Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.1% → 42.4%

Time: 2.4min

Alternatives: 42

Speedup: 2.1×

• 89.1% 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: 30.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 42.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := j \cdot y3 - k \cdot y2\\ t_3 := t \cdot j - y \cdot k\\ t_4 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot t\_2 - i \cdot t\_3\right)\right)\\ t_5 := y4 \cdot \left(\left(b \cdot t\_3 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_6 := z \cdot t\_1\\ t_7 := y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + t\_6\right)\right)\\ \mathbf{if}\;y5 \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y5 \leq -7.2 \cdot 10^{-78}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y5 \leq -2.35 \cdot 10^{-235}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) - y4 \cdot t\_2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.05 \cdot 10^{-264}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{-176}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{-143}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;y5 \leq 3.5 \cdot 10^{-103}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+54}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t\_1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.65 \cdot 10^{+91}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - t\_6\right)\right)\\ \mathbf{elif}\;y5 \leq 6.5 \cdot 10^{+112}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* j y3) (* k y2)))
        (t_3 (- (* t j) (* y k)))
        (t_4 (* y5 (+ (* a (- (* t y2) (* y y3))) (- (* y0 t_2) (* i t_3)))))
        (t_5
         (*
          y4
          (+
           (+ (* b t_3) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_6 (* z t_1))
        (t_7 (* y3 (- (* c (* y y4)) (+ (* j (* y1 y4)) t_6)))))
   (if (<= y5 -7.2e-13)
     t_4
     (if (<= y5 -7.2e-78)
       t_5
       (if (<= y5 -2.35e-235)
         (*
          y1
          (+
           (* i (- (* x j) (* z k)))
           (- (* a (- (* z y3) (* x y2))) (* y4 t_2))))
         (if (<= y5 2.05e-264)
           t_5
           (if (<= y5 6e-176)
             t_7
             (if (<= y5 1.15e-143)
               (* (* x c) (- (* y0 y2) (* y i)))
               (if (<= y5 3.5e-103)
                 t_7
                 (if (<= y5 2.5e+54)
                   (*
                    y2
                    (+
                     (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_1))
                     (* t (- (* a y5) (* c y4)))))
                   (if (<= y5 1.65e+91)
                     (*
                      y3
                      (+
                       (* y (- (* c y4) (* a y5)))
                       (- (* j (- (* y0 y5) (* y1 y4))) t_6)))
                     (if (<= y5 6.5e+112)
                       (* y1 (* y3 (- (* z a) (* j y4))))
                       t_4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (j * y3) - (k * y2);
	double t_3 = (t * j) - (y * k);
	double t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * t_2) - (i * t_3)));
	double t_5 = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_6 = z * t_1;
	double t_7 = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + t_6));
	double tmp;
	if (y5 <= -7.2e-13) {
		tmp = t_4;
	} else if (y5 <= -7.2e-78) {
		tmp = t_5;
	} else if (y5 <= -2.35e-235) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * t_2)));
	} else if (y5 <= 2.05e-264) {
		tmp = t_5;
	} else if (y5 <= 6e-176) {
		tmp = t_7;
	} else if (y5 <= 1.15e-143) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (y5 <= 3.5e-103) {
		tmp = t_7;
	} else if (y5 <= 2.5e+54) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= 1.65e+91) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - t_6));
	} else if (y5 <= 6.5e+112) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (j * y3) - (k * y2)
    t_3 = (t * j) - (y * k)
    t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * t_2) - (i * t_3)))
    t_5 = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_6 = z * t_1
    t_7 = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + t_6))
    if (y5 <= (-7.2d-13)) then
        tmp = t_4
    else if (y5 <= (-7.2d-78)) then
        tmp = t_5
    else if (y5 <= (-2.35d-235)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * t_2)))
    else if (y5 <= 2.05d-264) then
        tmp = t_5
    else if (y5 <= 6d-176) then
        tmp = t_7
    else if (y5 <= 1.15d-143) then
        tmp = (x * c) * ((y0 * y2) - (y * i))
    else if (y5 <= 3.5d-103) then
        tmp = t_7
    else if (y5 <= 2.5d+54) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
    else if (y5 <= 1.65d+91) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - t_6))
    else if (y5 <= 6.5d+112) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (j * y3) - (k * y2);
	double t_3 = (t * j) - (y * k);
	double t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * t_2) - (i * t_3)));
	double t_5 = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_6 = z * t_1;
	double t_7 = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + t_6));
	double tmp;
	if (y5 <= -7.2e-13) {
		tmp = t_4;
	} else if (y5 <= -7.2e-78) {
		tmp = t_5;
	} else if (y5 <= -2.35e-235) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * t_2)));
	} else if (y5 <= 2.05e-264) {
		tmp = t_5;
	} else if (y5 <= 6e-176) {
		tmp = t_7;
	} else if (y5 <= 1.15e-143) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (y5 <= 3.5e-103) {
		tmp = t_7;
	} else if (y5 <= 2.5e+54) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= 1.65e+91) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - t_6));
	} else if (y5 <= 6.5e+112) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (j * y3) - (k * y2)
	t_3 = (t * j) - (y * k)
	t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * t_2) - (i * t_3)))
	t_5 = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_6 = z * t_1
	t_7 = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + t_6))
	tmp = 0
	if y5 <= -7.2e-13:
		tmp = t_4
	elif y5 <= -7.2e-78:
		tmp = t_5
	elif y5 <= -2.35e-235:
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * t_2)))
	elif y5 <= 2.05e-264:
		tmp = t_5
	elif y5 <= 6e-176:
		tmp = t_7
	elif y5 <= 1.15e-143:
		tmp = (x * c) * ((y0 * y2) - (y * i))
	elif y5 <= 3.5e-103:
		tmp = t_7
	elif y5 <= 2.5e+54:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
	elif y5 <= 1.65e+91:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - t_6))
	elif y5 <= 6.5e+112:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(j * y3) - Float64(k * y2))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	t_4 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(y0 * t_2) - Float64(i * t_3))))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * t_3) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_6 = Float64(z * t_1)
	t_7 = Float64(y3 * Float64(Float64(c * Float64(y * y4)) - Float64(Float64(j * Float64(y1 * y4)) + t_6)))
	tmp = 0.0
	if (y5 <= -7.2e-13)
		tmp = t_4;
	elseif (y5 <= -7.2e-78)
		tmp = t_5;
	elseif (y5 <= -2.35e-235)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(a * Float64(Float64(z * y3) - Float64(x * y2))) - Float64(y4 * t_2))));
	elseif (y5 <= 2.05e-264)
		tmp = t_5;
	elseif (y5 <= 6e-176)
		tmp = t_7;
	elseif (y5 <= 1.15e-143)
		tmp = Float64(Float64(x * c) * Float64(Float64(y0 * y2) - Float64(y * i)));
	elseif (y5 <= 3.5e-103)
		tmp = t_7;
	elseif (y5 <= 2.5e+54)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_1)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y5 <= 1.65e+91)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - t_6)));
	elseif (y5 <= 6.5e+112)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (j * y3) - (k * y2);
	t_3 = (t * j) - (y * k);
	t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * t_2) - (i * t_3)));
	t_5 = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_6 = z * t_1;
	t_7 = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + t_6));
	tmp = 0.0;
	if (y5 <= -7.2e-13)
		tmp = t_4;
	elseif (y5 <= -7.2e-78)
		tmp = t_5;
	elseif (y5 <= -2.35e-235)
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * t_2)));
	elseif (y5 <= 2.05e-264)
		tmp = t_5;
	elseif (y5 <= 6e-176)
		tmp = t_7;
	elseif (y5 <= 1.15e-143)
		tmp = (x * c) * ((y0 * y2) - (y * i));
	elseif (y5 <= 3.5e-103)
		tmp = t_7;
	elseif (y5 <= 2.5e+54)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	elseif (y5 <= 1.65e+91)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - t_6));
	elseif (y5 <= 6.5e+112)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * t$95$2), $MachinePrecision] - N[(i * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * t$95$3), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(z * t$95$1), $MachinePrecision]}, Block[{t$95$7 = N[(y3 * N[(N[(c * N[(y * y4), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -7.2e-13], t$95$4, If[LessEqual[y5, -7.2e-78], t$95$5, If[LessEqual[y5, -2.35e-235], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.05e-264], t$95$5, If[LessEqual[y5, 6e-176], t$95$7, If[LessEqual[y5, 1.15e-143], N[(N[(x * c), $MachinePrecision] * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.5e-103], t$95$7, If[LessEqual[y5, 2.5e+54], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.65e+91], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6.5e+112], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y5 < -7.1999999999999996e-13 or 6.4999999999999998e112 < y5

   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 y5 around -inf 65.0%

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

   if -7.1999999999999996e-13 < y5 < -7.2000000000000005e-78 or -2.35e-235 < y5 < 2.05000000000000011e-264

   1. Initial program 26.2%

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

   3. Taylor expanded in y4 around inf 56.9%

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

   if -7.2000000000000005e-78 < y5 < -2.35e-235

   1. Initial program 37.9%

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

   3. Taylor expanded in y1 around -inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. distribute-rgt-neg-in 53.0%

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

      3. +-commutative 53.0%

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

      4. mul-1-neg 53.0%

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

      5. unsub-neg 53.0%

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

      6. *-commutative 53.0%

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

      7. *-commutative 53.0%

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

      8. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   if 2.05000000000000011e-264 < y5 < 6e-176 or 1.15000000000000006e-143 < y5 < 3.50000000000000016e-103

   1. Initial program 29.6%

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

   3. Taylor expanded in y5 around 0 25.9%

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

   4. Taylor expanded in y3 around -inf 60.0%

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

   if 6e-176 < y5 < 1.15000000000000006e-143

   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 y5 around 0 22.2%

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

   4. Taylor expanded in x around inf 34.1%

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

   5. Taylor expanded in c around inf 45.4%

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

      1. associate-*r* 56.0%

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

      2. +-commutative 56.0%

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

      3. mul-1-neg 56.0%

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

      4. unsub-neg 56.0%

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

      5. *-commutative 56.0%

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

   7. Simplified 56.0%

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

   if 3.50000000000000016e-103 < y5 < 2.50000000000000003e54

   1. Initial program 59.9%

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

   3. Taylor expanded in y2 around inf 68.5%

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

   if 2.50000000000000003e54 < y5 < 1.65000000000000009e91

   1. Initial program 16.4%

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

   3. Taylor expanded in y3 around -inf 83.1%

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

   if 1.65000000000000009e91 < y5 < 6.4999999999999998e112

   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 y1 around -inf 43.5%

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

      1. mul-1-neg 43.5%

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

      2. distribute-rgt-neg-in 43.5%

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

      3. +-commutative 43.5%

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

      4. mul-1-neg 43.5%

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

      5. unsub-neg 43.5%

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

      6. *-commutative 43.5%

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

      7. *-commutative 43.5%

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

      8. *-commutative 43.5%

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

   5. Simplified 43.5%

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

   6. Taylor expanded in y3 around -inf 71.8%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -7.2 \cdot 10^{-78}:\\ \;\;\;\;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}\;y5 \leq -2.35 \cdot 10^{-235}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) - y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.05 \cdot 10^{-264}:\\ \;\;\;\;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}\;y5 \leq 6 \cdot 10^{-176}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{-143}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;y5 \leq 3.5 \cdot 10^{-103}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+54}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.65 \cdot 10^{+91}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 6.5 \cdot 10^{+112}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := a \cdot b - c \cdot i\\ t_4 := \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_5 := b \cdot y4 - i \cdot y5\\ t_6 := t \cdot y2 - y \cdot y3\\ t_7 := t\_6 \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_8 := \sqrt[3]{t\_4}\\ \mathbf{if}\;\left(\left(\left(\left(t\_3 \cdot \left(x \cdot y - z \cdot t\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot t\_2\right) + t\_5 \cdot t\_1\right) + t\_7\right) + t\_4 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t\_8 \cdot t\_8, t\_8, \mathsf{fma}\left(t\_1, t\_5, \mathsf{fma}\left(t\_2, \mathsf{fma}\left(c, y0, a \cdot \left(-y1\right)\right), t\_3 \cdot \mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \mathsf{fma}\left(b, y0, i \cdot \left(-y1\right)\right)\right)\right) + t\_7\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(a \cdot t\_6 + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.5%

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

   4. Applied egg-rr 95.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \cdot \sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}, \sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, \mathsf{fma}\left(c, y0, -a \cdot y1\right), \mathsf{fma}\left(x, y, \left(-z\right) \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, \left(-z\right) \cdot k\right) \cdot \mathsf{fma}\left(b, y0, \left(-y1\right) \cdot i\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y5 around -inf 40.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \cdot \sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}, \sqrt[3]{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, \mathsf{fma}\left(c, y0, a \cdot \left(-y1\right)\right), \left(a \cdot b - c \cdot i\right) \cdot \mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \mathsf{fma}\left(b, y0, i \cdot \left(-y1\right)\right)\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.5% accurate, 0.5× speedup

Math

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

FPCore

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

Java

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.5%

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

   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 y5 around -inf 40.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.3%

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

Alternative 4: 38.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_2 := b \cdot y4 - i \cdot y5\\ t_3 := i \cdot y1 - b \cdot y0\\ t_4 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t\_3\right)\\ \mathbf{if}\;k \leq -6.5 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -1.25 \cdot 10^{-23}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;k \leq -9.2 \cdot 10^{-272}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t\_2 + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t\_3\right)\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{-160}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-97}:\\ \;\;\;\;t\_2 \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{+108}:\\ \;\;\;\;\left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+162}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{+192}:\\ \;\;\;\;i \cdot \left(z \cdot \left(k \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{+233}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+251}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.7 \cdot 10^{+273}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          k
          (+
           (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1))))))
        (t_2 (- (* b y4) (* i y5)))
        (t_3 (- (* i y1) (* b y0)))
        (t_4
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j t_3)))))
   (if (<= k -6.5e+89)
     t_1
     (if (<= k -1.25e-23)
       t_4
       (if (<= k -9.2e-272)
         (* j (+ (+ (* t t_2) (* y3 (- (* y0 y5) (* y1 y4)))) (* x t_3)))
         (if (<= k 1.7e-160)
           t_4
           (if (<= k 2.7e-97)
             (* t_2 (* t j))
             (if (<= k 2.9e+20)
               (* a (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t)))))
               (if (<= k 1.85e+108)
                 (* (- (* c y4) (* a y5)) (* y y3))
                 (if (<= k 1.05e+152)
                   t_1
                   (if (<= k 1.4e+162)
                     (* y0 (+ (* y5 (- (* j y3) (* k y2))) (* c (* x y2))))
                     (if (<= k 4.6e+192)
                       (* i (* z (* k (- y1))))
                       (if (<= k 2.5e+233)
                         (* c (- (* x (* y0 y2)) (* y4 (- (* t y2) (* y y3)))))
                         (if (<= k 4e+251)
                           (* y0 (* k (* y2 (- y5))))
                           (if (<= k 3.7e+273)
                             (* i (* y1 (- (* x j) (* z k))))
                             t_1)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	double tmp;
	if (k <= -6.5e+89) {
		tmp = t_1;
	} else if (k <= -1.25e-23) {
		tmp = t_4;
	} else if (k <= -9.2e-272) {
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	} else if (k <= 1.7e-160) {
		tmp = t_4;
	} else if (k <= 2.7e-97) {
		tmp = t_2 * (t * j);
	} else if (k <= 2.9e+20) {
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	} else if (k <= 1.85e+108) {
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	} else if (k <= 1.05e+152) {
		tmp = t_1;
	} else if (k <= 1.4e+162) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else if (k <= 4.6e+192) {
		tmp = i * (z * (k * -y1));
	} else if (k <= 2.5e+233) {
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	} else if (k <= 4e+251) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (k <= 3.7e+273) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    t_2 = (b * y4) - (i * y5)
    t_3 = (i * y1) - (b * y0)
    t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3))
    if (k <= (-6.5d+89)) then
        tmp = t_1
    else if (k <= (-1.25d-23)) then
        tmp = t_4
    else if (k <= (-9.2d-272)) then
        tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
    else if (k <= 1.7d-160) then
        tmp = t_4
    else if (k <= 2.7d-97) then
        tmp = t_2 * (t * j)
    else if (k <= 2.9d+20) then
        tmp = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))))
    else if (k <= 1.85d+108) then
        tmp = ((c * y4) - (a * y5)) * (y * y3)
    else if (k <= 1.05d+152) then
        tmp = t_1
    else if (k <= 1.4d+162) then
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
    else if (k <= 4.6d+192) then
        tmp = i * (z * (k * -y1))
    else if (k <= 2.5d+233) then
        tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))))
    else if (k <= 4d+251) then
        tmp = y0 * (k * (y2 * -y5))
    else if (k <= 3.7d+273) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	double tmp;
	if (k <= -6.5e+89) {
		tmp = t_1;
	} else if (k <= -1.25e-23) {
		tmp = t_4;
	} else if (k <= -9.2e-272) {
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	} else if (k <= 1.7e-160) {
		tmp = t_4;
	} else if (k <= 2.7e-97) {
		tmp = t_2 * (t * j);
	} else if (k <= 2.9e+20) {
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	} else if (k <= 1.85e+108) {
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	} else if (k <= 1.05e+152) {
		tmp = t_1;
	} else if (k <= 1.4e+162) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else if (k <= 4.6e+192) {
		tmp = i * (z * (k * -y1));
	} else if (k <= 2.5e+233) {
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	} else if (k <= 4e+251) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (k <= 3.7e+273) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	t_2 = (b * y4) - (i * y5)
	t_3 = (i * y1) - (b * y0)
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3))
	tmp = 0
	if k <= -6.5e+89:
		tmp = t_1
	elif k <= -1.25e-23:
		tmp = t_4
	elif k <= -9.2e-272:
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
	elif k <= 1.7e-160:
		tmp = t_4
	elif k <= 2.7e-97:
		tmp = t_2 * (t * j)
	elif k <= 2.9e+20:
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))))
	elif k <= 1.85e+108:
		tmp = ((c * y4) - (a * y5)) * (y * y3)
	elif k <= 1.05e+152:
		tmp = t_1
	elif k <= 1.4e+162:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
	elif k <= 4.6e+192:
		tmp = i * (z * (k * -y1))
	elif k <= 2.5e+233:
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))))
	elif k <= 4e+251:
		tmp = y0 * (k * (y2 * -y5))
	elif k <= 3.7e+273:
		tmp = i * (y1 * ((x * j) - (z * k)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	t_3 = Float64(Float64(i * y1) - Float64(b * y0))
	t_4 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_3)))
	tmp = 0.0
	if (k <= -6.5e+89)
		tmp = t_1;
	elseif (k <= -1.25e-23)
		tmp = t_4;
	elseif (k <= -9.2e-272)
		tmp = Float64(j * Float64(Float64(Float64(t * t_2) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_3)));
	elseif (k <= 1.7e-160)
		tmp = t_4;
	elseif (k <= 2.7e-97)
		tmp = Float64(t_2 * Float64(t * j));
	elseif (k <= 2.9e+20)
		tmp = Float64(a * Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))));
	elseif (k <= 1.85e+108)
		tmp = Float64(Float64(Float64(c * y4) - Float64(a * y5)) * Float64(y * y3));
	elseif (k <= 1.05e+152)
		tmp = t_1;
	elseif (k <= 1.4e+162)
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(x * y2))));
	elseif (k <= 4.6e+192)
		tmp = Float64(i * Float64(z * Float64(k * Float64(-y1))));
	elseif (k <= 2.5e+233)
		tmp = Float64(c * Float64(Float64(x * Float64(y0 * y2)) - Float64(y4 * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (k <= 4e+251)
		tmp = Float64(y0 * Float64(k * Float64(y2 * Float64(-y5))));
	elseif (k <= 3.7e+273)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	t_2 = (b * y4) - (i * y5);
	t_3 = (i * y1) - (b * y0);
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	tmp = 0.0;
	if (k <= -6.5e+89)
		tmp = t_1;
	elseif (k <= -1.25e-23)
		tmp = t_4;
	elseif (k <= -9.2e-272)
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	elseif (k <= 1.7e-160)
		tmp = t_4;
	elseif (k <= 2.7e-97)
		tmp = t_2 * (t * j);
	elseif (k <= 2.9e+20)
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	elseif (k <= 1.85e+108)
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	elseif (k <= 1.05e+152)
		tmp = t_1;
	elseif (k <= 1.4e+162)
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	elseif (k <= 4.6e+192)
		tmp = i * (z * (k * -y1));
	elseif (k <= 2.5e+233)
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	elseif (k <= 4e+251)
		tmp = y0 * (k * (y2 * -y5));
	elseif (k <= 3.7e+273)
		tmp = i * (y1 * ((x * j) - (z * k)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -6.5e+89], t$95$1, If[LessEqual[k, -1.25e-23], t$95$4, If[LessEqual[k, -9.2e-272], N[(j * N[(N[(N[(t * t$95$2), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.7e-160], t$95$4, If[LessEqual[k, 2.7e-97], N[(t$95$2 * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.9e+20], N[(a * N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.85e+108], N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * N[(y * y3), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.05e+152], t$95$1, If[LessEqual[k, 1.4e+162], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.6e+192], N[(i * N[(z * N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.5e+233], N[(c * N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4e+251], N[(y0 * N[(k * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.7e+273], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if k < -6.4999999999999996e89 or 1.8499999999999999e108 < k < 1.0500000000000001e152 or 3.6999999999999999e273 < k

   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 k around inf 64.8%

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

      1. sub-neg 64.8%

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

      2. +-commutative 64.8%

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

      3. mul-1-neg 64.8%

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

      4. unsub-neg 64.8%

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

      5. *-commutative 64.8%

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

      6. mul-1-neg 64.8%

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

      7. remove-double-neg 64.8%

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

   5. Simplified 64.8%

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

   if -6.4999999999999996e89 < k < -1.2500000000000001e-23 or -9.19999999999999955e-272 < k < 1.70000000000000011e-160

   1. Initial program 41.9%

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

   3. Taylor expanded in y5 around 0 42.0%

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

   4. Taylor expanded in x around inf 63.3%

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

   if -1.2500000000000001e-23 < k < -9.19999999999999955e-272

   1. Initial program 37.2%

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

   3. Taylor expanded in j around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

      4. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   if 1.70000000000000011e-160 < k < 2.69999999999999985e-97

   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 j around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in t around inf 50.9%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 50.9%

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

      2. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   if 2.69999999999999985e-97 < k < 2.9e20

   1. Initial program 57.0%

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

   3. Taylor expanded in y5 around 0 47.9%

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

   4. Taylor expanded in a around inf 62.7%

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

   if 2.9e20 < k < 1.8499999999999999e108

   1. Initial program 20.0%

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

   3. Taylor expanded in y2 around inf 50.0%

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

      1. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y around inf 51.4%

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

      1. associate-*r* 51.5%

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

      2. *-commutative 51.5%

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

      3. *-commutative 51.5%

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

      4. *-commutative 51.5%

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

   8. Simplified 51.5%

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

   if 1.0500000000000001e152 < k < 1.39999999999999995e162

   1. Initial program 0.0%

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

   3. Taylor expanded in y2 around inf 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in y0 around inf 100.0%

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

   if 1.39999999999999995e162 < k < 4.5999999999999999e192

   1. Initial program 30.0%

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

   3. Taylor expanded in y1 around -inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. distribute-rgt-neg-in 50.5%

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

      3. +-commutative 50.5%

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

      4. mul-1-neg 50.5%

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

      5. unsub-neg 50.5%

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

      6. *-commutative 50.5%

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

      7. *-commutative 50.5%

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

      8. *-commutative 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in z around -inf 22.3%

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

      1. mul-1-neg 22.3%

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

      2. associate-*r* 22.3%

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

      3. *-commutative 22.3%

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

      4. *-commutative 22.3%

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

   8. Simplified 22.3%

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

   9. Taylor expanded in k around inf 22.1%

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

       1. add0 22.1%

          \[\leadsto -\color{blue}{\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right) + 0\right)} \]

       2. associate-*r* 22.0%

          \[\leadsto -\left(\color{blue}{\left(i \cdot k\right) \cdot \left(y1 \cdot z\right)} + 0\right) \]

   11. Applied egg-rr 22.0%

       \[\leadsto -\color{blue}{\left(\left(i \cdot k\right) \cdot \left(y1 \cdot z\right) + 0\right)} \]
   12. Step-by-step derivation

       1. add0 22.0%

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

       2. associate-*l* 22.1%

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

       3. associate-*r* 50.8%

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

       4. *-commutative 50.8%

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

   13. Simplified 50.8%

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

   if 4.5999999999999999e192 < k < 2.50000000000000004e233

   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 y2 around inf 37.9%

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

      1. *-commutative 37.9%

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

   5. Simplified 37.9%

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

   6. Taylor expanded in c around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. *-commutative 75.4%

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

      3. *-commutative 75.4%

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

      4. *-commutative 75.4%

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

   8. Simplified 75.4%

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

   if 2.50000000000000004e233 < k < 4.0000000000000002e251

   1. Initial program 16.7%

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

   3. Taylor expanded in y2 around inf 50.0%

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

      1. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y0 around inf 83.3%

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

   7. Taylor expanded in k around inf 83.3%

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

      1. mul-1-neg 83.3%

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

   9. Simplified 83.3%

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

   if 4.0000000000000002e251 < k < 3.6999999999999999e273

   1. Initial program 20.0%

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

   3. Taylor expanded in y1 around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. +-commutative 100.0%

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

      4. mul-1-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. *-commutative 100.0%

