t * (y2 * -y4));
	} else {
		tmp = k * (z * (i * -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 (i <= (-3000000.0d0)) then
        tmp = t * (c * (z * i))
    else if (i <= 6.3d-307) then
        tmp = a * ((x * y) * b)
    else if (i <= 125000000.0d0) then
        tmp = c * (t * (y2 * -y4))
    else
        tmp = k * (z * (i * -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 (i <= -3000000.0) {
		tmp = t * (c * (z * i));
	} else if (i <= 6.3e-307) {
		tmp = a * ((x * y) * b);
	} else if (i <= 125000000.0) {
		tmp = c * (t * (y2 * -y4));
	} else {
		tmp = k * (z * (i * -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 i <= -3000000.0:
		tmp = t * (c * (z * i))
	elif i <= 6.3e-307:
		tmp = a * ((x * y) * b)
	elif i <= 125000000.0:
		tmp = c * (t * (y2 * -y4))
	else:
		tmp = k * (z * (i * -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 (i <= -3000000.0)
		tmp = Float64(t * Float64(c * Float64(z * i)));
	elseif (i <= 6.3e-307)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (i <= 125000000.0)
		tmp = Float64(c * Float64(t * Float64(y2 * Float64(-y4))));
	else
		tmp = Float64(k * Float64(z * Float64(i * 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)
	tmp = 0.0;
	if (i <= -3000000.0)
		tmp = t * (c * (z * i));
	elseif (i <= 6.3e-307)
		tmp = a * ((x * y) * b);
	elseif (i <= 125000000.0)
		tmp = c * (t * (y2 * -y4));
	else
		tmp = k * (z * (i * -y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[i, -3000000.0], N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.3e-307], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 125000000.0], N[(c * N[(t * N[(y2 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(z * N[(i * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3e6

   1. Initial program 22.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 46.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 46.2%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 46.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 46.2%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 46.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 48.3%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 48.3%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 48.3%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 48.3%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 48.3%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   9. Taylor expanded in i around inf 40.3%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 40.3%

          \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(z \cdot i\right)}\right) \]

   11. Simplified 40.3%

       \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(z \cdot i\right)\right)} \]

   if -3e6 < i < 6.3000000000000003e-307

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 47.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 28.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if 6.3000000000000003e-307 < i < 1.25e8

   1. Initial program 34.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 39.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 39.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 39.9%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 39.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 39.9%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 39.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 32.5%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 32.5%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 32.5%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 32.5%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 32.5%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 32.5%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   9. Taylor expanded in i around 0 31.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 31.1%

          \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   11. Simplified 31.1%

       \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

   if 1.25e8 < i

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 44.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 44.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 44.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 44.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 44.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 44.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 44.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 39.5%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   7. Taylor expanded in b around 0 31.8%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y1\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 31.8%

         \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-i \cdot y1\right)}\right) \]

      2. distribute-rgt-neg-in 31.8%

         \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(i \cdot \left(-y1\right)\right)}\right) \]

   9. Simplified 31.8%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(i \cdot \left(-y1\right)\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3000000:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;i \leq 6.3 \cdot 10^{-307}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;i \leq 125000000:\\ \;\;\;\;c \cdot \left(t \cdot \left(y2 \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(i \cdot \left(-y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 22.8% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{if}\;k \leq -2.7 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;k \leq 0.52:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* z (* k y0)))))
   (if (<= k -2.7e+78)
     t_1
     (if (<= k 4.1e-147)
       (* a (* (* x y) b))
       (if (<= k 0.52) (* c (* (* z t) i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (z * (k * y0));
	double tmp;
	if (k <= -2.7e+78) {
		tmp = t_1;
	} else if (k <= 4.1e-147) {
		tmp = a * ((x * y) * b);
	} else if (k <= 0.52) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (z * (k * y0))
    if (k <= (-2.7d+78)) then
        tmp = t_1
    else if (k <= 4.1d-147) then
        tmp = a * ((x * y) * b)
    else if (k <= 0.52d0) then
        tmp = c * ((z * t) * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (z * (k * y0));
	double tmp;
	if (k <= -2.7e+78) {
		tmp = t_1;
	} else if (k <= 4.1e-147) {
		tmp = a * ((x * y) * b);
	} else if (k <= 0.52) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (z * (k * y0))
	tmp = 0
	if k <= -2.7e+78:
		tmp = t_1
	elif k <= 4.1e-147:
		tmp = a * ((x * y) * b)
	elif k <= 0.52:
		tmp = c * ((z * t) * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(z * Float64(k * y0)))
	tmp = 0.0
	if (k <= -2.7e+78)
		tmp = t_1;
	elseif (k <= 4.1e-147)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (k <= 0.52)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (z * (k * y0));
	tmp = 0.0;
	if (k <= -2.7e+78)
		tmp = t_1;
	elseif (k <= 4.1e-147)
		tmp = a * ((x * y) * b);
	elseif (k <= 0.52)
		tmp = c * ((z * t) * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(z * N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.7e+78], t$95$1, If[LessEqual[k, 4.1e-147], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 0.52], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if k < -2.70000000000000004e78 or 0.52000000000000002 < k

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 49.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 49.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 49.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 49.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 49.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 49.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 49.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 39.7%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   7. Taylor expanded in b around inf 35.0%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.5%

         \[\leadsto b \cdot \color{blue}{\left(\left(k \cdot y0\right) \cdot z\right)} \]