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

      7. *-commutative 100.0%

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

      8. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in i around inf 80.0%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6.5 \cdot 10^{+89}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -1.25 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq -9.2 \cdot 10^{-272}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-97}:\\ \;\;\;\;\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{+108}:\\ \;\;\;\;\left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+152}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+162}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{+192}:\\ \;\;\;\;i \cdot \left(z \cdot \left(k \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{+233}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+251}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.7 \cdot 10^{+273}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 34.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t\_2\right)\\ t_4 := y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{if}\;y5 \leq -1.6 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t\_1\right) + j \cdot t\_2\right)\\ \mathbf{elif}\;y5 \leq -1.5 \cdot 10^{+179}:\\ \;\;\;\;y5 \cdot \left(k \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -3.3 \cdot 10^{-18}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y5 \leq -4.4 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.9 \cdot 10^{-83}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y5 \leq -8 \cdot 10^{-278}:\\ \;\;\;\;a \cdot t\_4\\ \mathbf{elif}\;y5 \leq 3.9 \cdot 10^{-290}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq 1.25 \cdot 10^{-172}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot t\_1\right)\right)\\ \mathbf{elif}\;y5 \leq 2.2 \cdot 10^{-106}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;y5 \leq 2.3 \cdot 10^{+144}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t\_1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.55 \cdot 10^{+171}:\\ \;\;\;\;\left(y \cdot y5\right) \cdot \left(i \cdot k - a \cdot y3\right)\\ \mathbf{elif}\;y5 \leq 1.2 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(t\_4 + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* i y1) (* b y0)))
        (t_3
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x t_2))))
        (t_4 (* y1 (- (* z y3) (* x y2)))))
   (if (<= y5 -1.6e+245)
     (* x (+ (+ (* y (- (* a b) (* c i))) (* y2 t_1)) (* j t_2)))
     (if (<= y5 -1.5e+179)
       (* y5 (* k (- (* y i) (* y0 y2))))
       (if (<= y5 -3.3e-18)
         t_3
         (if (<= y5 -4.4e-59)
           (* c (- (* x (* y0 y2)) (* y4 (- (* t y2) (* y y3)))))
           (if (<= y5 -1.9e-83)
             t_3
             (if (<= y5 -8e-278)
               (* a t_4)
               (if (<= y5 3.9e-290)
                 (* i (* x (- (* j y1) (* y c))))
                 (if (<= y5 1.25e-172)
                   (* y3 (- (* c (* y y4)) (+ (* j (* y1 y4)) (* z t_1))))
                   (if (<= y5 2.2e-106)
                     (* (* x c) (- (* y0 y2) (* y i)))
                     (if (<= y5 2.3e+144)
                       (*
                        y2
                        (+
                         (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_1))
                         (* t (- (* a y5) (* c y4)))))
                       (if (<= y5 1.55e+171)
                         (* (* y y5) (- (* i k) (* a y3)))
                         (if (<= y5 1.2e+208)
                           (* a (+ t_4 (* b (- (* x y) (* z t)))))
                           (* (* i y5) (- (* y k) (* t j)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	double t_4 = y1 * ((z * y3) - (x * y2));
	double tmp;
	if (y5 <= -1.6e+245) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	} else if (y5 <= -1.5e+179) {
		tmp = y5 * (k * ((y * i) - (y0 * y2)));
	} else if (y5 <= -3.3e-18) {
		tmp = t_3;
	} else if (y5 <= -4.4e-59) {
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	} else if (y5 <= -1.9e-83) {
		tmp = t_3;
	} else if (y5 <= -8e-278) {
		tmp = a * t_4;
	} else if (y5 <= 3.9e-290) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (y5 <= 1.25e-172) {
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_1)));
	} else if (y5 <= 2.2e-106) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (y5 <= 2.3e+144) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= 1.55e+171) {
		tmp = (y * y5) * ((i * k) - (a * y3));
	} else if (y5 <= 1.2e+208) {
		tmp = a * (t_4 + (b * ((x * y) - (z * t))));
	} else {
		tmp = (i * y5) * ((y * k) - (t * 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) :: t_4
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (i * y1) - (b * y0)
    t_3 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2))
    t_4 = y1 * ((z * y3) - (x * y2))
    if (y5 <= (-1.6d+245)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2))
    else if (y5 <= (-1.5d+179)) then
        tmp = y5 * (k * ((y * i) - (y0 * y2)))
    else if (y5 <= (-3.3d-18)) then
        tmp = t_3
    else if (y5 <= (-4.4d-59)) then
        tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))))
    else if (y5 <= (-1.9d-83)) then
        tmp = t_3
    else if (y5 <= (-8d-278)) then
        tmp = a * t_4
    else if (y5 <= 3.9d-290) then
        tmp = i * (x * ((j * y1) - (y * c)))
    else if (y5 <= 1.25d-172) then
        tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_1)))
    else if (y5 <= 2.2d-106) then
        tmp = (x * c) * ((y0 * y2) - (y * i))
    else if (y5 <= 2.3d+144) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
    else if (y5 <= 1.55d+171) then
        tmp = (y * y5) * ((i * k) - (a * y3))
    else if (y5 <= 1.2d+208) then
        tmp = a * (t_4 + (b * ((x * y) - (z * t))))
    else
        tmp = (i * y5) * ((y * k) - (t * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	double t_4 = y1 * ((z * y3) - (x * y2));
	double tmp;
	if (y5 <= -1.6e+245) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	} else if (y5 <= -1.5e+179) {
		tmp = y5 * (k * ((y * i) - (y0 * y2)));
	} else if (y5 <= -3.3e-18) {
		tmp = t_3;
	} else if (y5 <= -4.4e-59) {
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	} else if (y5 <= -1.9e-83) {
		tmp = t_3;
	} else if (y5 <= -8e-278) {
		tmp = a * t_4;
	} else if (y5 <= 3.9e-290) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (y5 <= 1.25e-172) {
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_1)));
	} else if (y5 <= 2.2e-106) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (y5 <= 2.3e+144) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= 1.55e+171) {
		tmp = (y * y5) * ((i * k) - (a * y3));
	} else if (y5 <= 1.2e+208) {
		tmp = a * (t_4 + (b * ((x * y) - (z * t))));
	} else {
		tmp = (i * y5) * ((y * k) - (t * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (i * y1) - (b * y0)
	t_3 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2))
	t_4 = y1 * ((z * y3) - (x * y2))
	tmp = 0
	if y5 <= -1.6e+245:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2))
	elif y5 <= -1.5e+179:
		tmp = y5 * (k * ((y * i) - (y0 * y2)))
	elif y5 <= -3.3e-18:
		tmp = t_3
	elif y5 <= -4.4e-59:
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))))
	elif y5 <= -1.9e-83:
		tmp = t_3
	elif y5 <= -8e-278:
		tmp = a * t_4
	elif y5 <= 3.9e-290:
		tmp = i * (x * ((j * y1) - (y * c)))
	elif y5 <= 1.25e-172:
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_1)))
	elif y5 <= 2.2e-106:
		tmp = (x * c) * ((y0 * y2) - (y * i))
	elif y5 <= 2.3e+144:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
	elif y5 <= 1.55e+171:
		tmp = (y * y5) * ((i * k) - (a * y3))
	elif y5 <= 1.2e+208:
		tmp = a * (t_4 + (b * ((x * y) - (z * t))))
	else:
		tmp = (i * y5) * ((y * k) - (t * 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(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	t_3 = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_2)))
	t_4 = Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))
	tmp = 0.0
	if (y5 <= -1.6e+245)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)) + Float64(j * t_2)));
	elseif (y5 <= -1.5e+179)
		tmp = Float64(y5 * Float64(k * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (y5 <= -3.3e-18)
		tmp = t_3;
	elseif (y5 <= -4.4e-59)
		tmp = Float64(c * Float64(Float64(x * Float64(y0 * y2)) - Float64(y4 * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y5 <= -1.9e-83)
		tmp = t_3;
	elseif (y5 <= -8e-278)
		tmp = Float64(a * t_4);
	elseif (y5 <= 3.9e-290)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (y5 <= 1.25e-172)
		tmp = Float64(y3 * Float64(Float64(c * Float64(y * y4)) - Float64(Float64(j * Float64(y1 * y4)) + Float64(z * t_1))));
	elseif (y5 <= 2.2e-106)
		tmp = Float64(Float64(x * c) * Float64(Float64(y0 * y2) - Float64(y * i)));
	elseif (y5 <= 2.3e+144)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_1)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y5 <= 1.55e+171)
		tmp = Float64(Float64(y * y5) * Float64(Float64(i * k) - Float64(a * y3)));
	elseif (y5 <= 1.2e+208)
		tmp = Float64(a * Float64(t_4 + Float64(b * Float64(Float64(x * y) - Float64(z * t)))));
	else
		tmp = Float64(Float64(i * y5) * Float64(Float64(y * k) - Float64(t * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (i * y1) - (b * y0);
	t_3 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	t_4 = y1 * ((z * y3) - (x * y2));
	tmp = 0.0;
	if (y5 <= -1.6e+245)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	elseif (y5 <= -1.5e+179)
		tmp = y5 * (k * ((y * i) - (y0 * y2)));
	elseif (y5 <= -3.3e-18)
		tmp = t_3;
	elseif (y5 <= -4.4e-59)
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	elseif (y5 <= -1.9e-83)
		tmp = t_3;
	elseif (y5 <= -8e-278)
		tmp = a * t_4;
	elseif (y5 <= 3.9e-290)
		tmp = i * (x * ((j * y1) - (y * c)));
	elseif (y5 <= 1.25e-172)
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_1)));
	elseif (y5 <= 2.2e-106)
		tmp = (x * c) * ((y0 * y2) - (y * i));
	elseif (y5 <= 2.3e+144)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	elseif (y5 <= 1.55e+171)
		tmp = (y * y5) * ((i * k) - (a * y3));
	elseif (y5 <= 1.2e+208)
		tmp = a * (t_4 + (b * ((x * y) - (z * t))));
	else
		tmp = (i * y5) * ((y * k) - (t * 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[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.6e+245], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.5e+179], N[(y5 * N[(k * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3.3e-18], t$95$3, If[LessEqual[y5, -4.4e-59], N[(c * N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.9e-83], t$95$3, If[LessEqual[y5, -8e-278], N[(a * t$95$4), $MachinePrecision], If[LessEqual[y5, 3.9e-290], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.25e-172], N[(y3 * N[(N[(c * N[(y * y4), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.2e-106], N[(N[(x * c), $MachinePrecision] * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.3e+144], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.55e+171], N[(N[(y * y5), $MachinePrecision] * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.2e+208], N[(a * N[(t$95$4 + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * y5), $MachinePrecision] * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if y5 < -1.60000000000000012e245

   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 y5 around 0 42.9%

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

   4. Taylor expanded in x around inf 64.5%

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

   if -1.60000000000000012e245 < y5 < -1.4999999999999999e179

   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 y5 around -inf 70.0%

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

   4. Taylor expanded in k around inf 80.0%

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

   if -1.4999999999999999e179 < y5 < -3.3000000000000002e-18 or -4.3999999999999998e-59 < y5 < -1.89999999999999988e-83

   1. Initial program 34.1%

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

   3. Taylor expanded in j around inf 60.1%

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

      1. +-commutative 60.1%

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

      2. mul-1-neg 60.1%

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

      3. unsub-neg 60.1%

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

      4. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   if -3.3000000000000002e-18 < y5 < -4.3999999999999998e-59

   1. Initial program 33.2%

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

   3. Taylor expanded in y2 around inf 39.9%

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

      1. *-commutative 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in c around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. *-commutative 54.0%

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

      3. *-commutative 54.0%

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

      4. *-commutative 54.0%

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

   8. Simplified 54.0%

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

   if -1.89999999999999988e-83 < y5 < -7.9999999999999995e-278

   1. Initial program 32.0%

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

   3. Taylor expanded in y1 around -inf 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-rgt-neg-in 48.2%

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

      3. +-commutative 48.2%

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

      4. mul-1-neg 48.2%

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

      5. unsub-neg 48.2%

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

      6. *-commutative 48.2%

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

      7. *-commutative 48.2%

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

      8. *-commutative 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in a around inf 47.8%

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

   if -7.9999999999999995e-278 < y5 < 3.89999999999999973e-290

   1. Initial program 29.4%

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

   3. Taylor expanded in y5 around 0 29.4%

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

   4. Taylor expanded in x around inf 57.9%

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

   5. Taylor expanded in i around inf 86.9%

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

      1. distribute-lft-out-- 86.9%

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

      2. *-commutative 86.9%

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

   7. Simplified 86.9%

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

   if 3.89999999999999973e-290 < y5 < 1.25e-172

   1. Initial program 25.0%

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

   3. Taylor expanded in y5 around 0 29.2%

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

   4. Taylor expanded in y3 around -inf 54.7%

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

   if 1.25e-172 < y5 < 2.19999999999999994e-106

   1. Initial program 38.5%

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

   3. Taylor expanded in y5 around 0 23.1%

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

   4. Taylor expanded in x around inf 39.2%

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

   5. Taylor expanded in c around inf 47.0%

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

      1. associate-*r* 54.4%

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

      2. +-commutative 54.4%

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

      3. mul-1-neg 54.4%

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

      4. unsub-neg 54.4%

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

      5. *-commutative 54.4%

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

   7. Simplified 54.4%

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

   if 2.19999999999999994e-106 < y5 < 2.3000000000000001e144

   1. Initial program 46.7%

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

   3. Taylor expanded in y2 around inf 59.9%

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

   if 2.3000000000000001e144 < y5 < 1.5499999999999999e171

   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 y5 around -inf 57.1%

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

   4. Taylor expanded in y around -inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. associate-*r* 85.7%

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

      3. *-commutative 85.7%

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

      4. *-commutative 85.7%

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

   6. Simplified 85.7%

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

   if 1.5499999999999999e171 < y5 < 1.19999999999999993e208

   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 y5 around 0 16.7%

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

   4. Taylor expanded in a around inf 83.8%

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

   if 1.19999999999999993e208 < y5

   1. Initial program 26.3%

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

   3. Taylor expanded in y5 around -inf 78.9%

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

   4. Taylor expanded in i around inf 79.2%

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

      1. associate-*r* 74.1%

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

      2. *-commutative 74.1%

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

   6. Simplified 74.1%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 12 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.6 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -1.5 \cdot 10^{+179}:\\ \;\;\;\;y5 \cdot \left(k \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -3.3 \cdot 10^{-18}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -4.4 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.9 \cdot 10^{-83}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -8 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 3.9 \cdot 10^{-290}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq 1.25 \cdot 10^{-172}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.2 \cdot 10^{-106}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;y5 \leq 2.3 \cdot 10^{+144}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.55 \cdot 10^{+171}:\\ \;\;\;\;\left(y \cdot y5\right) \cdot \left(i \cdot k - a \cdot y3\right)\\ \mathbf{elif}\;y5 \leq 1.2 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) - y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ t_4 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot t\_2\right)\right)\\ t_5 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;t \leq -7.7 \cdot 10^{+217}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1 - t \cdot y5\right)\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(y2 \cdot t\_2\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+63}:\\ \;\;\;\;t\_5 \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-185}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-201}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t\_1 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-162}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 2.06 \cdot 10^{-54}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_1 + x \cdot t\_2\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-7}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+115}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+183}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot t\_5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3
         (*
          y1
          (+
           (* i (- (* x j) (* z k)))
           (- (* a (- (* z y3) (* x y2))) (* y4 (- (* j y3) (* k y2)))))))
        (t_4
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (- (* j (- (* y0 y5) (* y1 y4))) (* z t_2)))))
        (t_5 (- (* b y4) (* i y5))))
   (if (<= t -7.7e+217)
     (* (* i j) (- (* x y1) (* t y5)))
     (if (<= t -1.95e+164)
       (* x (* y2 t_2))
       (if (<= t -7.5e+63)
         (* t_5 (* t j))
         (if (<= t -1.45e-185)
           t_3
           (if (<= t 6.5e-201)
             (*
              k
              (+
               (+ (* y2 t_1) (* y (- (* i y5) (* b y4))))
               (* z (- (* b y0) (* i y1)))))
             (if (<= t 1.85e-162)
               t_3
               (if (<= t 2.06e-54)
                 (* y2 (+ (+ (* k t_1) (* x t_2)) (* t (- (* a y5) (* c y4)))))
                 (if (<= t 3.7e-7)
                   t_4
                   (if (<= t 7.6e+115)
                     (* i (* x (- (* j y1) (* y c))))
                     (if (<= t 8.5e+183) t_4 (* j (* t t_5))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * ((j * y3) - (k * y2)))));
	double t_4 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)));
	double t_5 = (b * y4) - (i * y5);
	double tmp;
	if (t <= -7.7e+217) {
		tmp = (i * j) * ((x * y1) - (t * y5));
	} else if (t <= -1.95e+164) {
		tmp = x * (y2 * t_2);
	} else if (t <= -7.5e+63) {
		tmp = t_5 * (t * j);
	} else if (t <= -1.45e-185) {
		tmp = t_3;
	} else if (t <= 6.5e-201) {
		tmp = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (t <= 1.85e-162) {
		tmp = t_3;
	} else if (t <= 2.06e-54) {
		tmp = y2 * (((k * t_1) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	} else if (t <= 3.7e-7) {
		tmp = t_4;
	} else if (t <= 7.6e+115) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (t <= 8.5e+183) {
		tmp = t_4;
	} else {
		tmp = j * (t * t_5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = (c * y0) - (a * y1)
    t_3 = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * ((j * y3) - (k * y2)))))
    t_4 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)))
    t_5 = (b * y4) - (i * y5)
    if (t <= (-7.7d+217)) then
        tmp = (i * j) * ((x * y1) - (t * y5))
    else if (t <= (-1.95d+164)) then
        tmp = x * (y2 * t_2)
    else if (t <= (-7.5d+63)) then
        tmp = t_5 * (t * j)
    else if (t <= (-1.45d-185)) then
        tmp = t_3
    else if (t <= 6.5d-201) then
        tmp = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    else if (t <= 1.85d-162) then
        tmp = t_3
    else if (t <= 2.06d-54) then
        tmp = y2 * (((k * t_1) + (x * t_2)) + (t * ((a * y5) - (c * y4))))
    else if (t <= 3.7d-7) then
        tmp = t_4
    else if (t <= 7.6d+115) then
        tmp = i * (x * ((j * y1) - (y * c)))
    else if (t <= 8.5d+183) then
        tmp = t_4
    else
        tmp = j * (t * t_5)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * ((j * y3) - (k * y2)))));
	double t_4 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)));
	double t_5 = (b * y4) - (i * y5);
	double tmp;
	if (t <= -7.7e+217) {
		tmp = (i * j) * ((x * y1) - (t * y5));
	} else if (t <= -1.95e+164) {
		tmp = x * (y2 * t_2);
	} else if (t <= -7.5e+63) {
		tmp = t_5 * (t * j);
	} else if (t <= -1.45e-185) {
		tmp = t_3;
	} else if (t <= 6.5e-201) {
		tmp = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (t <= 1.85e-162) {
		tmp = t_3;
	} else if (t <= 2.06e-54) {
		tmp = y2 * (((k * t_1) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	} else if (t <= 3.7e-7) {
		tmp = t_4;
	} else if (t <= 7.6e+115) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (t <= 8.5e+183) {
		tmp = t_4;
	} else {
		tmp = j * (t * t_5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = (c * y0) - (a * y1)
	t_3 = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * ((j * y3) - (k * y2)))))
	t_4 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)))
	t_5 = (b * y4) - (i * y5)
	tmp = 0
	if t <= -7.7e+217:
		tmp = (i * j) * ((x * y1) - (t * y5))
	elif t <= -1.95e+164:
		tmp = x * (y2 * t_2)
	elif t <= -7.5e+63:
		tmp = t_5 * (t * j)
	elif t <= -1.45e-185:
		tmp = t_3
	elif t <= 6.5e-201:
		tmp = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	elif t <= 1.85e-162:
		tmp = t_3
	elif t <= 2.06e-54:
		tmp = y2 * (((k * t_1) + (x * t_2)) + (t * ((a * y5) - (c * y4))))
	elif t <= 3.7e-7:
		tmp = t_4
	elif t <= 7.6e+115:
		tmp = i * (x * ((j * y1) - (y * c)))
	elif t <= 8.5e+183:
		tmp = t_4
	else:
		tmp = j * (t * t_5)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(a * Float64(Float64(z * y3) - Float64(x * y2))) - Float64(y4 * Float64(Float64(j * y3) - Float64(k * y2))))))
	t_4 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(z * t_2))))
	t_5 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (t <= -7.7e+217)
		tmp = Float64(Float64(i * j) * Float64(Float64(x * y1) - Float64(t * y5)));
	elseif (t <= -1.95e+164)
		tmp = Float64(x * Float64(y2 * t_2));
	elseif (t <= -7.5e+63)
		tmp = Float64(t_5 * Float64(t * j));
	elseif (t <= -1.45e-185)
		tmp = t_3;
	elseif (t <= 6.5e-201)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_1) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (t <= 1.85e-162)
		tmp = t_3;
	elseif (t <= 2.06e-54)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * t_2)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (t <= 3.7e-7)
		tmp = t_4;
	elseif (t <= 7.6e+115)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (t <= 8.5e+183)
		tmp = t_4;
	else
		tmp = Float64(j * Float64(t * t_5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = (c * y0) - (a * y1);
	t_3 = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * ((j * y3) - (k * y2)))));
	t_4 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)));
	t_5 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (t <= -7.7e+217)
		tmp = (i * j) * ((x * y1) - (t * y5));
	elseif (t <= -1.95e+164)
		tmp = x * (y2 * t_2);
	elseif (t <= -7.5e+63)
		tmp = t_5 * (t * j);
	elseif (t <= -1.45e-185)
		tmp = t_3;
	elseif (t <= 6.5e-201)
		tmp = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	elseif (t <= 1.85e-162)
		tmp = t_3;
	elseif (t <= 2.06e-54)
		tmp = y2 * (((k * t_1) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	elseif (t <= 3.7e-7)
		tmp = t_4;
	elseif (t <= 7.6e+115)
		tmp = i * (x * ((j * y1) - (y * c)));
	elseif (t <= 8.5e+183)
		tmp = t_4;
	else
		tmp = j * (t * t_5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.7e+217], N[(N[(i * j), $MachinePrecision] * N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.95e+164], N[(x * N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.5e+63], N[(t$95$5 * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.45e-185], t$95$3, If[LessEqual[t, 6.5e-201], N[(k * N[(N[(N[(y2 * t$95$1), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-162], t$95$3, If[LessEqual[t, 2.06e-54], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-7], t$95$4, If[LessEqual[t, 7.6e+115], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+183], t$95$4, N[(j * N[(t * t$95$5), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if t < -7.7e217

   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 j around inf 38.6%

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

      1. +-commutative 38.6%

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

      2. mul-1-neg 38.6%

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

      3. unsub-neg 38.6%

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

      4. *-commutative 38.6%

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

   5. Simplified 38.6%

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

   6. Taylor expanded in i around -inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. associate-*r* 69.8%

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

      3. *-commutative 69.8%

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

      4. *-commutative 69.8%

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

   8. Simplified 69.8%

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

   if -7.7e217 < t < -1.94999999999999993e164

   1. Initial program 12.4%

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

   3. Taylor expanded in y2 around inf 31.2%

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

      1. *-commutative 31.2%

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

   5. Simplified 31.2%

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

   6. Taylor expanded in x around inf 57.4%

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

      1. *-commutative 57.4%

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

   8. Simplified 57.4%

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

   if -1.94999999999999993e164 < t < -7.5000000000000005e63

   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 j around inf 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

      4. *-commutative 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in t around inf 51.6%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 56.1%

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

      2. *-commutative 56.1%

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

   8. Simplified 56.1%

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

   if -7.5000000000000005e63 < t < -1.44999999999999997e-185 or 6.49999999999999974e-201 < t < 1.8500000000000001e-162

   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 y1 around -inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. distribute-rgt-neg-in 63.8%

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

      3. +-commutative 63.8%

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

      4. mul-1-neg 63.8%

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

      5. unsub-neg 63.8%

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

      6. *-commutative 63.8%

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

      7. *-commutative 63.8%

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

      8. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   if -1.44999999999999997e-185 < t < 6.49999999999999974e-201

   1. Initial program 34.2%

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

   3. Taylor expanded in k around inf 50.6%

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

      1. sub-neg 50.6%

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

      2. +-commutative 50.6%

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

      3. mul-1-neg 50.6%

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

      4. unsub-neg 50.6%

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

      5. *-commutative 50.6%

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

      6. mul-1-neg 50.6%

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

      7. remove-double-neg 50.6%

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

   5. Simplified 50.6%

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

   if 1.8500000000000001e-162 < t < 2.06000000000000009e-54

   1. Initial program 55.8%

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

   3. Taylor expanded in y2 around inf 67.0%

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

   if 2.06000000000000009e-54 < t < 3.70000000000000004e-7 or 7.6000000000000001e115 < t < 8.5000000000000004e183

   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 y3 around -inf 71.5%

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

   if 3.70000000000000004e-7 < t < 7.6000000000000001e115

   1. Initial program 16.7%

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

   3. Taylor expanded in y5 around 0 17.0%

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

   4. Taylor expanded in x around inf 27.9%

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

   5. Taylor expanded in i around inf 56.1%

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

      1. distribute-lft-out-- 56.1%

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

      2. *-commutative 56.1%

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

   7. Simplified 56.1%

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

   if 8.5000000000000004e183 < t

   1. Initial program 24.2%

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

   3. Taylor expanded in j around inf 44.8%

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

      1. +-commutative 44.8%

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

      2. mul-1-neg 44.8%

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

      3. unsub-neg 44.8%

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

      4. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in t around inf 66.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 66.0%

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

   8. Simplified 66.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - y5 \cdot i\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.7 \cdot 10^{+217}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1 - t \cdot y5\right)\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+63}:\\ \;\;\;\;\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-185}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) - y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-201}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-162}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) - y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.06 \cdot 10^{-54}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-7}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+115}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+183}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) - y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ t_4 := k \cdot \left(\left(y2 \cdot t\_1 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_5 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;t \leq -1.72 \cdot 10^{+218}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1 - t \cdot y5\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(y2 \cdot t\_2\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+63}:\\ \;\;\;\;t\_5 \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-183}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-201}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-162}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-62}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_1 + x \cdot t\_2\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+17}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+185}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot t\_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot t\_5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3
         (*
          y1
          (+
           (* i (- (* x j) (* z k)))
           (- (* a (- (* z y3) (* x y2))) (* y4 (- (* j y3) (* k y2)))))))
        (t_4
         (*
          k
          (+
           (+ (* y2 t_1) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1))))))
        (t_5 (- (* b y4) (* i y5))))
   (if (<= t -1.72e+218)
     (* (* i j) (- (* x y1) (* t y5)))
     (if (<= t -8e+160)
       (* x (* y2 t_2))
       (if (<= t -1.55e+63)
         (* t_5 (* t j))
         (if (<= t -2.75e-183)
           t_3
           (if (<= t 6.3e-201)
             t_4
             (if (<= t 4.9e-162)
               t_3
               (if (<= t 5.5e-62)
                 (* y2 (+ (+ (* k t_1) (* x t_2)) (* t (- (* a y5) (* c y4)))))
                 (if (<= t 8.6e+17)
                   t_4
                   (if (<= t 5.2e+185)
                     (* y3 (- (* c (* y y4)) (+ (* j (* y1 y4)) (* z t_2))))
                     (* j (* t t_5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * ((j * y3) - (k * y2)))));
	double t_4 = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_5 = (b * y4) - (i * y5);
	double tmp;
	if (t <= -1.72e+218) {
		tmp = (i * j) * ((x * y1) - (t * y5));
	} else if (t <= -8e+160) {
		tmp = x * (y2 * t_2);
	} else if (t <= -1.55e+63) {
		tmp = t_5 * (t * j);
	} else if (t <= -2.75e-183) {
		tmp = t_3;
	} else if (t <= 6.3e-201) {
		tmp = t_4;
	} else if (t <= 4.9e-162) {
		tmp = t_3;
	} else if (t <= 5.5e-62) {
		tmp = y2 * (((k * t_1) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	} else if (t <= 8.6e+17) {
		tmp = t_4;
	} else if (t <= 5.2e+185) {
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_2)));
	} else {
		tmp = j * (t * t_5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = (c * y0) - (a * y1)
    t_3 = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * ((j * y3) - (k * y2)))))
    t_4 = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    t_5 = (b * y4) - (i * y5)
    if (t <= (-1.72d+218)) then
        tmp = (i * j) * ((x * y1) - (t * y5))
    else if (t <= (-8d+160)) then
        tmp = x * (y2 * t_2)
    else if (t <= (-1.55d+63)) then
        tmp = t_5 * (t * j)
    else if (t <= (-2.75d-183)) then
        tmp = t_3
    else if (t <= 6.3d-201) then
        tmp = t_4
    else if (t <= 4.9d-162) then
        tmp = t_3
    else if (t <= 5.5d-62) then
        tmp = y2 * (((k * t_1) + (x * t_2)) + (t * ((a * y5) - (c * y4))))
    else if (t <= 8.6d+17) then
        tmp = t_4
    else if (t <= 5.2d+185) then
        tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_2)))
    else
        tmp = j * (t * t_5)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * ((j * y3) - (k * y2)))));
	double t_4 = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_5 = (b * y4) - (i * y5);
	double tmp;
	if (t <= -1.72e+218) {
		tmp = (i * j) * ((x * y1) - (t * y5));
	} else if (t <= -8e+160) {
		tmp = x * (y2 * t_2);
	} else if (t <= -1.55e+63) {
		tmp = t_5 * (t * j);
	} else if (t <= -2.75e-183) {
		tmp = t_3;
	} else if (t <= 6.3e-201) {
		tmp = t_4;
	} else if (t <= 4.9e-162) {
		tmp = t_3;
	} else if (t <= 5.5e-62) {
		tmp = y2 * (((k * t_1) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	} else if (t <= 8.6e+17) {
		tmp = t_4;
	} else if (t <= 5.2e+185) {
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_2)));
	} else {
		tmp = j * (t * t_5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = (c * y0) - (a * y1)
	t_3 = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * ((j * y3) - (k * y2)))))
	t_4 = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	t_5 = (b * y4) - (i * y5)
	tmp = 0
	if t <= -1.72e+218:
		tmp = (i * j) * ((x * y1) - (t * y5))
	elif t <= -8e+160:
		tmp = x * (y2 * t_2)
	elif t <= -1.55e+63:
		tmp = t_5 * (t * j)
	elif t <= -2.75e-183:
		tmp = t_3
	elif t <= 6.3e-201:
		tmp = t_4
	elif t <= 4.9e-162:
		tmp = t_3
	elif t <= 5.5e-62:
		tmp = y2 * (((k * t_1) + (x * t_2)) + (t * ((a * y5) - (c * y4))))
	elif t <= 8.6e+17:
		tmp = t_4
	elif t <= 5.2e+185:
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_2)))
	else:
		tmp = j * (t * t_5)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(a * Float64(Float64(z * y3) - Float64(x * y2))) - Float64(y4 * Float64(Float64(j * y3) - Float64(k * y2))))))
	t_4 = Float64(k * Float64(Float64(Float64(y2 * t_1) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_5 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (t <= -1.72e+218)
		tmp = Float64(Float64(i * j) * Float64(Float64(x * y1) - Float64(t * y5)));
	elseif (t <= -8e+160)
		tmp = Float64(x * Float64(y2 * t_2));
	elseif (t <= -1.55e+63)
		tmp = Float64(t_5 * Float64(t * j));
	elseif (t <= -2.75e-183)
		tmp = t_3;
	elseif (t <= 6.3e-201)
		tmp = t_4;
	elseif (t <= 4.9e-162)
		tmp = t_3;
	elseif (t <= 5.5e-62)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * t_2)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (t <= 8.6e+17)
		tmp = t_4;
	elseif (t <= 5.2e+185)
		tmp = Float64(y3 * Float64(Float64(c * Float64(y * y4)) - Float64(Float64(j * Float64(y1 * y4)) + Float64(z * t_2))));
	else
		tmp = Float64(j * Float64(t * t_5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = (c * y0) - (a * y1);
	t_3 = y1 * ((i * ((x * j) - (z * k))) + ((a * ((z * y3) - (x * y2))) - (y4 * ((j * y3) - (k * y2)))));
	t_4 = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	t_5 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (t <= -1.72e+218)
		tmp = (i * j) * ((x * y1) - (t * y5));
	elseif (t <= -8e+160)
		tmp = x * (y2 * t_2);
	elseif (t <= -1.55e+63)
		tmp = t_5 * (t * j);
	elseif (t <= -2.75e-183)
		tmp = t_3;
	elseif (t <= 6.3e-201)
		tmp = t_4;
	elseif (t <= 4.9e-162)
		tmp = t_3;
	elseif (t <= 5.5e-62)
		tmp = y2 * (((k * t_1) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	elseif (t <= 8.6e+17)
		tmp = t_4;
	elseif (t <= 5.2e+185)
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_2)));
	else
		tmp = j * (t * t_5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(k * N[(N[(N[(y2 * t$95$1), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.72e+218], N[(N[(i * j), $MachinePrecision] * N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e+160], N[(x * N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.55e+63], N[(t$95$5 * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.75e-183], t$95$3, If[LessEqual[t, 6.3e-201], t$95$4, If[LessEqual[t, 4.9e-162], t$95$3, If[LessEqual[t, 5.5e-62], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e+17], t$95$4, If[LessEqual[t, 5.2e+185], N[(y3 * N[(N[(c * N[(y * y4), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * t$95$5), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -1.72e218

   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 j around inf 38.6%

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

      1. +-commutative 38.6%

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

      2. mul-1-neg 38.6%

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

      3. unsub-neg 38.6%

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

      4. *-commutative 38.6%

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

   5. Simplified 38.6%

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

   6. Taylor expanded in i around -inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. associate-*r* 69.8%

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

      3. *-commutative 69.8%

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

      4. *-commutative 69.8%

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

   8. Simplified 69.8%

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

   if -1.72e218 < t < -8.00000000000000005e160

   1. Initial program 12.4%

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

   3. Taylor expanded in y2 around inf 31.2%

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

      1. *-commutative 31.2%

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

   5. Simplified 31.2%

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

   6. Taylor expanded in x around inf 57.4%

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

      1. *-commutative 57.4%

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

   8. Simplified 57.4%

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

   if -8.00000000000000005e160 < t < -1.55e63

   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 j around inf 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

      4. *-commutative 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in t around inf 51.6%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 56.1%

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

      2. *-commutative 56.1%

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

   8. Simplified 56.1%

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

   if -1.55e63 < t < -2.75e-183 or 6.3e-201 < t < 4.89999999999999976e-162

   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 y1 around -inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. distribute-rgt-neg-in 63.8%

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

      3. +-commutative 63.8%

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

      4. mul-1-neg 63.8%

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

      5. unsub-neg 63.8%

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

      6. *-commutative 63.8%

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

      7. *-commutative 63.8%

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

      8. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   if -2.75e-183 < t < 6.3e-201 or 5.50000000000000022e-62 < t < 8.6e17

   1. Initial program 33.4%

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

   3. Taylor expanded in k around inf 52.2%

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

      1. sub-neg 52.2%

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

      2. +-commutative 52.2%

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

      3. mul-1-neg 52.2%

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

      4. unsub-neg 52.2%

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

      5. *-commutative 52.2%

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

      6. mul-1-neg 52.2%

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

      7. remove-double-neg 52.2%

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

   5. Simplified 52.2%

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

   if 4.89999999999999976e-162 < t < 5.50000000000000022e-62

   1. Initial program 56.5%

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

   3. Taylor expanded in y2 around inf 69.1%

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

   if 8.6e17 < t < 5.20000000000000001e185

   1. Initial program 24.4%

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

   3. Taylor expanded in y5 around 0 27.7%

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

   4. Taylor expanded in y3 around -inf 52.7%

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

   if 5.20000000000000001e185 < t

   1. Initial program 24.2%

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

   3. Taylor expanded in j around inf 44.8%

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

      1. +-commutative 44.8%

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

      2. mul-1-neg 44.8%

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

      3. unsub-neg 44.8%

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

      4. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in t around inf 66.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 66.0%

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

   8. Simplified 66.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.72 \cdot 10^{+218}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1 - t \cdot y5\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+63}:\\ \;\;\;\;\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-183}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) - y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-201}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-162}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) - y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-62}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+17}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+185}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := i \cdot y1 - b \cdot y0\\ t_4 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t\_2\right) + j \cdot t\_3\right)\\ \mathbf{if}\;k \leq -2 \cdot 10^{+93}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -9.2 \cdot 10^{-23}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;k \leq -6 \cdot 10^{-272}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t\_3\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-160}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+153}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot t\_2\right)\right)\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{+208}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* i y1) (* b y0)))
        (t_4 (* x (+ (+ (* y (- (* a b) (* c i))) (* y2 t_2)) (* j t_3)))))
   (if (<= k -2e+93)
     (*
      k
      (+
       (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* i y5) (* b y4))))
       (* z (- (* b y0) (* i y1)))))
     (if (<= k -9.2e-23)
       t_4
       (if (<= k -6e-272)
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x t_3)))
         (if (<= k 2.4e-160)
           t_4
           (if (<= k 2.9e-97)
             t_1
             (if (<= k 4e+17)
               (* a (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t)))))
               (if (<= k 5.6e+144)
                 t_1
                 (if (<= k 5.6e+153)
                   (* y3 (- (* c (* y y4)) (+ (* j (* y1 y4)) (* z t_2))))
                   (if (<= k 4.2e+208)
                     (* (* i y5) (- (* y k) (* t j)))
                     (*
                      y0
                      (+
                       (* y5 (- (* j y3) (* k y2)))
                       (* c (* x y2)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_3));
	double tmp;
	if (k <= -2e+93) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (k <= -9.2e-23) {
		tmp = t_4;
	} else if (k <= -6e-272) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	} else if (k <= 2.4e-160) {
		tmp = t_4;
	} else if (k <= 2.9e-97) {
		tmp = t_1;
	} else if (k <= 4e+17) {
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	} else if (k <= 5.6e+144) {
		tmp = t_1;
	} else if (k <= 5.6e+153) {
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_2)));
	} else if (k <= 4.2e+208) {
		tmp = (i * y5) * ((y * k) - (t * j));
	} else {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_2 = (c * y0) - (a * y1)
    t_3 = (i * y1) - (b * y0)
    t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_3))
    if (k <= (-2d+93)) then
        tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    else if (k <= (-9.2d-23)) then
        tmp = t_4
    else if (k <= (-6d-272)) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
    else if (k <= 2.4d-160) then
        tmp = t_4
    else if (k <= 2.9d-97) then
        tmp = t_1
    else if (k <= 4d+17) then
        tmp = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))))
    else if (k <= 5.6d+144) then
        tmp = t_1
    else if (k <= 5.6d+153) then
        tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_2)))
    else if (k <= 4.2d+208) then
        tmp = (i * y5) * ((y * k) - (t * j))
    else
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_3));
	double tmp;
	if (k <= -2e+93) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (k <= -9.2e-23) {
		tmp = t_4;
	} else if (k <= -6e-272) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	} else if (k <= 2.4e-160) {
		tmp = t_4;
	} else if (k <= 2.9e-97) {
		tmp = t_1;
	} else if (k <= 4e+17) {
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	} else if (k <= 5.6e+144) {
		tmp = t_1;
	} else if (k <= 5.6e+153) {
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_2)));
	} else if (k <= 4.2e+208) {
		tmp = (i * y5) * ((y * k) - (t * j));
	} else {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_2 = (c * y0) - (a * y1)
	t_3 = (i * y1) - (b * y0)
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_3))
	tmp = 0
	if k <= -2e+93:
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	elif k <= -9.2e-23:
		tmp = t_4
	elif k <= -6e-272:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
	elif k <= 2.4e-160:
		tmp = t_4
	elif k <= 2.9e-97:
		tmp = t_1
	elif k <= 4e+17:
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))))
	elif k <= 5.6e+144:
		tmp = t_1
	elif k <= 5.6e+153:
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_2)))
	elif k <= 4.2e+208:
		tmp = (i * y5) * ((y * k) - (t * j))
	else:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(i * y1) - Float64(b * y0))
	t_4 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * t_3)))
	tmp = 0.0
	if (k <= -2e+93)
		tmp = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (k <= -9.2e-23)
		tmp = t_4;
	elseif (k <= -6e-272)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_3)));
	elseif (k <= 2.4e-160)
		tmp = t_4;
	elseif (k <= 2.9e-97)
		tmp = t_1;
	elseif (k <= 4e+17)
		tmp = Float64(a * Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))));
	elseif (k <= 5.6e+144)
		tmp = t_1;
	elseif (k <= 5.6e+153)
		tmp = Float64(y3 * Float64(Float64(c * Float64(y * y4)) - Float64(Float64(j * Float64(y1 * y4)) + Float64(z * t_2))));
	elseif (k <= 4.2e+208)
		tmp = Float64(Float64(i * y5) * Float64(Float64(y * k) - Float64(t * j)));
	else
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(x * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_2 = (c * y0) - (a * y1);
	t_3 = (i * y1) - (b * y0);
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_3));
	tmp = 0.0;
	if (k <= -2e+93)
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	elseif (k <= -9.2e-23)
		tmp = t_4;
	elseif (k <= -6e-272)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	elseif (k <= 2.4e-160)
		tmp = t_4;
	elseif (k <= 2.9e-97)
		tmp = t_1;
	elseif (k <= 4e+17)
		tmp = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	elseif (k <= 5.6e+144)
		tmp = t_1;
	elseif (k <= 5.6e+153)
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * t_2)));
	elseif (k <= 4.2e+208)
		tmp = (i * y5) * ((y * k) - (t * j));
	else
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2e+93], N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -9.2e-23], t$95$4, If[LessEqual[k, -6e-272], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.4e-160], t$95$4, If[LessEqual[k, 2.9e-97], t$95$1, If[LessEqual[k, 4e+17], N[(a * N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.6e+144], t$95$1, If[LessEqual[k, 5.6e+153], N[(y3 * N[(N[(c * N[(y * y4), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.2e+208], N[(N[(i * y5), $MachinePrecision] * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -2.00000000000000009e93

   1. Initial program 25.3%

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

   3. Taylor expanded in k around inf 60.5%

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

      1. sub-neg 60.5%

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

      2. +-commutative 60.5%

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

      3. mul-1-neg 60.5%

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

      4. unsub-neg 60.5%

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

      5. *-commutative 60.5%

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

      6. mul-1-neg 60.5%

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

      7. remove-double-neg 60.5%

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

   5. Simplified 60.5%

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

   if -2.00000000000000009e93 < k < -9.2000000000000004e-23 or -6.0000000000000006e-272 < k < 2.39999999999999991e-160

   1. Initial program 41.9%

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

   3. Taylor expanded in y5 around 0 42.0%

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

   4. Taylor expanded in x around inf 63.3%

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

   if -9.2000000000000004e-23 < k < -6.0000000000000006e-272

   1. Initial program 37.2%

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

   3. Taylor expanded in j around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

      4. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   if 2.39999999999999991e-160 < k < 2.8999999999999999e-97 or 4e17 < k < 5.60000000000000013e144

   1. Initial program 19.1%

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

   3. Taylor expanded in y4 around inf 54.9%

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

   if 2.8999999999999999e-97 < k < 4e17

   1. Initial program 57.0%

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

   3. Taylor expanded in y5 around 0 47.9%

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

   4. Taylor expanded in a around inf 62.7%

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

   if 5.60000000000000013e144 < k < 5.5999999999999997e153

   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 y5 around 0 0.0%

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

   4. Taylor expanded in y3 around -inf 85.7%

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

   if 5.5999999999999997e153 < k < 4.1999999999999997e208

   1. Initial program 25.0%

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

   3. Taylor expanded in y5 around -inf 31.6%

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

   4. Taylor expanded in i around inf 56.6%

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

      1. associate-*r* 50.3%

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

      2. *-commutative 50.3%

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

   6. Simplified 50.3%

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

   if 4.1999999999999997e208 < k

   1. Initial program 27.3%

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

   3. Taylor expanded in y2 around inf 32.2%

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

      1. *-commutative 32.2%

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

   5. Simplified 32.2%

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

   6. Taylor expanded in y0 around inf 55.2%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2 \cdot 10^{+93}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -9.2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq -6 \cdot 10^{-272}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-97}:\\ \;\;\;\;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}\;k \leq 4 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+144}:\\ \;\;\;\;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}\;k \leq 5.6 \cdot 10^{+153}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{+208}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;k \leq -4.5 \cdot 10^{+96}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y1 \cdot \left(y2 \cdot y4\right) - b \cdot \left(y \cdot y4\right)\right)\right)\\ \mathbf{elif}\;k \leq -3.2 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -3.8 \cdot 10^{-284}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 2.15 \cdot 10^{-185}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 5.7 \cdot 10^{+113}:\\ \;\;\;\;\left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3\right)\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{+153}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(k \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t))))))
        (t_2
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0)))))))
   (if (<= k -4.5e+96)
     (* k (+ (* z (- (* b y0) (* i y1))) (- (* y1 (* y2 y4)) (* b (* y y4)))))
     (if (<= k -3.2e-22)
       t_1
       (if (<= k -3.8e-284)
         t_2
         (if (<= k 2.15e-185)
           (* i (+ (* y1 (- (* x j) (* z k))) (* c (- (* z t) (* x y)))))
           (if (<= k 2.7e-97)
             t_2
             (if (<= k 2.8e+20)
               t_1
               (if (<= k 5.7e+113)
                 (* (- (* c y4) (* a y5)) (* y y3))
                 (if (<= k 1.95e+153)
                   (*
                    y3
                    (-
                     (* c (* y y4))
                     (+ (* j (* y1 y4)) (* z (- (* c y0) (* a y1))))))
                   (* y5 (* k (- (* y i) (* y0 y2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	double t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (k <= -4.5e+96) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + ((y1 * (y2 * y4)) - (b * (y * y4))));
	} else if (k <= -3.2e-22) {
		tmp = t_1;
	} else if (k <= -3.8e-284) {
		tmp = t_2;
	} else if (k <= 2.15e-185) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + (c * ((z * t) - (x * y))));
	} else if (k <= 2.7e-97) {
		tmp = t_2;
	} else if (k <= 2.8e+20) {
		tmp = t_1;
	} else if (k <= 5.7e+113) {
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	} else if (k <= 1.95e+153) {
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * ((c * y0) - (a * y1)))));
	} else {
		tmp = y5 * (k * ((y * i) - (y0 * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))))
    t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    if (k <= (-4.5d+96)) then
        tmp = k * ((z * ((b * y0) - (i * y1))) + ((y1 * (y2 * y4)) - (b * (y * y4))))
    else if (k <= (-3.2d-22)) then
        tmp = t_1
    else if (k <= (-3.8d-284)) then
        tmp = t_2
    else if (k <= 2.15d-185) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + (c * ((z * t) - (x * y))))
    else if (k <= 2.7d-97) then
        tmp = t_2
    else if (k <= 2.8d+20) then
        tmp = t_1
    else if (k <= 5.7d+113) then
        tmp = ((c * y4) - (a * y5)) * (y * y3)
    else if (k <= 1.95d+153) then
        tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * ((c * y0) - (a * y1)))))
    else
        tmp = y5 * (k * ((y * i) - (y0 * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	double t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (k <= -4.5e+96) {
		tmp = k * ((z * ((b * y0) - (i * y1))) + ((y1 * (y2 * y4)) - (b * (y * y4))));
	} else if (k <= -3.2e-22) {
		tmp = t_1;
	} else if (k <= -3.8e-284) {
		tmp = t_2;
	} else if (k <= 2.15e-185) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + (c * ((z * t) - (x * y))));
	} else if (k <= 2.7e-97) {
		tmp = t_2;
	} else if (k <= 2.8e+20) {
		tmp = t_1;
	} else if (k <= 5.7e+113) {
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	} else if (k <= 1.95e+153) {
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * ((c * y0) - (a * y1)))));
	} else {
		tmp = y5 * (k * ((y * i) - (y0 * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))))
	t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	tmp = 0
	if k <= -4.5e+96:
		tmp = k * ((z * ((b * y0) - (i * y1))) + ((y1 * (y2 * y4)) - (b * (y * y4))))
	elif k <= -3.2e-22:
		tmp = t_1
	elif k <= -3.8e-284:
		tmp = t_2
	elif k <= 2.15e-185:
		tmp = i * ((y1 * ((x * j) - (z * k))) + (c * ((z * t) - (x * y))))
	elif k <= 2.7e-97:
		tmp = t_2
	elif k <= 2.8e+20:
		tmp = t_1
	elif k <= 5.7e+113:
		tmp = ((c * y4) - (a * y5)) * (y * y3)
	elif k <= 1.95e+153:
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * ((c * y0) - (a * y1)))))
	else:
		tmp = y5 * (k * ((y * i) - (y0 * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))))
	t_2 = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (k <= -4.5e+96)
		tmp = Float64(k * Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(y1 * Float64(y2 * y4)) - Float64(b * Float64(y * y4)))));
	elseif (k <= -3.2e-22)
		tmp = t_1;
	elseif (k <= -3.8e-284)
		tmp = t_2;
	elseif (k <= 2.15e-185)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(c * Float64(Float64(z * t) - Float64(x * y)))));
	elseif (k <= 2.7e-97)
		tmp = t_2;
	elseif (k <= 2.8e+20)
		tmp = t_1;
	elseif (k <= 5.7e+113)
		tmp = Float64(Float64(Float64(c * y4) - Float64(a * y5)) * Float64(y * y3));
	elseif (k <= 1.95e+153)
		tmp = Float64(y3 * Float64(Float64(c * Float64(y * y4)) - Float64(Float64(j * Float64(y1 * y4)) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	else
		tmp = Float64(y5 * Float64(k * Float64(Float64(y * i) - Float64(y0 * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (k <= -4.5e+96)
		tmp = k * ((z * ((b * y0) - (i * y1))) + ((y1 * (y2 * y4)) - (b * (y * y4))));
	elseif (k <= -3.2e-22)
		tmp = t_1;
	elseif (k <= -3.8e-284)
		tmp = t_2;
	elseif (k <= 2.15e-185)
		tmp = i * ((y1 * ((x * j) - (z * k))) + (c * ((z * t) - (x * y))));
	elseif (k <= 2.7e-97)
		tmp = t_2;
	elseif (k <= 2.8e+20)
		tmp = t_1;
	elseif (k <= 5.7e+113)
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	elseif (k <= 1.95e+153)
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * ((c * y0) - (a * y1)))));
	else
		tmp = y5 * (k * ((y * i) - (y0 * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -4.5e+96], N[(k * N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.2e-22], t$95$1, If[LessEqual[k, -3.8e-284], t$95$2, If[LessEqual[k, 2.15e-185], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.7e-97], t$95$2, If[LessEqual[k, 2.8e+20], t$95$1, If[LessEqual[k, 5.7e+113], N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * N[(y * y3), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.95e+153], N[(y3 * N[(N[(c * N[(y * y4), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(k * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -4.49999999999999957e96

   1. Initial program 25.3%

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

   3. Taylor expanded in y5 around 0 15.3%

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

   4. Taylor expanded in k around inf 53.0%

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

   if -4.49999999999999957e96 < k < -3.19999999999999987e-22 or 2.69999999999999985e-97 < k < 2.8e20

   1. Initial program 44.6%

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

   3. Taylor expanded in y5 around 0 42.6%

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

   4. Taylor expanded in a around inf 54.2%

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

   if -3.19999999999999987e-22 < k < -3.7999999999999999e-284 or 2.15e-185 < k < 2.69999999999999985e-97

   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 j around inf 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. unsub-neg 51.9%