   9. Simplified 39.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot y0\right) \cdot z\right)} \]

   if -2.70000000000000004e78 < k < 4.1e-147

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 33.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 23.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if 4.1e-147 < k < 0.52000000000000002

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 45.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 45.1%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 45.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 45.1%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 45.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 43.4%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 43.4%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 43.4%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 43.4%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 43.4%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 43.4%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   9. Taylor expanded in i around inf 27.8%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 27.8%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   11. Simplified 27.8%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.7 \cdot 10^{+78}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;k \leq 0.52:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 22.9% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -2.7 \cdot 10^{+78} \lor \neg \left(k \leq 3350000000\right):\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= k -2.7e+78) (not (<= k 3350000000.0)))
   (* b (* z (* k y0)))
   (* a (* (* x y) b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((k <= -2.7e+78) || !(k <= 3350000000.0)) {
		tmp = b * (z * (k * y0));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((k <= (-2.7d+78)) .or. (.not. (k <= 3350000000.0d0))) then
        tmp = b * (z * (k * y0))
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((k <= -2.7e+78) || !(k <= 3350000000.0)) {
		tmp = b * (z * (k * y0));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (k <= -2.7e+78) or not (k <= 3350000000.0):
		tmp = b * (z * (k * y0))
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((k <= -2.7e+78) || !(k <= 3350000000.0))
		tmp = Float64(b * Float64(z * Float64(k * y0)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((k <= -2.7e+78) || ~((k <= 3350000000.0)))
		tmp = b * (z * (k * y0));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[k, -2.7e+78], N[Not[LessEqual[k, 3350000000.0]], $MachinePrecision]], N[(b * N[(z * N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -2.70000000000000004e78 or 3.35e9 < k

   1. Initial program 24.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 50.9%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 50.9%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 50.9%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 50.9%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 50.9%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 50.9%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 50.9%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 40.8%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   7. Taylor expanded in b around inf 35.9%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 40.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(k \cdot y0\right) \cdot z\right)} \]

   9. Simplified 40.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot y0\right) \cdot z\right)} \]

   if -2.70000000000000004e78 < k < 3.35e9

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 31.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 20.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.7 \cdot 10^{+78} \lor \neg \left(k \leq 3350000000\right):\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 22.3% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-50}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -4.5e-50)
   (* k (* z (* b y0)))
   (if (<= z 1.42e+76) (* a (* (* x y) b)) (* t (* c (* z i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -4.5e-50) {
		tmp = k * (z * (b * y0));
	} else if (z <= 1.42e+76) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = t * (c * (z * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (z <= (-4.5d-50)) then
        tmp = k * (z * (b * y0))
    else if (z <= 1.42d+76) then
        tmp = a * ((x * y) * b)
    else
        tmp = t * (c * (z * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -4.5e-50) {
		tmp = k * (z * (b * y0));
	} else if (z <= 1.42e+76) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = t * (c * (z * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -4.5e-50:
		tmp = k * (z * (b * y0))
	elif z <= 1.42e+76:
		tmp = a * ((x * y) * b)
	else:
		tmp = t * (c * (z * i))
	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 (z <= -4.5e-50)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (z <= 1.42e+76)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = Float64(t * Float64(c * Float64(z * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (z <= -4.5e-50)
		tmp = k * (z * (b * y0));
	elseif (z <= 1.42e+76)
		tmp = a * ((x * y) * b);
	else
		tmp = t * (c * (z * i));
	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[z, -4.5e-50], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e+76], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999962e-50

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 35.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 35.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 35.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 35.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 35.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 35.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 35.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 35.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 37.2%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   7. Taylor expanded in b around inf 28.5%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(b \cdot y0\right)}\right) \]

   if -4.49999999999999962e-50 < z < 1.41999999999999996e76

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 42.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 28.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 27.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if 1.41999999999999996e76 < z

   1. Initial program 18.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 44.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. mul-1-neg 44.4%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. unsub-neg 44.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative 44.4%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   5. Simplified 44.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in c around -inf 46.7%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 46.7%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 46.7%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 46.7%

         \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \]

      4. *-commutative 46.7%

         \[\leadsto t \cdot \left(c \cdot \left(i \cdot z - \color{blue}{y4 \cdot y2}\right)\right) \]

   8. Simplified 46.7%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   9. Taylor expanded in i around inf 37.8%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(i \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 37.8%

          \[\leadsto t \cdot \left(c \cdot \color{blue}{\left(z \cdot i\right)}\right) \]

   11. Simplified 37.8%

       \[\leadsto t \cdot \color{blue}{\left(c \cdot \left(z \cdot i\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-50}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 17.4% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 28.8%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 39.8%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

4. Taylor expanded in a around inf 29.7%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

5. Taylor expanded in x around inf 19.1%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

6. Final simplification 19.1%

   \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
7. Add Preprocessing

Developer target: 27.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t\_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t\_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t\_9\\ t_11 := t\_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t\_4 \cdot t\_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t\_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t\_3 \cdot t\_1 - t\_14\right)\right) + \left(t\_8 - \left(t\_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t\_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t\_13\right)\right) + \left(t\_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t\_10 - \left(y \cdot x - z \cdot t\right) \cdot t\_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t\_8 - \left(t\_11 - t\_6\right)\right) - \left(\frac{t\_3}{\frac{1}{t\_1}} - t\_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t\_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t\_2 - \left(t\_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t\_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t\_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t\_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t\_5\right) - t\_17 \cdot t\_1\right) + t\_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024079 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))