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

      4. *-commutative 51.9%

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

   5. Simplified 51.9%

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

   if -3.7999999999999999e-284 < k < 2.15e-185

   1. Initial program 44.8%

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

   3. Taylor expanded in y5 around 0 45.0%

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

   4. Taylor expanded in i around -inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. *-commutative 62.5%

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

   6. Simplified 62.5%

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

   if 2.8e20 < k < 5.6999999999999998e113

   1. Initial program 16.7%

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

   3. Taylor expanded in y2 around inf 41.7%

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

      1. *-commutative 41.7%

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

   5. Simplified 41.7%

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

   6. Taylor expanded in y around inf 59.5%

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

      1. associate-*r* 59.6%

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

      2. *-commutative 59.6%

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

      3. *-commutative 59.6%

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

      4. *-commutative 59.6%

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

   8. Simplified 59.6%

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

   if 5.6999999999999998e113 < k < 1.94999999999999992e153

   1. Initial program 6.6%

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

   3. Taylor expanded in y5 around 0 12.9%

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

   4. Taylor expanded in y3 around -inf 57.1%

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

   if 1.94999999999999992e153 < k

   1. Initial program 26.3%

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

   3. Taylor expanded in y5 around -inf 44.9%

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

   4. Taylor expanded in k around inf 50.3%

      \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -4.5 \cdot 10^{+96}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y1 \cdot \left(y2 \cdot y4\right) - b \cdot \left(y \cdot y4\right)\right)\right)\\ \mathbf{elif}\;k \leq -3.2 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq -3.8 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.15 \cdot 10^{-185}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-97}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 5.7 \cdot 10^{+113}:\\ \;\;\;\;\left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3\right)\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{+153}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(k \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_2 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;k \leq -3.5 \cdot 10^{+86}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -2.5 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq -1.18 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{-185}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 2.25 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 3 \cdot 10^{+112}:\\ \;\;\;\;\left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3\right)\\ \mathbf{elif}\;k \leq 1.65 \cdot 10^{+153}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(k \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0))))))
        (t_2 (* a (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t)))))))
   (if (<= k -3.5e+86)
     (*
      k
      (+
       (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* i y5) (* b y4))))
       (* z (- (* b y0) (* i y1)))))
     (if (<= k -2.5e-25)
       t_2
       (if (<= k -1.18e-287)
         t_1
         (if (<= k 1.35e-185)
           (* i (+ (* y1 (- (* x j) (* z k))) (* c (- (* z t) (* x y)))))
           (if (<= k 1.6e-97)
             t_1
             (if (<= k 2.25e+19)
               t_2
               (if (<= k 3e+112)
                 (* (- (* c y4) (* a y5)) (* y y3))
                 (if (<= k 1.65e+153)
                   (*
                    y3
                    (-
                     (* c (* y y4))
                     (+ (* j (* y1 y4)) (* z (- (* c y0) (* a y1))))))
                   (* y5 (* k (- (* y i) (* y0 y2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_2 = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	double tmp;
	if (k <= -3.5e+86) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (k <= -2.5e-25) {
		tmp = t_2;
	} else if (k <= -1.18e-287) {
		tmp = t_1;
	} else if (k <= 1.35e-185) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + (c * ((z * t) - (x * y))));
	} else if (k <= 1.6e-97) {
		tmp = t_1;
	} else if (k <= 2.25e+19) {
		tmp = t_2;
	} else if (k <= 3e+112) {
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	} else if (k <= 1.65e+153) {
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * ((c * y0) - (a * y1)))));
	} else {
		tmp = y5 * (k * ((y * i) - (y0 * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    t_2 = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))))
    if (k <= (-3.5d+86)) then
        tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    else if (k <= (-2.5d-25)) then
        tmp = t_2
    else if (k <= (-1.18d-287)) then
        tmp = t_1
    else if (k <= 1.35d-185) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + (c * ((z * t) - (x * y))))
    else if (k <= 1.6d-97) then
        tmp = t_1
    else if (k <= 2.25d+19) then
        tmp = t_2
    else if (k <= 3d+112) then
        tmp = ((c * y4) - (a * y5)) * (y * y3)
    else if (k <= 1.65d+153) then
        tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * ((c * y0) - (a * y1)))))
    else
        tmp = y5 * (k * ((y * i) - (y0 * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_2 = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	double tmp;
	if (k <= -3.5e+86) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (k <= -2.5e-25) {
		tmp = t_2;
	} else if (k <= -1.18e-287) {
		tmp = t_1;
	} else if (k <= 1.35e-185) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + (c * ((z * t) - (x * y))));
	} else if (k <= 1.6e-97) {
		tmp = t_1;
	} else if (k <= 2.25e+19) {
		tmp = t_2;
	} else if (k <= 3e+112) {
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	} else if (k <= 1.65e+153) {
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * ((c * y0) - (a * y1)))));
	} else {
		tmp = y5 * (k * ((y * i) - (y0 * y2)));
	}
	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))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	t_2 = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))))
	tmp = 0
	if k <= -3.5e+86:
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	elif k <= -2.5e-25:
		tmp = t_2
	elif k <= -1.18e-287:
		tmp = t_1
	elif k <= 1.35e-185:
		tmp = i * ((y1 * ((x * j) - (z * k))) + (c * ((z * t) - (x * y))))
	elif k <= 1.6e-97:
		tmp = t_1
	elif k <= 2.25e+19:
		tmp = t_2
	elif k <= 3e+112:
		tmp = ((c * y4) - (a * y5)) * (y * y3)
	elif k <= 1.65e+153:
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * ((c * y0) - (a * y1)))))
	else:
		tmp = y5 * (k * ((y * i) - (y0 * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_2 = Float64(a * Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))))
	tmp = 0.0
	if (k <= -3.5e+86)
		tmp = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (k <= -2.5e-25)
		tmp = t_2;
	elseif (k <= -1.18e-287)
		tmp = t_1;
	elseif (k <= 1.35e-185)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(c * Float64(Float64(z * t) - Float64(x * y)))));
	elseif (k <= 1.6e-97)
		tmp = t_1;
	elseif (k <= 2.25e+19)
		tmp = t_2;
	elseif (k <= 3e+112)
		tmp = Float64(Float64(Float64(c * y4) - Float64(a * y5)) * Float64(y * y3));
	elseif (k <= 1.65e+153)
		tmp = Float64(y3 * Float64(Float64(c * Float64(y * y4)) - Float64(Float64(j * Float64(y1 * y4)) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	else
		tmp = Float64(y5 * Float64(k * Float64(Float64(y * i) - Float64(y0 * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	t_2 = a * ((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t))));
	tmp = 0.0;
	if (k <= -3.5e+86)
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	elseif (k <= -2.5e-25)
		tmp = t_2;
	elseif (k <= -1.18e-287)
		tmp = t_1;
	elseif (k <= 1.35e-185)
		tmp = i * ((y1 * ((x * j) - (z * k))) + (c * ((z * t) - (x * y))));
	elseif (k <= 1.6e-97)
		tmp = t_1;
	elseif (k <= 2.25e+19)
		tmp = t_2;
	elseif (k <= 3e+112)
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	elseif (k <= 1.65e+153)
		tmp = y3 * ((c * (y * y4)) - ((j * (y1 * y4)) + (z * ((c * y0) - (a * y1)))));
	else
		tmp = y5 * (k * ((y * i) - (y0 * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.5e+86], N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.5e-25], t$95$2, If[LessEqual[k, -1.18e-287], t$95$1, If[LessEqual[k, 1.35e-185], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.6e-97], t$95$1, If[LessEqual[k, 2.25e+19], t$95$2, If[LessEqual[k, 3e+112], N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * N[(y * y3), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.65e+153], N[(y3 * N[(N[(c * N[(y * y4), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(y1 * y4), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(k * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -3.50000000000000019e86

   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 60.0%

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

      1. sub-neg 60.0%

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

      2. +-commutative 60.0%

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

      3. mul-1-neg 60.0%

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

      4. unsub-neg 60.0%

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

      5. *-commutative 60.0%

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

      6. mul-1-neg 60.0%

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

      7. remove-double-neg 60.0%

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

   5. Simplified 60.0%

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

   if -3.50000000000000019e86 < k < -2.49999999999999981e-25 or 1.5999999999999999e-97 < k < 2.25e19

   1. Initial program 46.6%

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

   3. Taylor expanded in y5 around 0 44.5%

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

   4. Taylor expanded in a around inf 54.4%

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

   if -2.49999999999999981e-25 < k < -1.18000000000000003e-287 or 1.34999999999999994e-185 < k < 1.5999999999999999e-97

   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 j around inf 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. unsub-neg 51.9%

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

      4. *-commutative 51.9%

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

   5. Simplified 51.9%

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

   if -1.18000000000000003e-287 < k < 1.34999999999999994e-185

   1. Initial program 44.8%

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

   3. Taylor expanded in y5 around 0 45.0%

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

   4. Taylor expanded in i around -inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. *-commutative 62.5%

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

   6. Simplified 62.5%

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

   if 2.25e19 < k < 2.99999999999999979e112

   1. Initial program 16.7%

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

   3. Taylor expanded in y2 around inf 41.7%

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

      1. *-commutative 41.7%

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

   5. Simplified 41.7%

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

   6. Taylor expanded in y around inf 59.5%

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

      1. associate-*r* 59.6%

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

      2. *-commutative 59.6%

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

      3. *-commutative 59.6%

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

      4. *-commutative 59.6%

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

   8. Simplified 59.6%

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

   if 2.99999999999999979e112 < k < 1.64999999999999997e153

   1. Initial program 6.6%

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

   3. Taylor expanded in y5 around 0 12.9%

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

   4. Taylor expanded in y3 around -inf 57.1%

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

   if 1.64999999999999997e153 < k

   1. Initial program 26.3%

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

   3. Taylor expanded in y5 around -inf 44.9%

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

   4. Taylor expanded in k around inf 50.3%

      \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.5 \cdot 10^{+86}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -2.5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq -1.18 \cdot 10^{-287}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{-185}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.25 \cdot 10^{+19}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 3 \cdot 10^{+112}:\\ \;\;\;\;\left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3\right)\\ \mathbf{elif}\;k \leq 1.65 \cdot 10^{+153}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right) - \left(j \cdot \left(y1 \cdot y4\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(k \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.55 \cdot 10^{+137}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -0.0056:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right)\\ \mathbf{elif}\;y4 \leq -2.3 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -4.4 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 1.95 \cdot 10^{-246}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1 - t \cdot y5\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y4 \leq 9 \cdot 10^{+40}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.55e+137)
   (* j (* b (- (* t y4) (* x y0))))
   (if (<= y4 -0.0056)
     (* (* i y5) (- (* y k) (* t j)))
     (if (<= y4 -2.3e-175)
       (* c (- (* x (* y0 y2)) (* y4 (- (* t y2) (* y y3)))))
       (if (<= y4 -4.4e-297)
         (* x (* y1 (- (* i j) (* a y2))))
         (if (<= y4 1.95e-246)
           (* (* i j) (- (* x y1) (* t y5)))
           (if (<= y4 7.5e-220)
             (* x (* y2 (- (* c y0) (* a y1))))
             (if (<= y4 6e-206)
               (* x (* y (- (* a b) (* c i))))
               (if (<= y4 9e+40)
                 (* y0 (+ (* y5 (- (* j y3) (* k y2))) (* c (* x y2))))
                 (* y1 (* y3 (- (* z a) (* j y4)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.55e+137) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else if (y4 <= -0.0056) {
		tmp = (i * y5) * ((y * k) - (t * j));
	} else if (y4 <= -2.3e-175) {
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	} else if (y4 <= -4.4e-297) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y4 <= 1.95e-246) {
		tmp = (i * j) * ((x * y1) - (t * y5));
	} else if (y4 <= 7.5e-220) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y4 <= 6e-206) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y4 <= 9e+40) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1.55d+137)) then
        tmp = j * (b * ((t * y4) - (x * y0)))
    else if (y4 <= (-0.0056d0)) then
        tmp = (i * y5) * ((y * k) - (t * j))
    else if (y4 <= (-2.3d-175)) then
        tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))))
    else if (y4 <= (-4.4d-297)) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else if (y4 <= 1.95d-246) then
        tmp = (i * j) * ((x * y1) - (t * y5))
    else if (y4 <= 7.5d-220) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y4 <= 6d-206) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y4 <= 9d+40) then
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
    else
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.55e+137) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else if (y4 <= -0.0056) {
		tmp = (i * y5) * ((y * k) - (t * j));
	} else if (y4 <= -2.3e-175) {
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	} else if (y4 <= -4.4e-297) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y4 <= 1.95e-246) {
		tmp = (i * j) * ((x * y1) - (t * y5));
	} else if (y4 <= 7.5e-220) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y4 <= 6e-206) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y4 <= 9e+40) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1.55e+137:
		tmp = j * (b * ((t * y4) - (x * y0)))
	elif y4 <= -0.0056:
		tmp = (i * y5) * ((y * k) - (t * j))
	elif y4 <= -2.3e-175:
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))))
	elif y4 <= -4.4e-297:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	elif y4 <= 1.95e-246:
		tmp = (i * j) * ((x * y1) - (t * y5))
	elif y4 <= 7.5e-220:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y4 <= 6e-206:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y4 <= 9e+40:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
	else:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.55e+137)
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y4 <= -0.0056)
		tmp = Float64(Float64(i * y5) * Float64(Float64(y * k) - Float64(t * j)));
	elseif (y4 <= -2.3e-175)
		tmp = Float64(c * Float64(Float64(x * Float64(y0 * y2)) - Float64(y4 * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y4 <= -4.4e-297)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	elseif (y4 <= 1.95e-246)
		tmp = Float64(Float64(i * j) * Float64(Float64(x * y1) - Float64(t * y5)));
	elseif (y4 <= 7.5e-220)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y4 <= 6e-206)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y4 <= 9e+40)
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(x * y2))));
	else
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1.55e+137)
		tmp = j * (b * ((t * y4) - (x * y0)));
	elseif (y4 <= -0.0056)
		tmp = (i * y5) * ((y * k) - (t * j));
	elseif (y4 <= -2.3e-175)
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	elseif (y4 <= -4.4e-297)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	elseif (y4 <= 1.95e-246)
		tmp = (i * j) * ((x * y1) - (t * y5));
	elseif (y4 <= 7.5e-220)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y4 <= 6e-206)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y4 <= 9e+40)
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	else
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.55e+137], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -0.0056], N[(N[(i * y5), $MachinePrecision] * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.3e-175], N[(c * N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -4.4e-297], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.95e-246], N[(N[(i * j), $MachinePrecision] * N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.5e-220], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6e-206], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 9e+40], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y4 < -1.55e137

   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 j around inf 38.0%

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

      1. +-commutative 38.0%

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

      2. mul-1-neg 38.0%

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

      3. unsub-neg 38.0%

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

      4. *-commutative 38.0%

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

   5. Simplified 38.0%

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

   6. Taylor expanded in b around inf 50.0%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 50.0%

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

   8. Simplified 50.0%

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

   if -1.55e137 < y4 < -0.00559999999999999994

   1. Initial program 23.3%

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

   3. Taylor expanded in y5 around -inf 54.1%

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

   4. Taylor expanded in i around inf 57.9%

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

      1. associate-*r* 51.4%

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

      2. *-commutative 51.4%

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

   6. Simplified 51.4%

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

   if -0.00559999999999999994 < y4 < -2.3e-175

   1. Initial program 24.5%

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

   3. Taylor expanded in y2 around inf 43.4%

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

      1. *-commutative 43.4%

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

   5. Simplified 43.4%

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

   6. Taylor expanded in c around inf 46.8%

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

      1. *-commutative 46.8%

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

      2. *-commutative 46.8%

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

      3. *-commutative 46.8%

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

      4. *-commutative 46.8%

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

   8. Simplified 46.8%

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

   if -2.3e-175 < y4 < -4.3999999999999997e-297

   1. Initial program 45.8%

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

   3. Taylor expanded in y1 around -inf 42.4%

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

      1. mul-1-neg 42.4%

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

      2. distribute-rgt-neg-in 42.4%

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

      3. +-commutative 42.4%

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

      4. mul-1-neg 42.4%

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

      5. unsub-neg 42.4%

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

      6. *-commutative 42.4%

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

      7. *-commutative 42.4%

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

      8. *-commutative 42.4%

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

   5. Simplified 42.4%

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

   6. Taylor expanded in x around inf 50.5%

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

   if -4.3999999999999997e-297 < y4 < 1.94999999999999989e-246

   1. Initial program 43.3%

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

   3. Taylor expanded in j around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

      4. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in i around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

      2. associate-*r* 57.1%

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

      3. *-commutative 57.1%

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

      4. *-commutative 57.1%

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

   8. Simplified 57.1%

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

   if 1.94999999999999989e-246 < y4 < 7.5000000000000002e-220

   1. Initial program 49.6%

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

   3. Taylor expanded in y2 around inf 90.5%

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

      1. *-commutative 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in x around inf 76.6%

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

      1. *-commutative 76.6%

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

   8. Simplified 76.6%

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

   if 7.5000000000000002e-220 < y4 < 6.0000000000000004e-206

   1. Initial program 60.0%

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

   3. Taylor expanded in y5 around 0 41.2%

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

   4. Taylor expanded in x around inf 60.4%

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

   5. Taylor expanded in y around inf 80.4%

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

   if 6.0000000000000004e-206 < y4 < 9.00000000000000064e40

   1. Initial program 45.4%

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

   3. Taylor expanded in y2 around inf 45.7%

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

      1. *-commutative 45.7%

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

   5. Simplified 45.7%

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

   6. Taylor expanded in y0 around inf 41.0%

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

   if 9.00000000000000064e40 < 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 y1 around -inf 52.4%

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

      1. mul-1-neg 52.4%

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

      2. distribute-rgt-neg-in 52.4%

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

      3. +-commutative 52.4%

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

      4. mul-1-neg 52.4%

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

      5. unsub-neg 52.4%

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

      6. *-commutative 52.4%

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

      7. *-commutative 52.4%

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

      8. *-commutative 52.4%

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

   5. Simplified 52.4%

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

   6. Taylor expanded in y3 around -inf 48.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(y3 \cdot \left(j \cdot y4 - a \cdot z\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.55 \cdot 10^{+137}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -0.0056:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right)\\ \mathbf{elif}\;y4 \leq -2.3 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -4.4 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 1.95 \cdot 10^{-246}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1 - t \cdot y5\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y4 \leq 9 \cdot 10^{+40}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -5.6 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -0.0045:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right)\\ \mathbf{elif}\;y4 \leq -1.22 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -1.85 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 5.5 \cdot 10^{-243}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1 - t \cdot y5\right)\\ \mathbf{elif}\;y4 \leq 1.1 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 80:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -5.6e+141)
   (* j (* b (- (* t y4) (* x y0))))
   (if (<= y4 -0.0045)
     (* (* i y5) (- (* y k) (* t j)))
     (if (<= y4 -1.22e-175)
       (* c (- (* x (* y0 y2)) (* y4 (- (* t y2) (* y y3)))))
       (if (<= y4 -1.85e-299)
         (* x (* y1 (- (* i j) (* a y2))))
         (if (<= y4 5.5e-243)
           (* (* i j) (- (* x y1) (* t y5)))
           (if (<= y4 1.1e-223)
             (* x (* y2 (- (* c y0) (* a y1))))
             (if (<= y4 80.0)
               (* y0 (+ (* c (- (* x y2) (* z y3))) (* b (- (* z k) (* x j)))))
               (* y1 (* y3 (- (* z a) (* j y4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -5.6e+141) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else if (y4 <= -0.0045) {
		tmp = (i * y5) * ((y * k) - (t * j));
	} else if (y4 <= -1.22e-175) {
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	} else if (y4 <= -1.85e-299) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y4 <= 5.5e-243) {
		tmp = (i * j) * ((x * y1) - (t * y5));
	} else if (y4 <= 1.1e-223) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y4 <= 80.0) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (b * ((z * k) - (x * j))));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-5.6d+141)) then
        tmp = j * (b * ((t * y4) - (x * y0)))
    else if (y4 <= (-0.0045d0)) then
        tmp = (i * y5) * ((y * k) - (t * j))
    else if (y4 <= (-1.22d-175)) then
        tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))))
    else if (y4 <= (-1.85d-299)) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else if (y4 <= 5.5d-243) then
        tmp = (i * j) * ((x * y1) - (t * y5))
    else if (y4 <= 1.1d-223) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y4 <= 80.0d0) then
        tmp = y0 * ((c * ((x * y2) - (z * y3))) + (b * ((z * k) - (x * j))))
    else
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -5.6e+141) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else if (y4 <= -0.0045) {
		tmp = (i * y5) * ((y * k) - (t * j));
	} else if (y4 <= -1.22e-175) {
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	} else if (y4 <= -1.85e-299) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y4 <= 5.5e-243) {
		tmp = (i * j) * ((x * y1) - (t * y5));
	} else if (y4 <= 1.1e-223) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y4 <= 80.0) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (b * ((z * k) - (x * j))));
	} else {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -5.6e+141:
		tmp = j * (b * ((t * y4) - (x * y0)))
	elif y4 <= -0.0045:
		tmp = (i * y5) * ((y * k) - (t * j))
	elif y4 <= -1.22e-175:
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))))
	elif y4 <= -1.85e-299:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	elif y4 <= 5.5e-243:
		tmp = (i * j) * ((x * y1) - (t * y5))
	elif y4 <= 1.1e-223:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y4 <= 80.0:
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (b * ((z * k) - (x * j))))
	else:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -5.6e+141)
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y4 <= -0.0045)
		tmp = Float64(Float64(i * y5) * Float64(Float64(y * k) - Float64(t * j)));
	elseif (y4 <= -1.22e-175)
		tmp = Float64(c * Float64(Float64(x * Float64(y0 * y2)) - Float64(y4 * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y4 <= -1.85e-299)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	elseif (y4 <= 5.5e-243)
		tmp = Float64(Float64(i * j) * Float64(Float64(x * y1) - Float64(t * y5)));
	elseif (y4 <= 1.1e-223)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y4 <= 80.0)
		tmp = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -5.6e+141)
		tmp = j * (b * ((t * y4) - (x * y0)));
	elseif (y4 <= -0.0045)
		tmp = (i * y5) * ((y * k) - (t * j));
	elseif (y4 <= -1.22e-175)
		tmp = c * ((x * (y0 * y2)) - (y4 * ((t * y2) - (y * y3))));
	elseif (y4 <= -1.85e-299)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	elseif (y4 <= 5.5e-243)
		tmp = (i * j) * ((x * y1) - (t * y5));
	elseif (y4 <= 1.1e-223)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y4 <= 80.0)
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (b * ((z * k) - (x * j))));
	else
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -5.6e+141], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -0.0045], N[(N[(i * y5), $MachinePrecision] * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.22e-175], N[(c * N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.85e-299], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.5e-243], N[(N[(i * j), $MachinePrecision] * N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.1e-223], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 80.0], N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y4 < -5.59999999999999982e141

   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 j around inf 38.0%

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

      1. +-commutative 38.0%

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

      2. mul-1-neg 38.0%

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

      3. unsub-neg 38.0%

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

      4. *-commutative 38.0%

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

   5. Simplified 38.0%

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

   6. Taylor expanded in b around inf 50.0%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 50.0%

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

   8. Simplified 50.0%

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

   if -5.59999999999999982e141 < y4 < -0.00449999999999999966

   1. Initial program 23.3%

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

   3. Taylor expanded in y5 around -inf 54.1%

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

   4. Taylor expanded in i around inf 57.9%

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

      1. associate-*r* 51.4%

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

      2. *-commutative 51.4%

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

   6. Simplified 51.4%

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

   if -0.00449999999999999966 < y4 < -1.2200000000000001e-175

   1. Initial program 24.5%

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

   3. Taylor expanded in y2 around inf 43.4%

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

      1. *-commutative 43.4%

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

   5. Simplified 43.4%

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

   6. Taylor expanded in c around inf 46.8%

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

      1. *-commutative 46.8%

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

      2. *-commutative 46.8%

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

      3. *-commutative 46.8%

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

      4. *-commutative 46.8%

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

   8. Simplified 46.8%

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

   if -1.2200000000000001e-175 < y4 < -1.85000000000000007e-299

   1. Initial program 45.8%

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

   3. Taylor expanded in y1 around -inf 42.4%

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

      1. mul-1-neg 42.4%

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

      2. distribute-rgt-neg-in 42.4%

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

      3. +-commutative 42.4%

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

      4. mul-1-neg 42.4%

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

      5. unsub-neg 42.4%

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

      6. *-commutative 42.4%

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

      7. *-commutative 42.4%

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

      8. *-commutative 42.4%

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

   5. Simplified 42.4%

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

   6. Taylor expanded in x around inf 50.5%

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

   if -1.85000000000000007e-299 < y4 < 5.50000000000000004e-243

   1. Initial program 43.3%

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

   3. Taylor expanded in j around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

      4. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in i around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

      2. associate-*r* 57.1%

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

      3. *-commutative 57.1%

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

      4. *-commutative 57.1%

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

   8. Simplified 57.1%

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

   if 5.50000000000000004e-243 < y4 < 1.10000000000000004e-223

   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 y2 around inf 87.4%

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

      1. *-commutative 87.4%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in x around inf 68.8%

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

      1. *-commutative 68.8%

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

   8. Simplified 68.8%

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

   if 1.10000000000000004e-223 < y4 < 80

   1. Initial program 45.6%

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

   3. Taylor expanded in y5 around 0 39.0%

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

   4. Taylor expanded in y0 around inf 46.1%

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

      1. *-commutative 46.1%

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

   6. Simplified 46.1%

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

   if 80 < y4

   1. Initial program 29.3%

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

   3. Taylor expanded in y1 around -inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. distribute-rgt-neg-in 52.5%

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

      3. +-commutative 52.5%

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

      4. mul-1-neg 52.5%

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

      5. unsub-neg 52.5%

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

      6. *-commutative 52.5%

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

      7. *-commutative 52.5%

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

      8. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in y3 around -inf 47.5%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -5.6 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -0.0045:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right)\\ \mathbf{elif}\;y4 \leq -1.22 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -1.85 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 5.5 \cdot 10^{-243}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1 - t \cdot y5\right)\\ \mathbf{elif}\;y4 \leq 1.1 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 80:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ t_2 := \left(i \cdot y5\right) \cdot \left(y \cdot k\right)\\ t_3 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{if}\;i \leq -4.4 \cdot 10^{+142}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{+85}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.36 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-271}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.42 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{+283}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (- (* z y3) (* x y2)))))
        (t_2 (* (* i y5) (* y k)))
        (t_3 (* i (* y1 (- (* x j) (* z k))))))
   (if (<= i -4.4e+142)
     (* (* i j) (* t (- y5)))
     (if (<= i -3.8e+85)
       t_3
       (if (<= i -4.2e+79)
         t_2
         (if (<= i -1.36e-281)
           t_1
           (if (<= i 5.8e-271)
             (* c (* y (* y3 y4)))
             (if (<= i 6e-106)
               t_1
               (if (<= i 1.42e+144)
                 (* j (* b (- (* t y4) (* x y0))))
                 (if (<= i 6.8e+283) t_3 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * ((z * y3) - (x * y2)));
	double t_2 = (i * y5) * (y * k);
	double t_3 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (i <= -4.4e+142) {
		tmp = (i * j) * (t * -y5);
	} else if (i <= -3.8e+85) {
		tmp = t_3;
	} else if (i <= -4.2e+79) {
		tmp = t_2;
	} else if (i <= -1.36e-281) {
		tmp = t_1;
	} else if (i <= 5.8e-271) {
		tmp = c * (y * (y3 * y4));
	} else if (i <= 6e-106) {
		tmp = t_1;
	} else if (i <= 1.42e+144) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else if (i <= 6.8e+283) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (y1 * ((z * y3) - (x * y2)))
    t_2 = (i * y5) * (y * k)
    t_3 = i * (y1 * ((x * j) - (z * k)))
    if (i <= (-4.4d+142)) then
        tmp = (i * j) * (t * -y5)
    else if (i <= (-3.8d+85)) then
        tmp = t_3
    else if (i <= (-4.2d+79)) then
        tmp = t_2
    else if (i <= (-1.36d-281)) then
        tmp = t_1
    else if (i <= 5.8d-271) then
        tmp = c * (y * (y3 * y4))
    else if (i <= 6d-106) then
        tmp = t_1
    else if (i <= 1.42d+144) then
        tmp = j * (b * ((t * y4) - (x * y0)))
    else if (i <= 6.8d+283) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * ((z * y3) - (x * y2)));
	double t_2 = (i * y5) * (y * k);
	double t_3 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (i <= -4.4e+142) {
		tmp = (i * j) * (t * -y5);
	} else if (i <= -3.8e+85) {
		tmp = t_3;
	} else if (i <= -4.2e+79) {
		tmp = t_2;
	} else if (i <= -1.36e-281) {
		tmp = t_1;
	} else if (i <= 5.8e-271) {
		tmp = c * (y * (y3 * y4));
	} else if (i <= 6e-106) {
		tmp = t_1;
	} else if (i <= 1.42e+144) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else if (i <= 6.8e+283) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * ((z * y3) - (x * y2)))
	t_2 = (i * y5) * (y * k)
	t_3 = i * (y1 * ((x * j) - (z * k)))
	tmp = 0
	if i <= -4.4e+142:
		tmp = (i * j) * (t * -y5)
	elif i <= -3.8e+85:
		tmp = t_3
	elif i <= -4.2e+79:
		tmp = t_2
	elif i <= -1.36e-281:
		tmp = t_1
	elif i <= 5.8e-271:
		tmp = c * (y * (y3 * y4))
	elif i <= 6e-106:
		tmp = t_1
	elif i <= 1.42e+144:
		tmp = j * (b * ((t * y4) - (x * y0)))
	elif i <= 6.8e+283:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	t_2 = Float64(Float64(i * y5) * Float64(y * k))
	t_3 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	tmp = 0.0
	if (i <= -4.4e+142)
		tmp = Float64(Float64(i * j) * Float64(t * Float64(-y5)));
	elseif (i <= -3.8e+85)
		tmp = t_3;
	elseif (i <= -4.2e+79)
		tmp = t_2;
	elseif (i <= -1.36e-281)
		tmp = t_1;
	elseif (i <= 5.8e-271)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (i <= 6e-106)
		tmp = t_1;
	elseif (i <= 1.42e+144)
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (i <= 6.8e+283)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * ((z * y3) - (x * y2)));
	t_2 = (i * y5) * (y * k);
	t_3 = i * (y1 * ((x * j) - (z * k)));
	tmp = 0.0;
	if (i <= -4.4e+142)
		tmp = (i * j) * (t * -y5);
	elseif (i <= -3.8e+85)
		tmp = t_3;
	elseif (i <= -4.2e+79)
		tmp = t_2;
	elseif (i <= -1.36e-281)
		tmp = t_1;
	elseif (i <= 5.8e-271)
		tmp = c * (y * (y3 * y4));
	elseif (i <= 6e-106)
		tmp = t_1;
	elseif (i <= 1.42e+144)
		tmp = j * (b * ((t * y4) - (x * y0)));
	elseif (i <= 6.8e+283)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y5), $MachinePrecision] * N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.4e+142], N[(N[(i * j), $MachinePrecision] * N[(t * (-y5)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.8e+85], t$95$3, If[LessEqual[i, -4.2e+79], t$95$2, If[LessEqual[i, -1.36e-281], t$95$1, If[LessEqual[i, 5.8e-271], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e-106], t$95$1, If[LessEqual[i, 1.42e+144], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.8e+283], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -4.39999999999999974e142

   1. Initial program 16.1%

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

   3. Taylor expanded in y5 around -inf 51.7%

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

   4. Taylor expanded in i around inf 48.9%

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

      1. associate-*r* 48.9%

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

      2. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   7. Taylor expanded in j around inf 36.8%

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

      1. associate-*r* 39.8%

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

      2. *-commutative 39.8%

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

      3. *-commutative 39.8%

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

   9. Simplified 39.8%

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

   if -4.39999999999999974e142 < i < -3.79999999999999992e85 or 1.42000000000000009e144 < i < 6.8000000000000003e283

   1. Initial program 33.4%

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

   3. Taylor expanded in y1 around -inf 50.7%

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

      1. mul-1-neg 50.7%

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

      2. distribute-rgt-neg-in 50.7%

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

      3. +-commutative 50.7%

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

      4. mul-1-neg 50.7%

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

      5. unsub-neg 50.7%

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

      6. *-commutative 50.7%

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

      7. *-commutative 50.7%

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

      8. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in i around inf 47.1%

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

   if -3.79999999999999992e85 < i < -4.20000000000000016e79 or 6.8000000000000003e283 < i

   1. Initial program 11.1%

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

   3. Taylor expanded in y5 around -inf 55.6%

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

   4. Taylor expanded in i around inf 77.8%

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

      1. associate-*r* 77.8%

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

      2. *-commutative 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in j around 0 78.0%

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

      1. mul-1-neg 78.0%

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

      2. distribute-lft-neg-out 78.0%

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

      3. *-commutative 78.0%

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

   9. Simplified 78.0%

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

   if -4.20000000000000016e79 < i < -1.35999999999999999e-281 or 5.80000000000000028e-271 < i < 6.00000000000000037e-106

   1. Initial program 38.2%

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

   3. Taylor expanded in y1 around -inf 45.1%

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

      1. mul-1-neg 45.1%

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

      2. distribute-rgt-neg-in 45.1%

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

      3. +-commutative 45.1%

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

      4. mul-1-neg 45.1%

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

      5. unsub-neg 45.1%

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

      6. *-commutative 45.1%

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

      7. *-commutative 45.1%

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

      8. *-commutative 45.1%

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

   5. Simplified 45.1%

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

   6. Taylor expanded in a around inf 42.8%

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

   if -1.35999999999999999e-281 < i < 5.80000000000000028e-271

   1. Initial program 20.0%

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

   3. Taylor expanded in y2 around inf 33.3%

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

      1. *-commutative 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in y around inf 47.7%

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

   7. Taylor expanded in c around inf 54.2%

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

   if 6.00000000000000037e-106 < i < 1.42000000000000009e144

   1. Initial program 39.2%

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

   3. Taylor expanded in j around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

      4. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in b around inf 42.7%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 42.7%

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

   8. Simplified 42.7%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - y0 \cdot x\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.4 \cdot 10^{+142}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{+79}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k\right)\\ \mathbf{elif}\;i \leq -1.36 \cdot 10^{-281}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-271}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.42 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{+283}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 21.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ t_2 := a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ t_3 := a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{if}\;c \leq -1.66 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{+20}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{-176}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-262}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-213}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y1 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+169}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y4 (* c y3))))
        (t_2 (* a (* y1 (* z y3))))
        (t_3 (* a (* y1 (* x (- y2))))))
   (if (<= c -1.66e+205)
     t_1
     (if (<= c -2.2e+20)
       (* y0 (* y2 (* x c)))
       (if (<= c -1e-143)
         t_2
         (if (<= c -2.9e-176)
           t_3
           (if (<= c 3.5e-262)
             (* j (* y5 (* y0 y3)))
             (if (<= c 2.65e-213)
               (* j (* y3 (* y1 (- y4))))
               (if (<= c 7.2e-210) t_2 (if (<= c 7.2e+169) t_3 t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y4 * (c * y3));
	double t_2 = a * (y1 * (z * y3));
	double t_3 = a * (y1 * (x * -y2));
	double tmp;
	if (c <= -1.66e+205) {
		tmp = t_1;
	} else if (c <= -2.2e+20) {
		tmp = y0 * (y2 * (x * c));
	} else if (c <= -1e-143) {
		tmp = t_2;
	} else if (c <= -2.9e-176) {
		tmp = t_3;
	} else if (c <= 3.5e-262) {
		tmp = j * (y5 * (y0 * y3));
	} else if (c <= 2.65e-213) {
		tmp = j * (y3 * (y1 * -y4));
	} else if (c <= 7.2e-210) {
		tmp = t_2;
	} else if (c <= 7.2e+169) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (y4 * (c * y3))
    t_2 = a * (y1 * (z * y3))
    t_3 = a * (y1 * (x * -y2))
    if (c <= (-1.66d+205)) then
        tmp = t_1
    else if (c <= (-2.2d+20)) then
        tmp = y0 * (y2 * (x * c))
    else if (c <= (-1d-143)) then
        tmp = t_2
    else if (c <= (-2.9d-176)) then
        tmp = t_3
    else if (c <= 3.5d-262) then
        tmp = j * (y5 * (y0 * y3))
    else if (c <= 2.65d-213) then
        tmp = j * (y3 * (y1 * -y4))
    else if (c <= 7.2d-210) then
        tmp = t_2
    else if (c <= 7.2d+169) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y4 * (c * y3));
	double t_2 = a * (y1 * (z * y3));
	double t_3 = a * (y1 * (x * -y2));
	double tmp;
	if (c <= -1.66e+205) {
		tmp = t_1;
	} else if (c <= -2.2e+20) {
		tmp = y0 * (y2 * (x * c));
	} else if (c <= -1e-143) {
		tmp = t_2;
	} else if (c <= -2.9e-176) {
		tmp = t_3;
	} else if (c <= 3.5e-262) {
		tmp = j * (y5 * (y0 * y3));
	} else if (c <= 2.65e-213) {
		tmp = j * (y3 * (y1 * -y4));
	} else if (c <= 7.2e-210) {
		tmp = t_2;
	} else if (c <= 7.2e+169) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (y4 * (c * y3))
	t_2 = a * (y1 * (z * y3))
	t_3 = a * (y1 * (x * -y2))
	tmp = 0
	if c <= -1.66e+205:
		tmp = t_1
	elif c <= -2.2e+20:
		tmp = y0 * (y2 * (x * c))
	elif c <= -1e-143:
		tmp = t_2
	elif c <= -2.9e-176:
		tmp = t_3
	elif c <= 3.5e-262:
		tmp = j * (y5 * (y0 * y3))
	elif c <= 2.65e-213:
		tmp = j * (y3 * (y1 * -y4))
	elif c <= 7.2e-210:
		tmp = t_2
	elif c <= 7.2e+169:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(y4 * Float64(c * y3)))
	t_2 = Float64(a * Float64(y1 * Float64(z * y3)))
	t_3 = Float64(a * Float64(y1 * Float64(x * Float64(-y2))))
	tmp = 0.0
	if (c <= -1.66e+205)
		tmp = t_1;
	elseif (c <= -2.2e+20)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (c <= -1e-143)
		tmp = t_2;
	elseif (c <= -2.9e-176)
		tmp = t_3;
	elseif (c <= 3.5e-262)
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	elseif (c <= 2.65e-213)
		tmp = Float64(j * Float64(y3 * Float64(y1 * Float64(-y4))));
	elseif (c <= 7.2e-210)
		tmp = t_2;
	elseif (c <= 7.2e+169)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (y4 * (c * y3));
	t_2 = a * (y1 * (z * y3));
	t_3 = a * (y1 * (x * -y2));
	tmp = 0.0;
	if (c <= -1.66e+205)
		tmp = t_1;
	elseif (c <= -2.2e+20)
		tmp = y0 * (y2 * (x * c));
	elseif (c <= -1e-143)
		tmp = t_2;
	elseif (c <= -2.9e-176)
		tmp = t_3;
	elseif (c <= 3.5e-262)
		tmp = j * (y5 * (y0 * y3));
	elseif (c <= 2.65e-213)
		tmp = j * (y3 * (y1 * -y4));
	elseif (c <= 7.2e-210)
		tmp = t_2;
	elseif (c <= 7.2e+169)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(y1 * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.66e+205], t$95$1, If[LessEqual[c, -2.2e+20], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1e-143], t$95$2, If[LessEqual[c, -2.9e-176], t$95$3, If[LessEqual[c, 3.5e-262], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.65e-213], N[(j * N[(y3 * N[(y1 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.2e-210], t$95$2, If[LessEqual[c, 7.2e+169], t$95$3, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.6600000000000001e205 or 7.20000000000000019e169 < c

   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 y2 around inf 25.8%

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

      1. *-commutative 25.8%

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

   5. Simplified 25.8%

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

   6. Taylor expanded in y around inf 49.4%

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

   7. Taylor expanded in c around inf 49.7%

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

      1. associate-*r* 59.6%

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

   9. Simplified 59.6%

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

   if -1.6600000000000001e205 < c < -2.2e20

   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 y2 around inf 45.4%

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

      1. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in y0 around inf 34.2%

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

   7. Taylor expanded in y5 around 0 30.3%

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

      1. associate-*r* 35.0%

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

      2. *-commutative 35.0%

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

   9. Simplified 35.0%

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

   if -2.2e20 < c < -9.9999999999999995e-144 or 2.65000000000000011e-213 < c < 7.1999999999999998e-210

   1. Initial program 38.7%

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

   3. Taylor expanded in y1 around -inf 33.3%

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

      1. mul-1-neg 33.3%

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

      2. distribute-rgt-neg-in 33.3%

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

      3. +-commutative 33.3%

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

      4. mul-1-neg 33.3%

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

      5. unsub-neg 33.3%

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

      6. *-commutative 33.3%

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

      7. *-commutative 33.3%

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

      8. *-commutative 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in a around inf 43.2%

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

   7. Taylor expanded in y3 around inf 33.5%

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

   if -9.9999999999999995e-144 < c < -2.90000000000000006e-176 or 7.1999999999999998e-210 < c < 7.20000000000000019e169

   1. Initial program 37.9%

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

   3. Taylor expanded in y1 around -inf 44.7%

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

      1. mul-1-neg 44.7%

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

      2. distribute-rgt-neg-in 44.7%

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

      3. +-commutative 44.7%

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

      4. mul-1-neg 44.7%

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

      5. unsub-neg 44.7%

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

      6. *-commutative 44.7%

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

      7. *-commutative 44.7%

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

      8. *-commutative 44.7%

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

   5. Simplified 44.7%

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

   6. Taylor expanded in a around inf 35.8%

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

   7. Taylor expanded in y3 around 0 31.3%

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

      1. neg-mul-1 31.3%

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

      2. distribute-lft-neg-in 31.3%

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

      3. *-commutative 31.3%

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

   9. Simplified 31.3%

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

   if -2.90000000000000006e-176 < c < 3.50000000000000011e-262

   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 y2 around inf 38.8%

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

      1. *-commutative 38.8%

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

   5. Simplified 38.8%

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

   6. Taylor expanded in y0 around inf 41.5%

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

   7. Taylor expanded in y2 around 0 30.8%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.1%

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

   9. Simplified 35.1%

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

   if 3.50000000000000011e-262 < c < 2.65000000000000011e-213

   1. Initial program 46.2%

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

   3. Taylor expanded in j around inf 46.7%

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

      1. +-commutative 46.7%

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

      2. mul-1-neg 46.7%

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

      3. unsub-neg 46.7%

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

      4. *-commutative 46.7%

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

   5. Simplified 46.7%

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

   6. Taylor expanded in y3 around inf 39.0%

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

      1. *-commutative 39.0%

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

      2. *-commutative 39.0%

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

   8. Simplified 39.0%

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

   9. Taylor expanded in y5 around 0 39.4%

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

       1. neg-mul-1 39.4%

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

       2. distribute-rgt-neg-in 39.4%

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

   11. Simplified 39.4%

       \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot \left(-y4\right)\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.66 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{+20}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{-176}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-262}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-213}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y1 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-210}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ t_2 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-205}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 0.0055:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* y1 (- (* i j) (* a y2)))))
        (t_2 (* j (* t (- (* b y4) (* i y5))))))
   (if (<= y -1.6e+68)
     (* x (* y (- (* a b) (* c i))))
     (if (<= y -5.8e-88)
       t_1
       (if (<= y -1.05e-221)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= y 3.2e-241)
           t_1
           (if (<= y 7.6e-205)
             t_2
             (if (<= y 0.0055)
               t_1
               (if (<= y 1.75e+86)
                 t_2
                 (* y (* y3 (- (* c y4) (* a y5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (y1 * ((i * j) - (a * y2)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (y <= -1.6e+68) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y <= -5.8e-88) {
		tmp = t_1;
	} else if (y <= -1.05e-221) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y <= 3.2e-241) {
		tmp = t_1;
	} else if (y <= 7.6e-205) {
		tmp = t_2;
	} else if (y <= 0.0055) {
		tmp = t_1;
	} else if (y <= 1.75e+86) {
		tmp = t_2;
	} else {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y1 * ((i * j) - (a * y2)))
    t_2 = j * (t * ((b * y4) - (i * y5)))
    if (y <= (-1.6d+68)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y <= (-5.8d-88)) then
        tmp = t_1
    else if (y <= (-1.05d-221)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y <= 3.2d-241) then
        tmp = t_1
    else if (y <= 7.6d-205) then
        tmp = t_2
    else if (y <= 0.0055d0) then
        tmp = t_1
    else if (y <= 1.75d+86) then
        tmp = t_2
    else
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (y1 * ((i * j) - (a * y2)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (y <= -1.6e+68) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y <= -5.8e-88) {
		tmp = t_1;
	} else if (y <= -1.05e-221) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y <= 3.2e-241) {
		tmp = t_1;
	} else if (y <= 7.6e-205) {
		tmp = t_2;
	} else if (y <= 0.0055) {
		tmp = t_1;
	} else if (y <= 1.75e+86) {
		tmp = t_2;
	} else {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (y1 * ((i * j) - (a * y2)))
	t_2 = j * (t * ((b * y4) - (i * y5)))
	tmp = 0
	if y <= -1.6e+68:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y <= -5.8e-88:
		tmp = t_1
	elif y <= -1.05e-221:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y <= 3.2e-241:
		tmp = t_1
	elif y <= 7.6e-205:
		tmp = t_2
	elif y <= 0.0055:
		tmp = t_1
	elif y <= 1.75e+86:
		tmp = t_2
	else:
		tmp = y * (y3 * ((c * y4) - (a * 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(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))))
	t_2 = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	tmp = 0.0
	if (y <= -1.6e+68)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y <= -5.8e-88)
		tmp = t_1;
	elseif (y <= -1.05e-221)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y <= 3.2e-241)
		tmp = t_1;
	elseif (y <= 7.6e-205)
		tmp = t_2;
	elseif (y <= 0.0055)
		tmp = t_1;
	elseif (y <= 1.75e+86)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (y1 * ((i * j) - (a * y2)));
	t_2 = j * (t * ((b * y4) - (i * y5)));
	tmp = 0.0;
	if (y <= -1.6e+68)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y <= -5.8e-88)
		tmp = t_1;
	elseif (y <= -1.05e-221)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y <= 3.2e-241)
		tmp = t_1;
	elseif (y <= 7.6e-205)
		tmp = t_2;
	elseif (y <= 0.0055)
		tmp = t_1;
	elseif (y <= 1.75e+86)
		tmp = t_2;
	else
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+68], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-88], t$95$1, If[LessEqual[y, -1.05e-221], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-241], t$95$1, If[LessEqual[y, 7.6e-205], t$95$2, If[LessEqual[y, 0.0055], t$95$1, If[LessEqual[y, 1.75e+86], t$95$2, N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.59999999999999997e68

   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 y5 around 0 17.8%

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

   4. Taylor expanded in x around inf 40.6%

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

   5. Taylor expanded in y around inf 49.8%

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

   if -1.59999999999999997e68 < y < -5.8000000000000003e-88 or -1.05e-221 < y < 3.2e-241 or 7.59999999999999983e-205 < y < 0.0054999999999999997

   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 y1 around -inf 47.5%

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

      1. mul-1-neg 47.5%

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

      2. distribute-rgt-neg-in 47.5%

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

      3. +-commutative 47.5%

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

      4. mul-1-neg 47.5%

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

      5. unsub-neg 47.5%

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

      6. *-commutative 47.5%

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

      7. *-commutative 47.5%

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

      8. *-commutative 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in x around inf 47.9%

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

   if -5.8000000000000003e-88 < y < -1.05e-221

   1. Initial program 42.3%

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

   3. Taylor expanded in y2 around inf 44.4%

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

      1. *-commutative 44.4%

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

   5. Simplified 44.4%

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

   6. Taylor expanded in x around inf 43.3%

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

      1. *-commutative 43.3%

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

   8. Simplified 43.3%

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

   if 3.2e-241 < y < 7.59999999999999983e-205 or 0.0054999999999999997 < y < 1.75000000000000009e86

   1. Initial program 26.8%

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

   3. Taylor expanded in j around inf 50.1%

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

      1. +-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in t around inf 54.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.2%

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

   8. Simplified 54.2%

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

   if 1.75000000000000009e86 < y

   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 y2 around inf 37.8%

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

      1. *-commutative 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in y around inf 44.0%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-205}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 0.0055:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+86}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ t_2 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-205}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 0.0245:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* y1 (- (* i j) (* a y2)))))
        (t_2 (* j (* t (- (* b y4) (* i y5))))))
   (if (<= y -1.8e+63)
     (* x (* y (- (* a b) (* c i))))
     (if (<= y -6.7e-88)
       t_1
       (if (<= y -1e-221)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= y 2.8e-241)
           t_1
           (if (<= y 3.5e-205)
             t_2
             (if (<= y 0.0245)
               t_1
               (if (<= y 7.6e+81)
                 t_2
                 (* (- (* c y4) (* a y5)) (* y 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 * (y1 * ((i * j) - (a * y2)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (y <= -1.8e+63) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y <= -6.7e-88) {
		tmp = t_1;
	} else if (y <= -1e-221) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y <= 2.8e-241) {
		tmp = t_1;
	} else if (y <= 3.5e-205) {
		tmp = t_2;
	} else if (y <= 0.0245) {
		tmp = t_1;
	} else if (y <= 7.6e+81) {
		tmp = t_2;
	} else {
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y1 * ((i * j) - (a * y2)))
    t_2 = j * (t * ((b * y4) - (i * y5)))
    if (y <= (-1.8d+63)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y <= (-6.7d-88)) then
        tmp = t_1
    else if (y <= (-1d-221)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y <= 2.8d-241) then
        tmp = t_1
    else if (y <= 3.5d-205) then
        tmp = t_2
    else if (y <= 0.0245d0) then
        tmp = t_1
    else if (y <= 7.6d+81) then
        tmp = t_2
    else
        tmp = ((c * y4) - (a * y5)) * (y * 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 * (y1 * ((i * j) - (a * y2)));
	double t_2 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (y <= -1.8e+63) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y <= -6.7e-88) {
		tmp = t_1;
	} else if (y <= -1e-221) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y <= 2.8e-241) {
		tmp = t_1;
	} else if (y <= 3.5e-205) {
		tmp = t_2;
	} else if (y <= 0.0245) {
		tmp = t_1;
	} else if (y <= 7.6e+81) {
		tmp = t_2;
	} else {
		tmp = ((c * y4) - (a * y5)) * (y * 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 * (y1 * ((i * j) - (a * y2)))
	t_2 = j * (t * ((b * y4) - (i * y5)))
	tmp = 0
	if y <= -1.8e+63:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y <= -6.7e-88:
		tmp = t_1
	elif y <= -1e-221:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y <= 2.8e-241:
		tmp = t_1
	elif y <= 3.5e-205:
		tmp = t_2
	elif y <= 0.0245:
		tmp = t_1
	elif y <= 7.6e+81:
		tmp = t_2
	else:
		tmp = ((c * y4) - (a * y5)) * (y * 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(y1 * Float64(Float64(i * j) - Float64(a * y2))))
	t_2 = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	tmp = 0.0
	if (y <= -1.8e+63)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y <= -6.7e-88)
		tmp = t_1;
	elseif (y <= -1e-221)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y <= 2.8e-241)
		tmp = t_1;
	elseif (y <= 3.5e-205)
		tmp = t_2;
	elseif (y <= 0.0245)
		tmp = t_1;
	elseif (y <= 7.6e+81)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(c * y4) - Float64(a * y5)) * Float64(y * 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 * (y1 * ((i * j) - (a * y2)));
	t_2 = j * (t * ((b * y4) - (i * y5)));
	tmp = 0.0;
	if (y <= -1.8e+63)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y <= -6.7e-88)
		tmp = t_1;
	elseif (y <= -1e-221)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y <= 2.8e-241)
		tmp = t_1;
	elseif (y <= 3.5e-205)
		tmp = t_2;
	elseif (y <= 0.0245)
		tmp = t_1;
	elseif (y <= 7.6e+81)
		tmp = t_2;
	else
		tmp = ((c * y4) - (a * y5)) * (y * 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[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+63], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.7e-88], t$95$1, If[LessEqual[y, -1e-221], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-241], t$95$1, If[LessEqual[y, 3.5e-205], t$95$2, If[LessEqual[y, 0.0245], t$95$1, If[LessEqual[y, 7.6e+81], t$95$2, N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * N[(y * y3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.79999999999999999e63

   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 y5 around 0 17.8%

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

   4. Taylor expanded in x around inf 40.6%

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

   5. Taylor expanded in y around inf 49.8%

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

   if -1.79999999999999999e63 < y < -6.69999999999999968e-88 or -1.00000000000000002e-221 < y < 2.7999999999999999e-241 or 3.5e-205 < y < 0.024500000000000001

   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 y1 around -inf 47.5%

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

      1. mul-1-neg 47.5%

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

      2. distribute-rgt-neg-in 47.5%

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

      3. +-commutative 47.5%

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

      4. mul-1-neg 47.5%

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

      5. unsub-neg 47.5%

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

      6. *-commutative 47.5%

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

      7. *-commutative 47.5%

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

      8. *-commutative 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in x around inf 47.9%

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

   if -6.69999999999999968e-88 < y < -1.00000000000000002e-221

   1. Initial program 42.3%

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

   3. Taylor expanded in y2 around inf 44.4%

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

      1. *-commutative 44.4%

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

   5. Simplified 44.4%

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

   6. Taylor expanded in x around inf 43.3%

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

      1. *-commutative 43.3%

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

   8. Simplified 43.3%

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

   if 2.7999999999999999e-241 < y < 3.5e-205 or 0.024500000000000001 < y < 7.599999999999999e81

   1. Initial program 26.8%

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

   3. Taylor expanded in j around inf 50.1%

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

      1. +-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in t around inf 54.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.2%

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

   8. Simplified 54.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - y5 \cdot i\right)\right)} \]

   if 7.599999999999999e81 < y

   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 y2 around inf 37.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 37.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 37.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 44.0%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 46.4%

         \[\leadsto \color{blue}{\left(y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)} \]

      2. *-commutative 46.4%

         \[\leadsto \color{blue}{\left(y3 \cdot y\right)} \cdot \left(c \cdot y4 - a \cdot y5\right) \]

      3. *-commutative 46.4%

         \[\leadsto \left(y3 \cdot y\right) \cdot \left(\color{blue}{y4 \cdot c} - a \cdot y5\right) \]

      4. *-commutative 46.4%

         \[\leadsto \left(y3 \cdot y\right) \cdot \left(y4 \cdot c - \color{blue}{y5 \cdot a}\right) \]

   8. Simplified 46.4%

      \[\leadsto \color{blue}{\left(y3 \cdot y\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-205}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 0.0245:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ t_2 := x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-241}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.0085:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3\right)\\ \end{array} \end{array} \]

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)))))
        (t_2 (* x (* y1 (- (* i j) (* a y2))))))
   (if (<= y -9e-5)
     (* x (* y (- (* a b) (* c i))))
     (if (<= y -1.5e-116)
       (* t (* y2 (- (* a y5) (* c y4))))
       (if (<= y -1.04e-221)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= y 6e-241)
           t_2
           (if (<= y 7.2e-205)
             t_1
             (if (<= y 0.0085)
               t_2
               (if (<= y 2.9e+86)
                 t_1
                 (* (- (* c y4) (* a y5)) (* y 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 = j * (t * ((b * y4) - (i * y5)));
	double t_2 = x * (y1 * ((i * j) - (a * y2)));
	double tmp;
	if (y <= -9e-5) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y <= -1.5e-116) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (y <= -1.04e-221) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y <= 6e-241) {
		tmp = t_2;
	} else if (y <= 7.2e-205) {
		tmp = t_1;
	} else if (y <= 0.0085) {
		tmp = t_2;
	} else if (y <= 2.9e+86) {
		tmp = t_1;
	} else {
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (t * ((b * y4) - (i * y5)))
    t_2 = x * (y1 * ((i * j) - (a * y2)))
    if (y <= (-9d-5)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y <= (-1.5d-116)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (y <= (-1.04d-221)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y <= 6d-241) then
        tmp = t_2
    else if (y <= 7.2d-205) then
        tmp = t_1
    else if (y <= 0.0085d0) then
        tmp = t_2
    else if (y <= 2.9d+86) then
        tmp = t_1
    else
        tmp = ((c * y4) - (a * y5)) * (y * 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 = j * (t * ((b * y4) - (i * y5)));
	double t_2 = x * (y1 * ((i * j) - (a * y2)));
	double tmp;
	if (y <= -9e-5) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y <= -1.5e-116) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (y <= -1.04e-221) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y <= 6e-241) {
		tmp = t_2;
	} else if (y <= 7.2e-205) {
		tmp = t_1;
	} else if (y <= 0.0085) {
		tmp = t_2;
	} else if (y <= 2.9e+86) {
		tmp = t_1;
	} else {
		tmp = ((c * y4) - (a * y5)) * (y * y3);
	}
	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)))
	t_2 = x * (y1 * ((i * j) - (a * y2)))
	tmp = 0
	if y <= -9e-5:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y <= -1.5e-116:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif y <= -1.04e-221:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y <= 6e-241:
		tmp = t_2
	elif y <= 7.2e-205:
		tmp = t_1
	elif y <= 0.0085:
		tmp = t_2
	elif y <= 2.9e+86:
		tmp = t_1
	else:
		tmp = ((c * y4) - (a * y5)) * (y * 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(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	t_2 = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))))
	tmp = 0.0
	if (y <= -9e-5)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y <= -1.5e-116)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (y <= -1.04e-221)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y <= 6e-241)
		tmp = t_2;
	elseif (y <= 7.2e-205)
		tmp = t_1;
	elseif (y <= 0.0085)
		tmp = t_2;
	elseif (y <= 2.9e+86)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(c * y4) - Float64(a * y5)) * Float64(y * 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 = j * (t * ((b * y4) - (i * y5)));
	t_2 = x * (y1 * ((i * j) - (a * y2)));
	tmp = 0.0;
	if (y <= -9e-5)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y <= -1.5e-116)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (y <= -1.04e-221)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y <= 6e-241)
		tmp = t_2;
	elseif (y <= 7.2e-205)
		tmp = t_1;
	elseif (y <= 0.0085)
		tmp = t_2;
	elseif (y <= 2.9e+86)
		tmp = t_1;
	else
		tmp = ((c * y4) - (a * y5)) * (y * 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[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-5], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e-116], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.04e-221], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-241], t$95$2, If[LessEqual[y, 7.2e-205], t$95$1, If[LessEqual[y, 0.0085], t$95$2, If[LessEqual[y, 2.9e+86], t$95$1, N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * N[(y * y3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -9.00000000000000057e-5

   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 y5 around 0 18.7%

      \[\leadsto \color{blue}{\left(b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) + \left(y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) - \left(c \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 47.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in y around inf 49.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if -9.00000000000000057e-5 < y < -1.50000000000000013e-116

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 29.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 29.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 29.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in t around inf 49.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 49.0%

         \[\leadsto \color{blue}{-t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. *-commutative 49.0%

         \[\leadsto -t \cdot \left(y2 \cdot \left(\color{blue}{y4 \cdot c} - a \cdot y5\right)\right) \]

      3. *-commutative 49.0%

         \[\leadsto -t \cdot \left(y2 \cdot \left(y4 \cdot c - \color{blue}{y5 \cdot a}\right)\right) \]

   8. Simplified 49.0%

      \[\leadsto \color{blue}{-t \cdot \left(y2 \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   if -1.50000000000000013e-116 < y < -1.0399999999999999e-221

   1. Initial program 40.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 46.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 46.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in x around inf 49.0%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 49.0%

         \[\leadsto x \cdot \left(y2 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right)\right) \]

   8. Simplified 49.0%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - a \cdot y1\right)\right)} \]

   if -1.0399999999999999e-221 < y < 5.9999999999999998e-241 or 7.1999999999999997e-205 < y < 0.0085000000000000006

   1. Initial program 41.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 49.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 49.1%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 49.1%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 49.1%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 49.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 49.1%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 49.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 49.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 49.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 49.1%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in x around inf 45.2%

      \[\leadsto \color{blue}{x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)} \]

   if 5.9999999999999998e-241 < y < 7.1999999999999997e-205 or 0.0085000000000000006 < y < 2.8999999999999999e86

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 50.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 50.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 50.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 50.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 50.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 54.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto j \cdot \left(t \cdot \left(b \cdot y4 - \color{blue}{y5 \cdot i}\right)\right) \]

   8. Simplified 54.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - y5 \cdot i\right)\right)} \]

   if 2.8999999999999999e86 < y

   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 y2 around inf 37.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 37.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 37.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 44.0%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 46.4%

         \[\leadsto \color{blue}{\left(y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)} \]

      2. *-commutative 46.4%

         \[\leadsto \color{blue}{\left(y3 \cdot y\right)} \cdot \left(c \cdot y4 - a \cdot y5\right) \]

      3. *-commutative 46.4%

         \[\leadsto \left(y3 \cdot y\right) \cdot \left(\color{blue}{y4 \cdot c} - a \cdot y5\right) \]

      4. *-commutative 46.4%

         \[\leadsto \left(y3 \cdot y\right) \cdot \left(y4 \cdot c - \color{blue}{y5 \cdot a}\right) \]

   8. Simplified 46.4%

      \[\leadsto \color{blue}{\left(y3 \cdot y\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-205}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 0.0085:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+86}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 21.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot y5\right) \cdot \left(t \cdot \left(-j\right)\right)\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+151}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+97}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-12}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-79}:\\ \;\;\;\;i \cdot \left(\left(-k\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* i y5) (* t (- j)))))
   (if (<= a -7.8e+151)
     (* (* a y1) (* z y3))
     (if (<= a -9.2e+97)
       (* i (* k (* y y5)))
       (if (<= a -3.5e-12)
         (* y0 (* y2 (* x c)))
         (if (<= a -2.3e-170)
           (* y (* y4 (* c y3)))
           (if (<= a 5e-155)
             t_1
             (if (<= a 5.4e-79)
               (* i (* (- k) (* z y1)))
               (if (<= a 6.4e+55) t_1 (* y (* y3 (* a (- y5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y5) * (t * -j);
	double tmp;
	if (a <= -7.8e+151) {
		tmp = (a * y1) * (z * y3);
	} else if (a <= -9.2e+97) {
		tmp = i * (k * (y * y5));
	} else if (a <= -3.5e-12) {
		tmp = y0 * (y2 * (x * c));
	} else if (a <= -2.3e-170) {
		tmp = y * (y4 * (c * y3));
	} else if (a <= 5e-155) {
		tmp = t_1;
	} else if (a <= 5.4e-79) {
		tmp = i * (-k * (z * y1));
	} else if (a <= 6.4e+55) {
		tmp = t_1;
	} else {
		tmp = y * (y3 * (a * -y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (i * y5) * (t * -j)
    if (a <= (-7.8d+151)) then
        tmp = (a * y1) * (z * y3)
    else if (a <= (-9.2d+97)) then
        tmp = i * (k * (y * y5))
    else if (a <= (-3.5d-12)) then
        tmp = y0 * (y2 * (x * c))
    else if (a <= (-2.3d-170)) then
        tmp = y * (y4 * (c * y3))
    else if (a <= 5d-155) then
        tmp = t_1
    else if (a <= 5.4d-79) then
        tmp = i * (-k * (z * y1))
    else if (a <= 6.4d+55) then
        tmp = t_1
    else
        tmp = y * (y3 * (a * -y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y5) * (t * -j);
	double tmp;
	if (a <= -7.8e+151) {
		tmp = (a * y1) * (z * y3);
	} else if (a <= -9.2e+97) {
		tmp = i * (k * (y * y5));
	} else if (a <= -3.5e-12) {
		tmp = y0 * (y2 * (x * c));
	} else if (a <= -2.3e-170) {
		tmp = y * (y4 * (c * y3));
	} else if (a <= 5e-155) {
		tmp = t_1;
	} else if (a <= 5.4e-79) {
		tmp = i * (-k * (z * y1));
	} else if (a <= 6.4e+55) {
		tmp = t_1;
	} else {
		tmp = y * (y3 * (a * -y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y5) * (t * -j)
	tmp = 0
	if a <= -7.8e+151:
		tmp = (a * y1) * (z * y3)
	elif a <= -9.2e+97:
		tmp = i * (k * (y * y5))
	elif a <= -3.5e-12:
		tmp = y0 * (y2 * (x * c))
	elif a <= -2.3e-170:
		tmp = y * (y4 * (c * y3))
	elif a <= 5e-155:
		tmp = t_1
	elif a <= 5.4e-79:
		tmp = i * (-k * (z * y1))
	elif a <= 6.4e+55:
		tmp = t_1
	else:
		tmp = y * (y3 * (a * -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(i * y5) * Float64(t * Float64(-j)))
	tmp = 0.0
	if (a <= -7.8e+151)
		tmp = Float64(Float64(a * y1) * Float64(z * y3));
	elseif (a <= -9.2e+97)
		tmp = Float64(i * Float64(k * Float64(y * y5)));
	elseif (a <= -3.5e-12)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (a <= -2.3e-170)
		tmp = Float64(y * Float64(y4 * Float64(c * y3)));
	elseif (a <= 5e-155)
		tmp = t_1;
	elseif (a <= 5.4e-79)
		tmp = Float64(i * Float64(Float64(-k) * Float64(z * y1)));
	elseif (a <= 6.4e+55)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-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 = (i * y5) * (t * -j);
	tmp = 0.0;
	if (a <= -7.8e+151)
		tmp = (a * y1) * (z * y3);
	elseif (a <= -9.2e+97)
		tmp = i * (k * (y * y5));
	elseif (a <= -3.5e-12)
		tmp = y0 * (y2 * (x * c));
	elseif (a <= -2.3e-170)
		tmp = y * (y4 * (c * y3));
	elseif (a <= 5e-155)
		tmp = t_1;
	elseif (a <= 5.4e-79)
		tmp = i * (-k * (z * y1));
	elseif (a <= 6.4e+55)
		tmp = t_1;
	else
		tmp = y * (y3 * (a * -y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(i * y5), $MachinePrecision] * N[(t * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e+151], N[(N[(a * y1), $MachinePrecision] * N[(z * y3), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.2e+97], N[(i * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.5e-12], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.3e-170], N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-155], t$95$1, If[LessEqual[a, 5.4e-79], N[(i * N[((-k) * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e+55], t$95$1, N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -7.79999999999999952e151

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 53.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 53.2%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 53.2%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 53.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 53.2%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 53.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 53.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 53.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 53.2%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 53.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around inf 37.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 49.3%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

      2. *-commutative 49.3%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z\right) \]

   9. Simplified 49.3%

      \[\leadsto \color{blue}{\left(y1 \cdot a\right) \cdot \left(y3 \cdot z\right)} \]

   if -7.79999999999999952e151 < a < -9.20000000000000022e97

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 40.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 60.8%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 35.1%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 35.1%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 35.1%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around 0 53.9%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 53.9%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)} \]

      2. *-commutative 53.9%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(k \cdot \left(y \cdot y5\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 53.9%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

   9. Simplified 53.9%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

   if -9.20000000000000022e97 < a < -3.5e-12

   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 y2 around inf 45.4%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 45.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 45.4%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 39.4%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 39.9%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.9%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

      2. *-commutative 39.9%

         \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   9. Simplified 39.9%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   if -3.5e-12 < a < -2.29999999999999987e-170

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 42.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 42.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 42.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 31.4%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 34.4%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   9. Simplified 31.6%

      \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   if -2.29999999999999987e-170 < a < 4.9999999999999999e-155 or 5.4000000000000004e-79 < a < 6.4000000000000005e55

   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 y5 around -inf 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 37.7%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 38.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 38.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 38.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around inf 31.1%

      \[\leadsto -1 \cdot \left(\left(y5 \cdot i\right) \cdot \color{blue}{\left(j \cdot t\right)}\right) \]

   if 4.9999999999999999e-155 < a < 5.4000000000000004e-79

   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 y1 around -inf 54.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 54.3%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 54.3%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 54.3%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 54.3%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z around -inf 46.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

      2. associate-*r* 46.6%

         \[\leadsto -\color{blue}{\left(y1 \cdot z\right) \cdot \left(i \cdot k - a \cdot y3\right)} \]

      3. *-commutative 46.6%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(\color{blue}{k \cdot i} - a \cdot y3\right) \]

      4. *-commutative 46.6%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(k \cdot i - \color{blue}{y3 \cdot a}\right) \]

   8. Simplified 46.6%

      \[\leadsto \color{blue}{-\left(y1 \cdot z\right) \cdot \left(k \cdot i - y3 \cdot a\right)} \]

   9. Taylor expanded in k around inf 46.9%

      \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

   if 6.4000000000000005e55 < a

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 32.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 32.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 40.4%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around 0 42.7%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y5\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 42.7%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(-a \cdot y5\right)}\right) \]

      2. distribute-lft-neg-in 42.7%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(\left(-a\right) \cdot y5\right)}\right) \]

      3. *-commutative 42.7%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-a\right)\right)}\right) \]

   9. Simplified 42.7%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-a\right)\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+151}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+97}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-12}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-155}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(t \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-79}:\\ \;\;\;\;i \cdot \left(\left(-k\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+55}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(t \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 21.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+151}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+99}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-8}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-152}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(t \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-107}:\\ \;\;\;\;i \cdot \left(\left(-k\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-18}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -6.8e+151)
   (* (* a y1) (* z y3))
   (if (<= a -6.5e+99)
     (* i (* k (* y y5)))
     (if (<= a -5.8e-8)
       (* y0 (* y2 (* x c)))
       (if (<= a -1.85e-171)
         (* y (* y4 (* c y3)))
         (if (<= a 2.8e-152)
           (* (* i y5) (* t (- j)))
           (if (<= a 2.2e-107)
             (* i (* (- k) (* z y1)))
             (if (<= a 3.2e-18)
               (* (* i y5) (* y k))
               (* y (* y3 (* a (- y5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -6.8e+151) {
		tmp = (a * y1) * (z * y3);
	} else if (a <= -6.5e+99) {
		tmp = i * (k * (y * y5));
	} else if (a <= -5.8e-8) {
		tmp = y0 * (y2 * (x * c));
	} else if (a <= -1.85e-171) {
		tmp = y * (y4 * (c * y3));
	} else if (a <= 2.8e-152) {
		tmp = (i * y5) * (t * -j);
	} else if (a <= 2.2e-107) {
		tmp = i * (-k * (z * y1));
	} else if (a <= 3.2e-18) {
		tmp = (i * y5) * (y * k);
	} else {
		tmp = y * (y3 * (a * -y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-6.8d+151)) then
        tmp = (a * y1) * (z * y3)
    else if (a <= (-6.5d+99)) then
        tmp = i * (k * (y * y5))
    else if (a <= (-5.8d-8)) then
        tmp = y0 * (y2 * (x * c))
    else if (a <= (-1.85d-171)) then
        tmp = y * (y4 * (c * y3))
    else if (a <= 2.8d-152) then
        tmp = (i * y5) * (t * -j)
    else if (a <= 2.2d-107) then
        tmp = i * (-k * (z * y1))
    else if (a <= 3.2d-18) then
        tmp = (i * y5) * (y * k)
    else
        tmp = y * (y3 * (a * -y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -6.8e+151) {
		tmp = (a * y1) * (z * y3);
	} else if (a <= -6.5e+99) {
		tmp = i * (k * (y * y5));
	} else if (a <= -5.8e-8) {
		tmp = y0 * (y2 * (x * c));
	} else if (a <= -1.85e-171) {
		tmp = y * (y4 * (c * y3));
	} else if (a <= 2.8e-152) {
		tmp = (i * y5) * (t * -j);
	} else if (a <= 2.2e-107) {
		tmp = i * (-k * (z * y1));
	} else if (a <= 3.2e-18) {
		tmp = (i * y5) * (y * k);
	} else {
		tmp = y * (y3 * (a * -y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -6.8e+151:
		tmp = (a * y1) * (z * y3)
	elif a <= -6.5e+99:
		tmp = i * (k * (y * y5))
	elif a <= -5.8e-8:
		tmp = y0 * (y2 * (x * c))
	elif a <= -1.85e-171:
		tmp = y * (y4 * (c * y3))
	elif a <= 2.8e-152:
		tmp = (i * y5) * (t * -j)
	elif a <= 2.2e-107:
		tmp = i * (-k * (z * y1))
	elif a <= 3.2e-18:
		tmp = (i * y5) * (y * k)
	else:
		tmp = y * (y3 * (a * -y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (a <= -6.8e+151)
		tmp = Float64(Float64(a * y1) * Float64(z * y3));
	elseif (a <= -6.5e+99)
		tmp = Float64(i * Float64(k * Float64(y * y5)));
	elseif (a <= -5.8e-8)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (a <= -1.85e-171)
		tmp = Float64(y * Float64(y4 * Float64(c * y3)));
	elseif (a <= 2.8e-152)
		tmp = Float64(Float64(i * y5) * Float64(t * Float64(-j)));
	elseif (a <= 2.2e-107)
		tmp = Float64(i * Float64(Float64(-k) * Float64(z * y1)));
	elseif (a <= 3.2e-18)
		tmp = Float64(Float64(i * y5) * Float64(y * k));
	else
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -6.8e+151)
		tmp = (a * y1) * (z * y3);
	elseif (a <= -6.5e+99)
		tmp = i * (k * (y * y5));
	elseif (a <= -5.8e-8)
		tmp = y0 * (y2 * (x * c));
	elseif (a <= -1.85e-171)
		tmp = y * (y4 * (c * y3));
	elseif (a <= 2.8e-152)
		tmp = (i * y5) * (t * -j);
	elseif (a <= 2.2e-107)
		tmp = i * (-k * (z * y1));
	elseif (a <= 3.2e-18)
		tmp = (i * y5) * (y * k);
	else
		tmp = y * (y3 * (a * -y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -6.8e+151], N[(N[(a * y1), $MachinePrecision] * N[(z * y3), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.5e+99], N[(i * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.8e-8], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.85e-171], N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-152], N[(N[(i * y5), $MachinePrecision] * N[(t * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-107], N[(i * N[((-k) * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-18], N[(N[(i * y5), $MachinePrecision] * N[(y * k), $MachinePrecision]), $MachinePrecision], N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -6.7999999999999999e151

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 53.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 53.2%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 53.2%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 53.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 53.2%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 53.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 53.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 53.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 53.2%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 53.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around inf 37.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 49.3%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

      2. *-commutative 49.3%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z\right) \]

   9. Simplified 49.3%

      \[\leadsto \color{blue}{\left(y1 \cdot a\right) \cdot \left(y3 \cdot z\right)} \]

   if -6.7999999999999999e151 < a < -6.5000000000000004e99

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 40.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 60.8%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 35.1%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 35.1%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 35.1%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around 0 53.9%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 53.9%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)} \]

      2. *-commutative 53.9%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(k \cdot \left(y \cdot y5\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 53.9%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

   9. Simplified 53.9%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

   if -6.5000000000000004e99 < a < -5.8000000000000003e-8

   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 y2 around inf 45.4%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 45.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 45.4%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 39.4%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 39.9%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.9%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

      2. *-commutative 39.9%

         \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   9. Simplified 39.9%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   if -5.8000000000000003e-8 < a < -1.85000000000000006e-171

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 42.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 42.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 42.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 31.4%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 34.4%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   9. Simplified 31.6%

      \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   if -1.85000000000000006e-171 < a < 2.79999999999999984e-152

   1. Initial program 36.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 48.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 40.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 40.8%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 40.8%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 40.8%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around inf 31.1%

      \[\leadsto -1 \cdot \left(\left(y5 \cdot i\right) \cdot \color{blue}{\left(j \cdot t\right)}\right) \]

   if 2.79999999999999984e-152 < a < 2.20000000000000012e-107

   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 y1 around -inf 45.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 45.1%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 45.1%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 45.1%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 45.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 45.1%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 45.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 45.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 45.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 45.1%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z around -inf 55.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 55.8%

         \[\leadsto \color{blue}{-y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

      2. associate-*r* 55.8%

         \[\leadsto -\color{blue}{\left(y1 \cdot z\right) \cdot \left(i \cdot k - a \cdot y3\right)} \]

      3. *-commutative 55.8%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(\color{blue}{k \cdot i} - a \cdot y3\right) \]

      4. *-commutative 55.8%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(k \cdot i - \color{blue}{y3 \cdot a}\right) \]

   8. Simplified 55.8%

      \[\leadsto \color{blue}{-\left(y1 \cdot z\right) \cdot \left(k \cdot i - y3 \cdot a\right)} \]

   9. Taylor expanded in k around inf 67.2%

      \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

   if 2.20000000000000012e-107 < a < 3.1999999999999999e-18

   1. Initial program 40.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 53.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 40.4%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 40.5%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 40.5%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 40.5%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around 0 35.0%

      \[\leadsto -1 \cdot \left(\left(y5 \cdot i\right) \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 35.0%

         \[\leadsto -1 \cdot \left(\left(y5 \cdot i\right) \cdot \color{blue}{\left(-k \cdot y\right)}\right) \]

      2. distribute-lft-neg-out 35.0%

         \[\leadsto -1 \cdot \left(\left(y5 \cdot i\right) \cdot \color{blue}{\left(\left(-k\right) \cdot y\right)}\right) \]

      3. *-commutative 35.0%

         \[\leadsto -1 \cdot \left(\left(y5 \cdot i\right) \cdot \color{blue}{\left(y \cdot \left(-k\right)\right)}\right) \]

   9. Simplified 35.0%

      \[\leadsto -1 \cdot \left(\left(y5 \cdot i\right) \cdot \color{blue}{\left(y \cdot \left(-k\right)\right)}\right) \]

   if 3.1999999999999999e-18 < a

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 38.3%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 38.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 38.3%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 38.1%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around 0 36.5%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y5\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 36.5%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(-a \cdot y5\right)}\right) \]

      2. distribute-lft-neg-in 36.5%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(\left(-a\right) \cdot y5\right)}\right) \]

      3. *-commutative 36.5%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-a\right)\right)}\right) \]

   9. Simplified 36.5%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-a\right)\right)}\right) \]
3. Recombined 8 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+151}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+99}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-8}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-152}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(t \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-107}:\\ \;\;\;\;i \cdot \left(\left(-k\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-18}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ t_2 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{if}\;y2 \leq -2.8 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -1.06 \cdot 10^{+81}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -5.6 \cdot 10^{-122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y2 \leq -4.1 \cdot 10^{-298}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y2 \leq 2.6 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (- (* z y3) (* x y2)))))
        (t_2 (* i (* y1 (- (* x j) (* z k))))))
   (if (<= y2 -2.8e+125)
     t_1
     (if (<= y2 -1.06e+81)
       (* y0 (* k (* y2 (- y5))))
       (if (<= y2 -5.6e-122)
         t_2
         (if (<= y2 -4.1e-298)
           (* i (* k (* y y5)))
           (if (<= y2 1e-97)
             t_2
             (if (<= y2 2.6e+222) t_1 (* y0 (* c (* x y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * ((z * y3) - (x * y2)));
	double t_2 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (y2 <= -2.8e+125) {
		tmp = t_1;
	} else if (y2 <= -1.06e+81) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (y2 <= -5.6e-122) {
		tmp = t_2;
	} else if (y2 <= -4.1e-298) {
		tmp = i * (k * (y * y5));
	} else if (y2 <= 1e-97) {
		tmp = t_2;
	} else if (y2 <= 2.6e+222) {
		tmp = t_1;
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y1 * ((z * y3) - (x * y2)))
    t_2 = i * (y1 * ((x * j) - (z * k)))
    if (y2 <= (-2.8d+125)) then
        tmp = t_1
    else if (y2 <= (-1.06d+81)) then
        tmp = y0 * (k * (y2 * -y5))
    else if (y2 <= (-5.6d-122)) then
        tmp = t_2
    else if (y2 <= (-4.1d-298)) then
        tmp = i * (k * (y * y5))
    else if (y2 <= 1d-97) then
        tmp = t_2
    else if (y2 <= 2.6d+222) then
        tmp = t_1
    else
        tmp = y0 * (c * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * ((z * y3) - (x * y2)));
	double t_2 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (y2 <= -2.8e+125) {
		tmp = t_1;
	} else if (y2 <= -1.06e+81) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (y2 <= -5.6e-122) {
		tmp = t_2;
	} else if (y2 <= -4.1e-298) {
		tmp = i * (k * (y * y5));
	} else if (y2 <= 1e-97) {
		tmp = t_2;
	} else if (y2 <= 2.6e+222) {
		tmp = t_1;
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * ((z * y3) - (x * y2)))
	t_2 = i * (y1 * ((x * j) - (z * k)))
	tmp = 0
	if y2 <= -2.8e+125:
		tmp = t_1
	elif y2 <= -1.06e+81:
		tmp = y0 * (k * (y2 * -y5))
	elif y2 <= -5.6e-122:
		tmp = t_2
	elif y2 <= -4.1e-298:
		tmp = i * (k * (y * y5))
	elif y2 <= 1e-97:
		tmp = t_2
	elif y2 <= 2.6e+222:
		tmp = t_1
	else:
		tmp = y0 * (c * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	t_2 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	tmp = 0.0
	if (y2 <= -2.8e+125)
		tmp = t_1;
	elseif (y2 <= -1.06e+81)
		tmp = Float64(y0 * Float64(k * Float64(y2 * Float64(-y5))));
	elseif (y2 <= -5.6e-122)
		tmp = t_2;
	elseif (y2 <= -4.1e-298)
		tmp = Float64(i * Float64(k * Float64(y * y5)));
	elseif (y2 <= 1e-97)
		tmp = t_2;
	elseif (y2 <= 2.6e+222)
		tmp = t_1;
	else
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * ((z * y3) - (x * y2)));
	t_2 = i * (y1 * ((x * j) - (z * k)));
	tmp = 0.0;
	if (y2 <= -2.8e+125)
		tmp = t_1;
	elseif (y2 <= -1.06e+81)
		tmp = y0 * (k * (y2 * -y5));
	elseif (y2 <= -5.6e-122)
		tmp = t_2;
	elseif (y2 <= -4.1e-298)
		tmp = i * (k * (y * y5));
	elseif (y2 <= 1e-97)
		tmp = t_2;
	elseif (y2 <= 2.6e+222)
		tmp = t_1;
	else
		tmp = y0 * (c * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.8e+125], t$95$1, If[LessEqual[y2, -1.06e+81], N[(y0 * N[(k * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.6e-122], t$95$2, If[LessEqual[y2, -4.1e-298], N[(i * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1e-97], t$95$2, If[LessEqual[y2, 2.6e+222], t$95$1, N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -2.8000000000000001e125 or 1.00000000000000004e-97 < y2 < 2.6000000000000001e222

   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 y1 around -inf 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 44.6%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 44.6%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 44.6%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 44.6%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 44.6%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 44.6%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 44.6%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 44.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 43.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if -2.8000000000000001e125 < y2 < -1.05999999999999993e81

   1. Initial program 38.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 53.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 53.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 69.8%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in k around inf 61.9%

      \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 61.9%

         \[\leadsto y0 \cdot \color{blue}{\left(-k \cdot \left(y2 \cdot y5\right)\right)} \]

   9. Simplified 61.9%

      \[\leadsto y0 \cdot \color{blue}{\left(-k \cdot \left(y2 \cdot y5\right)\right)} \]

   if -1.05999999999999993e81 < y2 < -5.5999999999999998e-122 or -4.0999999999999999e-298 < y2 < 1.00000000000000004e-97

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 42.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 42.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 42.9%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 42.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 42.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 42.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 42.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 42.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 42.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 42.9%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in i around inf 40.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if -5.5999999999999998e-122 < y2 < -4.0999999999999999e-298

   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 y5 around -inf 41.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 37.5%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 35.3%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 35.3%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 35.3%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around 0 28.6%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 28.6%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)} \]

      2. *-commutative 28.6%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(k \cdot \left(y \cdot y5\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 28.6%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

   9. Simplified 28.6%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

   if 2.6000000000000001e222 < y2

   1. Initial program 31.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 27.3%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 27.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 27.3%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 45.5%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 50.3%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.8 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.06 \cdot 10^{+81}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -5.6 \cdot 10^{-122}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -4.1 \cdot 10^{-298}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 10^{-97}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 2.6 \cdot 10^{+222}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;y5 \leq -3 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 7.6 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq 5.2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 2.2 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2.35 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (- (* z y3) (* x y2))))))
   (if (<= y5 -3e-49)
     (* j (* t (- (* b y4) (* i y5))))
     (if (<= y5 7.6e-174)
       t_1
       (if (<= y5 1.7e-104)
         (* y0 (* y2 (* x c)))
         (if (<= y5 5.2e+28)
           t_1
           (if (<= y5 2.2e+144)
             (* j (* y3 (- (* y0 y5) (* y1 y4))))
             (if (<= y5 2.35e+204) t_1 (* i (* k (* y 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 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y5 <= -3e-49) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y5 <= 7.6e-174) {
		tmp = t_1;
	} else if (y5 <= 1.7e-104) {
		tmp = y0 * (y2 * (x * c));
	} else if (y5 <= 5.2e+28) {
		tmp = t_1;
	} else if (y5 <= 2.2e+144) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y5 <= 2.35e+204) {
		tmp = t_1;
	} else {
		tmp = i * (k * (y * 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) :: tmp
    t_1 = a * (y1 * ((z * y3) - (x * y2)))
    if (y5 <= (-3d-49)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y5 <= 7.6d-174) then
        tmp = t_1
    else if (y5 <= 1.7d-104) then
        tmp = y0 * (y2 * (x * c))
    else if (y5 <= 5.2d+28) then
        tmp = t_1
    else if (y5 <= 2.2d+144) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (y5 <= 2.35d+204) then
        tmp = t_1
    else
        tmp = i * (k * (y * 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 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y5 <= -3e-49) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y5 <= 7.6e-174) {
		tmp = t_1;
	} else if (y5 <= 1.7e-104) {
		tmp = y0 * (y2 * (x * c));
	} else if (y5 <= 5.2e+28) {
		tmp = t_1;
	} else if (y5 <= 2.2e+144) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y5 <= 2.35e+204) {
		tmp = t_1;
	} else {
		tmp = i * (k * (y * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * ((z * y3) - (x * y2)))
	tmp = 0
	if y5 <= -3e-49:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y5 <= 7.6e-174:
		tmp = t_1
	elif y5 <= 1.7e-104:
		tmp = y0 * (y2 * (x * c))
	elif y5 <= 5.2e+28:
		tmp = t_1
	elif y5 <= 2.2e+144:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif y5 <= 2.35e+204:
		tmp = t_1
	else:
		tmp = i * (k * (y * 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(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (y5 <= -3e-49)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y5 <= 7.6e-174)
		tmp = t_1;
	elseif (y5 <= 1.7e-104)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (y5 <= 5.2e+28)
		tmp = t_1;
	elseif (y5 <= 2.2e+144)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (y5 <= 2.35e+204)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(k * Float64(y * 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 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (y5 <= -3e-49)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y5 <= 7.6e-174)
		tmp = t_1;
	elseif (y5 <= 1.7e-104)
		tmp = y0 * (y2 * (x * c));
	elseif (y5 <= 5.2e+28)
		tmp = t_1;
	elseif (y5 <= 2.2e+144)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (y5 <= 2.35e+204)
		tmp = t_1;
	else
		tmp = i * (k * (y * 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[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3e-49], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.6e-174], t$95$1, If[LessEqual[y5, 1.7e-104], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5.2e+28], t$95$1, If[LessEqual[y5, 2.2e+144], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.35e+204], t$95$1, N[(i * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -3e-49

   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 j around inf 49.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 49.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 49.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 49.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 49.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 46.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 46.2%

         \[\leadsto j \cdot \left(t \cdot \left(b \cdot y4 - \color{blue}{y5 \cdot i}\right)\right) \]

   8. Simplified 46.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - y5 \cdot i\right)\right)} \]

   if -3e-49 < y5 < 7.60000000000000042e-174 or 1.70000000000000008e-104 < y5 < 5.2000000000000004e28 or 2.19999999999999988e144 < y5 < 2.3500000000000001e204

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 41.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 41.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 41.9%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 41.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 41.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 41.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 41.9%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 40.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 7.60000000000000042e-174 < y5 < 1.70000000000000008e-104

   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 y2 around inf 33.9%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 33.9%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 33.9%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 28.6%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 34.8%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 41.2%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

      2. *-commutative 41.2%

         \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   9. Simplified 41.2%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   if 5.2000000000000004e28 < y5 < 2.19999999999999988e144

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 31.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 31.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 31.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 31.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 31.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 31.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 47.2%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.2%

         \[\leadsto j \cdot \left(y3 \cdot \left(\color{blue}{y5 \cdot y0} - y1 \cdot y4\right)\right) \]

      2. *-commutative 47.2%

         \[\leadsto j \cdot \left(y3 \cdot \left(y5 \cdot y0 - \color{blue}{y4 \cdot y1}\right)\right) \]

   8. Simplified 47.2%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0 - y4 \cdot y1\right)\right)} \]

   if 2.3500000000000001e204 < y5

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 80.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 80.2%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 70.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 70.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 70.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around 0 61.8%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 61.8%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)} \]

      2. *-commutative 61.8%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(k \cdot \left(y \cdot y5\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 61.8%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

   9. Simplified 61.8%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 7.6 \cdot 10^{-174}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq 5.2 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.2 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2.35 \cdot 10^{+204}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 5.6 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 5 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;i \cdot \left(z \cdot \left(k \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 4.3 \cdot 10^{+203}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -5.6e-55)
   (* j (* t (- (* b y4) (* i y5))))
   (if (<= y5 5.6e-192)
     (* x (* y1 (- (* i j) (* a y2))))
     (if (<= y5 5e+41)
       (* x (* y2 (- (* c y0) (* a y1))))
       (if (<= y5 9.5e+54)
         (* i (* z (* k (- y1))))
         (if (<= y5 2e+144)
           (* j (* y3 (- (* y0 y5) (* y1 y4))))
           (if (<= y5 4.3e+203)
             (* a (* y1 (- (* z y3) (* x y2))))
             (* i (* k (* y y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -5.6e-55) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y5 <= 5.6e-192) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y5 <= 5e+41) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y5 <= 9.5e+54) {
		tmp = i * (z * (k * -y1));
	} else if (y5 <= 2e+144) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y5 <= 4.3e+203) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = i * (k * (y * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-5.6d-55)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y5 <= 5.6d-192) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else if (y5 <= 5d+41) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y5 <= 9.5d+54) then
        tmp = i * (z * (k * -y1))
    else if (y5 <= 2d+144) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (y5 <= 4.3d+203) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else
        tmp = i * (k * (y * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -5.6e-55) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y5 <= 5.6e-192) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y5 <= 5e+41) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y5 <= 9.5e+54) {
		tmp = i * (z * (k * -y1));
	} else if (y5 <= 2e+144) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y5 <= 4.3e+203) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = i * (k * (y * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -5.6e-55:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y5 <= 5.6e-192:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	elif y5 <= 5e+41:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y5 <= 9.5e+54:
		tmp = i * (z * (k * -y1))
	elif y5 <= 2e+144:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif y5 <= 4.3e+203:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	else:
		tmp = i * (k * (y * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -5.6e-55)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y5 <= 5.6e-192)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	elseif (y5 <= 5e+41)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y5 <= 9.5e+54)
		tmp = Float64(i * Float64(z * Float64(k * Float64(-y1))));
	elseif (y5 <= 2e+144)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (y5 <= 4.3e+203)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(i * Float64(k * Float64(y * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -5.6e-55)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y5 <= 5.6e-192)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	elseif (y5 <= 5e+41)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y5 <= 9.5e+54)
		tmp = i * (z * (k * -y1));
	elseif (y5 <= 2e+144)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (y5 <= 4.3e+203)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	else
		tmp = i * (k * (y * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -5.6e-55], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5.6e-192], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5e+41], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9.5e+54], N[(i * N[(z * N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2e+144], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.3e+203], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y5 < -5.59999999999999968e-55

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 49.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 49.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 49.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 49.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 49.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 44.4%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 44.4%

         \[\leadsto j \cdot \left(t \cdot \left(b \cdot y4 - \color{blue}{y5 \cdot i}\right)\right) \]

   8. Simplified 44.4%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - y5 \cdot i\right)\right)} \]

   if -5.59999999999999968e-55 < y5 < 5.60000000000000007e-192

   1. Initial program 35.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 45.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 45.0%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 45.0%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 45.0%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 45.0%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 45.0%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 45.0%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 45.0%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 45.0%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 45.0%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in x around inf 41.5%

      \[\leadsto \color{blue}{x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)} \]

   if 5.60000000000000007e-192 < y5 < 5.00000000000000022e41

   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 y2 around inf 45.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 45.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 45.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in x around inf 38.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right)\right) \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - a \cdot y1\right)\right)} \]

   if 5.00000000000000022e41 < y5 < 9.4999999999999999e54

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 67.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 67.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 67.7%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 67.7%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 67.7%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 67.7%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 67.7%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 67.7%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 67.7%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 67.7%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z around -inf 51.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

      2. associate-*r* 36.0%

         \[\leadsto -\color{blue}{\left(y1 \cdot z\right) \cdot \left(i \cdot k - a \cdot y3\right)} \]

      3. *-commutative 36.0%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(\color{blue}{k \cdot i} - a \cdot y3\right) \]

      4. *-commutative 36.0%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(k \cdot i - \color{blue}{y3 \cdot a}\right) \]

   8. Simplified 36.0%

      \[\leadsto \color{blue}{-\left(y1 \cdot z\right) \cdot \left(k \cdot i - y3 \cdot a\right)} \]

   9. Taylor expanded in k around inf 51.6%

      \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. add0 51.6%

          \[\leadsto -\color{blue}{\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right) + 0\right)} \]

       2. associate-*r* 35.9%

          \[\leadsto -\left(\color{blue}{\left(i \cdot k\right) \cdot \left(y1 \cdot z\right)} + 0\right) \]

   11. Applied egg-rr 35.9%

       \[\leadsto -\color{blue}{\left(\left(i \cdot k\right) \cdot \left(y1 \cdot z\right) + 0\right)} \]
   12. Step-by-step derivation

       1. add0 35.9%

          \[\leadsto -\color{blue}{\left(i \cdot k\right) \cdot \left(y1 \cdot z\right)} \]

       2. associate-*l* 51.6%

          \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       3. associate-*r* 67.2%

          \[\leadsto -i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)} \]

       4. *-commutative 67.2%

          \[\leadsto -i \cdot \left(\color{blue}{\left(y1 \cdot k\right)} \cdot z\right) \]

   13. Simplified 67.2%

       \[\leadsto -\color{blue}{i \cdot \left(\left(y1 \cdot k\right) \cdot z\right)} \]

   if 9.4999999999999999e54 < y5 < 2.00000000000000005e144

   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 j around inf 27.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 27.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 27.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 27.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 27.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 27.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 48.4%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto j \cdot \left(y3 \cdot \left(\color{blue}{y5 \cdot y0} - y1 \cdot y4\right)\right) \]

      2. *-commutative 48.4%

         \[\leadsto j \cdot \left(y3 \cdot \left(y5 \cdot y0 - \color{blue}{y4 \cdot y1}\right)\right) \]

   8. Simplified 48.4%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0 - y4 \cdot y1\right)\right)} \]

   if 2.00000000000000005e144 < y5 < 4.3e203

   1. Initial program 7.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 31.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 31.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 31.2%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 31.2%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 31.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 31.2%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 31.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 31.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 31.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 31.2%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 54.9%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 4.3e203 < y5

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 80.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 80.2%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 70.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 70.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 70.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around 0 61.8%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 61.8%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)} \]

      2. *-commutative 61.8%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(k \cdot \left(y \cdot y5\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 61.8%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

   9. Simplified 61.8%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 5.6 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 5 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;i \cdot \left(z \cdot \left(k \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 4.3 \cdot 10^{+203}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ t_2 := a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{if}\;c \leq -1.8 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-188}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 7.3 \cdot 10^{+169}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y4 (* c y3)))) (t_2 (* a (* y1 (* x (- y2))))))
   (if (<= c -1.8e+205)
     t_1
     (if (<= c -5.8e+19)
       (* y0 (* y2 (* x c)))
       (if (<= c -3.5e-140)
         (* a (* y1 (* z y3)))
         (if (<= c -7.6e-178)
           t_2
           (if (<= c 2.7e-188)
             (* j (* y5 (* y0 y3)))
             (if (<= c 7.3e+169) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y4 * (c * y3));
	double t_2 = a * (y1 * (x * -y2));
	double tmp;
	if (c <= -1.8e+205) {
		tmp = t_1;
	} else if (c <= -5.8e+19) {
		tmp = y0 * (y2 * (x * c));
	} else if (c <= -3.5e-140) {
		tmp = a * (y1 * (z * y3));
	} else if (c <= -7.6e-178) {
		tmp = t_2;
	} else if (c <= 2.7e-188) {
		tmp = j * (y5 * (y0 * y3));
	} else if (c <= 7.3e+169) {
		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 = y * (y4 * (c * y3))
    t_2 = a * (y1 * (x * -y2))
    if (c <= (-1.8d+205)) then
        tmp = t_1
    else if (c <= (-5.8d+19)) then
        tmp = y0 * (y2 * (x * c))
    else if (c <= (-3.5d-140)) then
        tmp = a * (y1 * (z * y3))
    else if (c <= (-7.6d-178)) then
        tmp = t_2
    else if (c <= 2.7d-188) then
        tmp = j * (y5 * (y0 * y3))
    else if (c <= 7.3d+169) 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 = y * (y4 * (c * y3));
	double t_2 = a * (y1 * (x * -y2));
	double tmp;
	if (c <= -1.8e+205) {
		tmp = t_1;
	} else if (c <= -5.8e+19) {
		tmp = y0 * (y2 * (x * c));
	} else if (c <= -3.5e-140) {
		tmp = a * (y1 * (z * y3));
	} else if (c <= -7.6e-178) {
		tmp = t_2;
	} else if (c <= 2.7e-188) {
		tmp = j * (y5 * (y0 * y3));
	} else if (c <= 7.3e+169) {
		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 = y * (y4 * (c * y3))
	t_2 = a * (y1 * (x * -y2))
	tmp = 0
	if c <= -1.8e+205:
		tmp = t_1
	elif c <= -5.8e+19:
		tmp = y0 * (y2 * (x * c))
	elif c <= -3.5e-140:
		tmp = a * (y1 * (z * y3))
	elif c <= -7.6e-178:
		tmp = t_2
	elif c <= 2.7e-188:
		tmp = j * (y5 * (y0 * y3))
	elif c <= 7.3e+169:
		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(y * Float64(y4 * Float64(c * y3)))
	t_2 = Float64(a * Float64(y1 * Float64(x * Float64(-y2))))
	tmp = 0.0
	if (c <= -1.8e+205)
		tmp = t_1;
	elseif (c <= -5.8e+19)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (c <= -3.5e-140)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	elseif (c <= -7.6e-178)
		tmp = t_2;
	elseif (c <= 2.7e-188)
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	elseif (c <= 7.3e+169)
		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 = y * (y4 * (c * y3));
	t_2 = a * (y1 * (x * -y2));
	tmp = 0.0;
	if (c <= -1.8e+205)
		tmp = t_1;
	elseif (c <= -5.8e+19)
		tmp = y0 * (y2 * (x * c));
	elseif (c <= -3.5e-140)
		tmp = a * (y1 * (z * y3));
	elseif (c <= -7.6e-178)
		tmp = t_2;
	elseif (c <= 2.7e-188)
		tmp = j * (y5 * (y0 * y3));
	elseif (c <= 7.3e+169)
		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[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.8e+205], t$95$1, If[LessEqual[c, -5.8e+19], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.5e-140], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.6e-178], t$95$2, If[LessEqual[c, 2.7e-188], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.3e+169], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.80000000000000001e205 or 7.3000000000000001e169 < c

   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 y2 around inf 25.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 25.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 25.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 49.4%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 49.7%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 59.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   9. Simplified 59.6%

      \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   if -1.80000000000000001e205 < c < -5.8e19

   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 y2 around inf 45.4%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 45.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 45.4%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 34.2%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 30.3%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.0%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

      2. *-commutative 35.0%

         \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   9. Simplified 35.0%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   if -5.8e19 < c < -3.4999999999999998e-140

   1. Initial program 39.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 33.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 33.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 33.2%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 33.2%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 33.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 33.2%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 33.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 33.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 33.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 33.2%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 40.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around inf 29.9%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -3.4999999999999998e-140 < c < -7.60000000000000029e-178 or 2.7000000000000001e-188 < c < 7.3000000000000001e169

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 43.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 43.3%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 43.3%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 43.3%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 43.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 43.3%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 43.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 43.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 43.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 35.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around 0 31.5%

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(x \cdot y2\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 31.5%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(-x \cdot y2\right)}\right) \]

      2. distribute-lft-neg-in 31.5%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(\left(-x\right) \cdot y2\right)}\right) \]

      3. *-commutative 31.5%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y2 \cdot \left(-x\right)\right)}\right) \]

   9. Simplified 31.5%

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y2 \cdot \left(-x\right)\right)}\right) \]

   if -7.60000000000000029e-178 < c < 2.7000000000000001e-188

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 39.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 39.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 39.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 38.1%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y2 around 0 26.2%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 30.6%

         \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   9. Simplified 30.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot y3\right) \cdot y5\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-188}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 7.3 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+172}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-174}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-76}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+17}:\\ \;\;\;\;i \cdot \left(z \cdot \left(k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (* x (- y2))))))
   (if (<= x -5.6e+250)
     t_1
     (if (<= x -3.2e+172)
       (* y0 (* c (* x y2)))
       (if (<= x -2e+24)
         t_1
         (if (<= x -2.75e-174)
           (* y (* y3 (* a (- y5))))
           (if (<= x 1.32e-76)
             (* (* a y1) (* z y3))
             (if (<= x 6e+17) (* i (* z (* k (- y1)))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (x * -y2));
	double tmp;
	if (x <= -5.6e+250) {
		tmp = t_1;
	} else if (x <= -3.2e+172) {
		tmp = y0 * (c * (x * y2));
	} else if (x <= -2e+24) {
		tmp = t_1;
	} else if (x <= -2.75e-174) {
		tmp = y * (y3 * (a * -y5));
	} else if (x <= 1.32e-76) {
		tmp = (a * y1) * (z * y3);
	} else if (x <= 6e+17) {
		tmp = i * (z * (k * -y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y1 * (x * -y2))
    if (x <= (-5.6d+250)) then
        tmp = t_1
    else if (x <= (-3.2d+172)) then
        tmp = y0 * (c * (x * y2))
    else if (x <= (-2d+24)) then
        tmp = t_1
    else if (x <= (-2.75d-174)) then
        tmp = y * (y3 * (a * -y5))
    else if (x <= 1.32d-76) then
        tmp = (a * y1) * (z * y3)
    else if (x <= 6d+17) then
        tmp = i * (z * (k * -y1))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (x * -y2));
	double tmp;
	if (x <= -5.6e+250) {
		tmp = t_1;
	} else if (x <= -3.2e+172) {
		tmp = y0 * (c * (x * y2));
	} else if (x <= -2e+24) {
		tmp = t_1;
	} else if (x <= -2.75e-174) {
		tmp = y * (y3 * (a * -y5));
	} else if (x <= 1.32e-76) {
		tmp = (a * y1) * (z * y3);
	} else if (x <= 6e+17) {
		tmp = i * (z * (k * -y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * (x * -y2))
	tmp = 0
	if x <= -5.6e+250:
		tmp = t_1
	elif x <= -3.2e+172:
		tmp = y0 * (c * (x * y2))
	elif x <= -2e+24:
		tmp = t_1
	elif x <= -2.75e-174:
		tmp = y * (y3 * (a * -y5))
	elif x <= 1.32e-76:
		tmp = (a * y1) * (z * y3)
	elif x <= 6e+17:
		tmp = i * (z * (k * -y1))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(x * Float64(-y2))))
	tmp = 0.0
	if (x <= -5.6e+250)
		tmp = t_1;
	elseif (x <= -3.2e+172)
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	elseif (x <= -2e+24)
		tmp = t_1;
	elseif (x <= -2.75e-174)
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-y5))));
	elseif (x <= 1.32e-76)
		tmp = Float64(Float64(a * y1) * Float64(z * y3));
	elseif (x <= 6e+17)
		tmp = Float64(i * Float64(z * Float64(k * Float64(-y1))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * (x * -y2));
	tmp = 0.0;
	if (x <= -5.6e+250)
		tmp = t_1;
	elseif (x <= -3.2e+172)
		tmp = y0 * (c * (x * y2));
	elseif (x <= -2e+24)
		tmp = t_1;
	elseif (x <= -2.75e-174)
		tmp = y * (y3 * (a * -y5));
	elseif (x <= 1.32e-76)
		tmp = (a * y1) * (z * y3);
	elseif (x <= 6e+17)
		tmp = i * (z * (k * -y1));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.6e+250], t$95$1, If[LessEqual[x, -3.2e+172], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2e+24], t$95$1, If[LessEqual[x, -2.75e-174], N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.32e-76], N[(N[(a * y1), $MachinePrecision] * N[(z * y3), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+17], N[(i * N[(z * N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.60000000000000019e250 or -3.19999999999999985e172 < x < -2e24 or 6e17 < x

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 45.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 45.5%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 45.5%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 45.5%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 45.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 45.5%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around 0 38.1%

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(x \cdot y2\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 38.1%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(-x \cdot y2\right)}\right) \]

      2. distribute-lft-neg-in 38.1%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(\left(-x\right) \cdot y2\right)}\right) \]

      3. *-commutative 38.1%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y2 \cdot \left(-x\right)\right)}\right) \]

   9. Simplified 38.1%

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y2 \cdot \left(-x\right)\right)}\right) \]

   if -5.60000000000000019e250 < x < -3.19999999999999985e172

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 28.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 28.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 28.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 66.9%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 56.0%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]

   if -2e24 < x < -2.7499999999999999e-174

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 36.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 36.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 29.2%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around 0 22.8%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y5\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 22.8%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(-a \cdot y5\right)}\right) \]

      2. distribute-lft-neg-in 22.8%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(\left(-a\right) \cdot y5\right)}\right) \]

      3. *-commutative 22.8%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-a\right)\right)}\right) \]

   9. Simplified 22.8%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-a\right)\right)}\right) \]

   if -2.7499999999999999e-174 < x < 1.31999999999999996e-76

   1. Initial program 41.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 43.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 43.8%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 43.8%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 43.8%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 43.8%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 43.8%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 43.8%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 43.8%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 43.8%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 43.8%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 25.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around inf 24.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 27.2%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

      2. *-commutative 27.2%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z\right) \]

   9. Simplified 27.2%

      \[\leadsto \color{blue}{\left(y1 \cdot a\right) \cdot \left(y3 \cdot z\right)} \]

   if 1.31999999999999996e-76 < x < 6e17

   1. Initial program 40.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 37.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 37.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 37.9%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 37.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 37.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 37.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 37.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 37.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 37.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 37.9%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z around -inf 23.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 23.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

      2. associate-*r* 27.2%

         \[\leadsto -\color{blue}{\left(y1 \cdot z\right) \cdot \left(i \cdot k - a \cdot y3\right)} \]

      3. *-commutative 27.2%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(\color{blue}{k \cdot i} - a \cdot y3\right) \]

      4. *-commutative 27.2%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(k \cdot i - \color{blue}{y3 \cdot a}\right) \]

   8. Simplified 27.2%

      \[\leadsto \color{blue}{-\left(y1 \cdot z\right) \cdot \left(k \cdot i - y3 \cdot a\right)} \]

   9. Taylor expanded in k around inf 16.9%

      \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. add0 16.9%

          \[\leadsto -\color{blue}{\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right) + 0\right)} \]

       2. associate-*r* 20.2%

          \[\leadsto -\left(\color{blue}{\left(i \cdot k\right) \cdot \left(y1 \cdot z\right)} + 0\right) \]

   11. Applied egg-rr 20.2%

       \[\leadsto -\color{blue}{\left(\left(i \cdot k\right) \cdot \left(y1 \cdot z\right) + 0\right)} \]
   12. Step-by-step derivation

       1. add0 20.2%

          \[\leadsto -\color{blue}{\left(i \cdot k\right) \cdot \left(y1 \cdot z\right)} \]

       2. associate-*l* 16.9%

          \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       3. associate-*r* 38.2%

          \[\leadsto -i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)} \]

       4. *-commutative 38.2%

          \[\leadsto -i \cdot \left(\color{blue}{\left(y1 \cdot k\right)} \cdot z\right) \]

   13. Simplified 38.2%

       \[\leadsto -\color{blue}{i \cdot \left(\left(y1 \cdot k\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+250}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+172}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-174}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-76}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+17}:\\ \;\;\;\;i \cdot \left(z \cdot \left(k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 21.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+170}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-212}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-81}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+16}:\\ \;\;\;\;i \cdot \left(z \cdot \left(k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (* x (- y2))))))
   (if (<= x -2.9e+250)
     t_1
     (if (<= x -1.02e+170)
       (* y0 (* c (* x y2)))
       (if (<= x -6e+24)
         t_1
         (if (<= x -8e-212)
           (* (- a) (* y (* y3 y5)))
           (if (<= x 1.1e-81)
             (* (* a y1) (* z y3))
             (if (<= x 3.8e+16) (* i (* z (* k (- y1)))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (x * -y2));
	double tmp;
	if (x <= -2.9e+250) {
		tmp = t_1;
	} else if (x <= -1.02e+170) {
		tmp = y0 * (c * (x * y2));
	} else if (x <= -6e+24) {
		tmp = t_1;
	} else if (x <= -8e-212) {
		tmp = -a * (y * (y3 * y5));
	} else if (x <= 1.1e-81) {
		tmp = (a * y1) * (z * y3);
	} else if (x <= 3.8e+16) {
		tmp = i * (z * (k * -y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y1 * (x * -y2))
    if (x <= (-2.9d+250)) then
        tmp = t_1
    else if (x <= (-1.02d+170)) then
        tmp = y0 * (c * (x * y2))
    else if (x <= (-6d+24)) then
        tmp = t_1
    else if (x <= (-8d-212)) then
        tmp = -a * (y * (y3 * y5))
    else if (x <= 1.1d-81) then
        tmp = (a * y1) * (z * y3)
    else if (x <= 3.8d+16) then
        tmp = i * (z * (k * -y1))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (x * -y2));
	double tmp;
	if (x <= -2.9e+250) {
		tmp = t_1;
	} else if (x <= -1.02e+170) {
		tmp = y0 * (c * (x * y2));
	} else if (x <= -6e+24) {
		tmp = t_1;
	} else if (x <= -8e-212) {
		tmp = -a * (y * (y3 * y5));
	} else if (x <= 1.1e-81) {
		tmp = (a * y1) * (z * y3);
	} else if (x <= 3.8e+16) {
		tmp = i * (z * (k * -y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * (x * -y2))
	tmp = 0
	if x <= -2.9e+250:
		tmp = t_1
	elif x <= -1.02e+170:
		tmp = y0 * (c * (x * y2))
	elif x <= -6e+24:
		tmp = t_1
	elif x <= -8e-212:
		tmp = -a * (y * (y3 * y5))
	elif x <= 1.1e-81:
		tmp = (a * y1) * (z * y3)
	elif x <= 3.8e+16:
		tmp = i * (z * (k * -y1))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(x * Float64(-y2))))
	tmp = 0.0
	if (x <= -2.9e+250)
		tmp = t_1;
	elseif (x <= -1.02e+170)
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	elseif (x <= -6e+24)
		tmp = t_1;
	elseif (x <= -8e-212)
		tmp = Float64(Float64(-a) * Float64(y * Float64(y3 * y5)));
	elseif (x <= 1.1e-81)
		tmp = Float64(Float64(a * y1) * Float64(z * y3));
	elseif (x <= 3.8e+16)
		tmp = Float64(i * Float64(z * Float64(k * Float64(-y1))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * (x * -y2));
	tmp = 0.0;
	if (x <= -2.9e+250)
		tmp = t_1;
	elseif (x <= -1.02e+170)
		tmp = y0 * (c * (x * y2));
	elseif (x <= -6e+24)
		tmp = t_1;
	elseif (x <= -8e-212)
		tmp = -a * (y * (y3 * y5));
	elseif (x <= 1.1e-81)
		tmp = (a * y1) * (z * y3);
	elseif (x <= 3.8e+16)
		tmp = i * (z * (k * -y1));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e+250], t$95$1, If[LessEqual[x, -1.02e+170], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e+24], t$95$1, If[LessEqual[x, -8e-212], N[((-a) * N[(y * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e-81], N[(N[(a * y1), $MachinePrecision] * N[(z * y3), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+16], N[(i * N[(z * N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.90000000000000009e250 or -1.02000000000000002e170 < x < -5.9999999999999999e24 or 3.8e16 < x

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 45.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 45.5%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 45.5%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 45.5%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 45.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 45.5%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around 0 38.1%

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(x \cdot y2\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 38.1%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(-x \cdot y2\right)}\right) \]

      2. distribute-lft-neg-in 38.1%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(\left(-x\right) \cdot y2\right)}\right) \]

      3. *-commutative 38.1%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y2 \cdot \left(-x\right)\right)}\right) \]

   9. Simplified 38.1%

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y2 \cdot \left(-x\right)\right)}\right) \]

   if -2.90000000000000009e250 < x < -1.02000000000000002e170

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 28.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 28.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 28.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 66.9%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 56.0%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]

   if -5.9999999999999999e24 < x < -7.99999999999999963e-212

   1. Initial program 36.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 39.5%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 39.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 39.5%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 31.3%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around 0 25.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 25.4%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 25.4%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y \cdot \left(y3 \cdot y5\right)\right) \]

   9. Simplified 25.4%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

   if -7.99999999999999963e-212 < x < 1.1e-81

   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 y1 around -inf 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 42.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 42.2%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 42.2%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 42.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 42.2%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 42.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 42.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 42.2%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 42.2%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 27.0%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around inf 25.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.6%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

      2. *-commutative 28.6%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z\right) \]

   9. Simplified 28.6%

      \[\leadsto \color{blue}{\left(y1 \cdot a\right) \cdot \left(y3 \cdot z\right)} \]

   if 1.1e-81 < x < 3.8e16

   1. Initial program 40.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 37.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 37.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 37.9%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 37.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 37.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 37.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 37.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 37.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 37.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 37.9%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z around -inf 23.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 23.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

      2. associate-*r* 27.2%

         \[\leadsto -\color{blue}{\left(y1 \cdot z\right) \cdot \left(i \cdot k - a \cdot y3\right)} \]

      3. *-commutative 27.2%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(\color{blue}{k \cdot i} - a \cdot y3\right) \]

      4. *-commutative 27.2%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(k \cdot i - \color{blue}{y3 \cdot a}\right) \]

   8. Simplified 27.2%

      \[\leadsto \color{blue}{-\left(y1 \cdot z\right) \cdot \left(k \cdot i - y3 \cdot a\right)} \]

   9. Taylor expanded in k around inf 16.9%

      \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. add0 16.9%

          \[\leadsto -\color{blue}{\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right) + 0\right)} \]

       2. associate-*r* 20.2%

          \[\leadsto -\left(\color{blue}{\left(i \cdot k\right) \cdot \left(y1 \cdot z\right)} + 0\right) \]

   11. Applied egg-rr 20.2%

       \[\leadsto -\color{blue}{\left(\left(i \cdot k\right) \cdot \left(y1 \cdot z\right) + 0\right)} \]
   12. Step-by-step derivation

       1. add0 20.2%

          \[\leadsto -\color{blue}{\left(i \cdot k\right) \cdot \left(y1 \cdot z\right)} \]

       2. associate-*l* 16.9%

          \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       3. associate-*r* 38.2%

          \[\leadsto -i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)} \]

       4. *-commutative 38.2%

          \[\leadsto -i \cdot \left(\color{blue}{\left(y1 \cdot k\right)} \cdot z\right) \]

   13. Simplified 38.2%

       \[\leadsto -\color{blue}{i \cdot \left(\left(y1 \cdot k\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+250}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+170}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-212}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-81}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+16}:\\ \;\;\;\;i \cdot \left(z \cdot \left(k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 21.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{if}\;a \leq -5 \cdot 10^{+130}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-8}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-169}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-79}:\\ \;\;\;\;i \cdot \left(\left(-k\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* i j) (* t (- y5)))))
   (if (<= a -5e+130)
     (* (* a y1) (* z y3))
     (if (<= a -8e-8)
       (* y0 (* y2 (* x c)))
       (if (<= a -4.9e-169)
         (* y (* y4 (* c y3)))
         (if (<= a 5.4e-155)
           t_1
           (if (<= a 5.4e-79)
             (* i (* (- k) (* z y1)))
             (if (<= a 7.2e+55) t_1 (* y (* y3 (* a (- y5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * j) * (t * -y5);
	double tmp;
	if (a <= -5e+130) {
		tmp = (a * y1) * (z * y3);
	} else if (a <= -8e-8) {
		tmp = y0 * (y2 * (x * c));
	} else if (a <= -4.9e-169) {
		tmp = y * (y4 * (c * y3));
	} else if (a <= 5.4e-155) {
		tmp = t_1;
	} else if (a <= 5.4e-79) {
		tmp = i * (-k * (z * y1));
	} else if (a <= 7.2e+55) {
		tmp = t_1;
	} else {
		tmp = y * (y3 * (a * -y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (i * j) * (t * -y5)
    if (a <= (-5d+130)) then
        tmp = (a * y1) * (z * y3)
    else if (a <= (-8d-8)) then
        tmp = y0 * (y2 * (x * c))
    else if (a <= (-4.9d-169)) then
        tmp = y * (y4 * (c * y3))
    else if (a <= 5.4d-155) then
        tmp = t_1
    else if (a <= 5.4d-79) then
        tmp = i * (-k * (z * y1))
    else if (a <= 7.2d+55) then
        tmp = t_1
    else
        tmp = y * (y3 * (a * -y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * j) * (t * -y5);
	double tmp;
	if (a <= -5e+130) {
		tmp = (a * y1) * (z * y3);
	} else if (a <= -8e-8) {
		tmp = y0 * (y2 * (x * c));
	} else if (a <= -4.9e-169) {
		tmp = y * (y4 * (c * y3));
	} else if (a <= 5.4e-155) {
		tmp = t_1;
	} else if (a <= 5.4e-79) {
		tmp = i * (-k * (z * y1));
	} else if (a <= 7.2e+55) {
		tmp = t_1;
	} else {
		tmp = y * (y3 * (a * -y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * j) * (t * -y5)
	tmp = 0
	if a <= -5e+130:
		tmp = (a * y1) * (z * y3)
	elif a <= -8e-8:
		tmp = y0 * (y2 * (x * c))
	elif a <= -4.9e-169:
		tmp = y * (y4 * (c * y3))
	elif a <= 5.4e-155:
		tmp = t_1
	elif a <= 5.4e-79:
		tmp = i * (-k * (z * y1))
	elif a <= 7.2e+55:
		tmp = t_1
	else:
		tmp = y * (y3 * (a * -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(i * j) * Float64(t * Float64(-y5)))
	tmp = 0.0
	if (a <= -5e+130)
		tmp = Float64(Float64(a * y1) * Float64(z * y3));
	elseif (a <= -8e-8)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (a <= -4.9e-169)
		tmp = Float64(y * Float64(y4 * Float64(c * y3)));
	elseif (a <= 5.4e-155)
		tmp = t_1;
	elseif (a <= 5.4e-79)
		tmp = Float64(i * Float64(Float64(-k) * Float64(z * y1)));
	elseif (a <= 7.2e+55)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-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 = (i * j) * (t * -y5);
	tmp = 0.0;
	if (a <= -5e+130)
		tmp = (a * y1) * (z * y3);
	elseif (a <= -8e-8)
		tmp = y0 * (y2 * (x * c));
	elseif (a <= -4.9e-169)
		tmp = y * (y4 * (c * y3));
	elseif (a <= 5.4e-155)
		tmp = t_1;
	elseif (a <= 5.4e-79)
		tmp = i * (-k * (z * y1));
	elseif (a <= 7.2e+55)
		tmp = t_1;
	else
		tmp = y * (y3 * (a * -y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(i * j), $MachinePrecision] * N[(t * (-y5)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e+130], N[(N[(a * y1), $MachinePrecision] * N[(z * y3), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8e-8], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.9e-169], N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e-155], t$95$1, If[LessEqual[a, 5.4e-79], N[(i * N[((-k) * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+55], t$95$1, N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.9999999999999996e130

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 48.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 48.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 48.9%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 48.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 48.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 48.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 48.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 48.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 48.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 48.9%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 46.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around inf 31.9%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 41.1%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

      2. *-commutative 41.1%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z\right) \]

   9. Simplified 41.1%

      \[\leadsto \color{blue}{\left(y1 \cdot a\right) \cdot \left(y3 \cdot z\right)} \]

   if -4.9999999999999996e130 < a < -8.0000000000000002e-8

   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 y2 around inf 40.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 40.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 40.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 35.9%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.3%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

      2. *-commutative 36.3%

         \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   9. Simplified 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   if -8.0000000000000002e-8 < a < -4.8999999999999999e-169

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 42.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 42.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 42.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 31.4%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 34.4%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   9. Simplified 31.6%

      \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   if -4.8999999999999999e-169 < a < 5.39999999999999962e-155 or 5.4000000000000004e-79 < a < 7.19999999999999975e55

   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 y5 around -inf 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 37.7%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 38.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 38.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 38.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around inf 28.1%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot \left(t \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 30.1%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot \left(t \cdot y5\right)\right)} \]

      2. *-commutative 30.1%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(j \cdot i\right)} \cdot \left(t \cdot y5\right)\right) \]

      3. *-commutative 30.1%

         \[\leadsto -1 \cdot \left(\left(j \cdot i\right) \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   9. Simplified 30.1%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot i\right) \cdot \left(y5 \cdot t\right)\right)} \]

   if 5.39999999999999962e-155 < a < 5.4000000000000004e-79

   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 y1 around -inf 54.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 54.3%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 54.3%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 54.3%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 54.3%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z around -inf 46.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

      2. associate-*r* 46.6%

         \[\leadsto -\color{blue}{\left(y1 \cdot z\right) \cdot \left(i \cdot k - a \cdot y3\right)} \]

      3. *-commutative 46.6%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(\color{blue}{k \cdot i} - a \cdot y3\right) \]

      4. *-commutative 46.6%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(k \cdot i - \color{blue}{y3 \cdot a}\right) \]

   8. Simplified 46.6%

      \[\leadsto \color{blue}{-\left(y1 \cdot z\right) \cdot \left(k \cdot i - y3 \cdot a\right)} \]

   9. Taylor expanded in k around inf 46.9%

      \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

   if 7.19999999999999975e55 < a

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 32.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 32.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 40.4%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around 0 42.7%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y5\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 42.7%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(-a \cdot y5\right)}\right) \]

      2. distribute-lft-neg-in 42.7%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(\left(-a\right) \cdot y5\right)}\right) \]

      3. *-commutative 42.7%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-a\right)\right)}\right) \]

   9. Simplified 42.7%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-a\right)\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+130}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-8}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-169}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-155}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-79}:\\ \;\;\;\;i \cdot \left(\left(-k\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+55}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 21.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot y5\right) \cdot \left(t \cdot \left(-j\right)\right)\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+130}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-12}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-172}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-78}:\\ \;\;\;\;i \cdot \left(\left(-k\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* i y5) (* t (- j)))))
   (if (<= a -6.8e+130)
     (* (* a y1) (* z y3))
     (if (<= a -9.5e-12)
       (* y0 (* y2 (* x c)))
       (if (<= a -1.6e-172)
         (* y (* y4 (* c y3)))
         (if (<= a 3.7e-152)
           t_1
           (if (<= a 1.7e-78)
             (* i (* (- k) (* z y1)))
             (if (<= a 6.2e+55) t_1 (* y (* y3 (* a (- y5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y5) * (t * -j);
	double tmp;
	if (a <= -6.8e+130) {
		tmp = (a * y1) * (z * y3);
	} else if (a <= -9.5e-12) {
		tmp = y0 * (y2 * (x * c));
	} else if (a <= -1.6e-172) {
		tmp = y * (y4 * (c * y3));
	} else if (a <= 3.7e-152) {
		tmp = t_1;
	} else if (a <= 1.7e-78) {
		tmp = i * (-k * (z * y1));
	} else if (a <= 6.2e+55) {
		tmp = t_1;
	} else {
		tmp = y * (y3 * (a * -y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (i * y5) * (t * -j)
    if (a <= (-6.8d+130)) then
        tmp = (a * y1) * (z * y3)
    else if (a <= (-9.5d-12)) then
        tmp = y0 * (y2 * (x * c))
    else if (a <= (-1.6d-172)) then
        tmp = y * (y4 * (c * y3))
    else if (a <= 3.7d-152) then
        tmp = t_1
    else if (a <= 1.7d-78) then
        tmp = i * (-k * (z * y1))
    else if (a <= 6.2d+55) then
        tmp = t_1
    else
        tmp = y * (y3 * (a * -y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y5) * (t * -j);
	double tmp;
	if (a <= -6.8e+130) {
		tmp = (a * y1) * (z * y3);
	} else if (a <= -9.5e-12) {
		tmp = y0 * (y2 * (x * c));
	} else if (a <= -1.6e-172) {
		tmp = y * (y4 * (c * y3));
	} else if (a <= 3.7e-152) {
		tmp = t_1;
	} else if (a <= 1.7e-78) {
		tmp = i * (-k * (z * y1));
	} else if (a <= 6.2e+55) {
		tmp = t_1;
	} else {
		tmp = y * (y3 * (a * -y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y5) * (t * -j)
	tmp = 0
	if a <= -6.8e+130:
		tmp = (a * y1) * (z * y3)
	elif a <= -9.5e-12:
		tmp = y0 * (y2 * (x * c))
	elif a <= -1.6e-172:
		tmp = y * (y4 * (c * y3))
	elif a <= 3.7e-152:
		tmp = t_1
	elif a <= 1.7e-78:
		tmp = i * (-k * (z * y1))
	elif a <= 6.2e+55:
		tmp = t_1
	else:
		tmp = y * (y3 * (a * -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(i * y5) * Float64(t * Float64(-j)))
	tmp = 0.0
	if (a <= -6.8e+130)
		tmp = Float64(Float64(a * y1) * Float64(z * y3));
	elseif (a <= -9.5e-12)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (a <= -1.6e-172)
		tmp = Float64(y * Float64(y4 * Float64(c * y3)));
	elseif (a <= 3.7e-152)
		tmp = t_1;
	elseif (a <= 1.7e-78)
		tmp = Float64(i * Float64(Float64(-k) * Float64(z * y1)));
	elseif (a <= 6.2e+55)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-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 = (i * y5) * (t * -j);
	tmp = 0.0;
	if (a <= -6.8e+130)
		tmp = (a * y1) * (z * y3);
	elseif (a <= -9.5e-12)
		tmp = y0 * (y2 * (x * c));
	elseif (a <= -1.6e-172)
		tmp = y * (y4 * (c * y3));
	elseif (a <= 3.7e-152)
		tmp = t_1;
	elseif (a <= 1.7e-78)
		tmp = i * (-k * (z * y1));
	elseif (a <= 6.2e+55)
		tmp = t_1;
	else
		tmp = y * (y3 * (a * -y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(i * y5), $MachinePrecision] * N[(t * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.8e+130], N[(N[(a * y1), $MachinePrecision] * N[(z * y3), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.5e-12], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.6e-172], N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e-152], t$95$1, If[LessEqual[a, 1.7e-78], N[(i * N[((-k) * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+55], t$95$1, N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -6.8000000000000001e130

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 48.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 48.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 48.9%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 48.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 48.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 48.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 48.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 48.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 48.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 48.9%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 46.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around inf 31.9%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 41.1%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

      2. *-commutative 41.1%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z\right) \]

   9. Simplified 41.1%

      \[\leadsto \color{blue}{\left(y1 \cdot a\right) \cdot \left(y3 \cdot z\right)} \]

   if -6.8000000000000001e130 < a < -9.4999999999999995e-12

   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 y2 around inf 40.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 40.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 40.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 35.9%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.3%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

      2. *-commutative 36.3%

         \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   9. Simplified 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   if -9.4999999999999995e-12 < a < -1.6000000000000001e-172

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 42.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 42.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 42.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 31.4%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 34.4%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   9. Simplified 31.6%

      \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   if -1.6000000000000001e-172 < a < 3.6999999999999998e-152 or 1.70000000000000006e-78 < a < 6.19999999999999987e55

   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 y5 around -inf 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 37.7%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 38.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 38.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 38.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around inf 31.1%

      \[\leadsto -1 \cdot \left(\left(y5 \cdot i\right) \cdot \color{blue}{\left(j \cdot t\right)}\right) \]

   if 3.6999999999999998e-152 < a < 1.70000000000000006e-78

   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 y1 around -inf 54.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 54.3%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 54.3%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 54.3%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 54.3%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 54.3%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z around -inf 46.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

      2. associate-*r* 46.6%

         \[\leadsto -\color{blue}{\left(y1 \cdot z\right) \cdot \left(i \cdot k - a \cdot y3\right)} \]

      3. *-commutative 46.6%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(\color{blue}{k \cdot i} - a \cdot y3\right) \]

      4. *-commutative 46.6%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(k \cdot i - \color{blue}{y3 \cdot a}\right) \]

   8. Simplified 46.6%

      \[\leadsto \color{blue}{-\left(y1 \cdot z\right) \cdot \left(k \cdot i - y3 \cdot a\right)} \]

   9. Taylor expanded in k around inf 46.9%

      \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

   if 6.19999999999999987e55 < a

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 32.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 32.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 40.4%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around 0 42.7%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y5\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 42.7%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(-a \cdot y5\right)}\right) \]

      2. distribute-lft-neg-in 42.7%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(\left(-a\right) \cdot y5\right)}\right) \]

      3. *-commutative 42.7%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-a\right)\right)}\right) \]

   9. Simplified 42.7%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-a\right)\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+130}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-12}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-172}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-152}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(t \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-78}:\\ \;\;\;\;i \cdot \left(\left(-k\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+55}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(t \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 27.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ t_2 := \left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{if}\;y4 \leq -2.3 \cdot 10^{+114}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -5300000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -6 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 6.2 \cdot 10^{-247}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq 5.1 \cdot 10^{+225}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y1 \cdot \left(-y4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (- (* z y3) (* x y2)))))
        (t_2 (* (* i j) (* t (- y5)))))
   (if (<= y4 -2.3e+114)
     (* c (* y (* y3 y4)))
     (if (<= y4 -5300000.0)
       t_2
       (if (<= y4 -6e-299)
         t_1
         (if (<= y4 6.2e-247)
           t_2
           (if (<= y4 5.1e+225) t_1 (* j (* y3 (* y1 (- 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 * ((z * y3) - (x * y2)));
	double t_2 = (i * j) * (t * -y5);
	double tmp;
	if (y4 <= -2.3e+114) {
		tmp = c * (y * (y3 * y4));
	} else if (y4 <= -5300000.0) {
		tmp = t_2;
	} else if (y4 <= -6e-299) {
		tmp = t_1;
	} else if (y4 <= 6.2e-247) {
		tmp = t_2;
	} else if (y4 <= 5.1e+225) {
		tmp = t_1;
	} else {
		tmp = j * (y3 * (y1 * -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 * ((z * y3) - (x * y2)))
    t_2 = (i * j) * (t * -y5)
    if (y4 <= (-2.3d+114)) then
        tmp = c * (y * (y3 * y4))
    else if (y4 <= (-5300000.0d0)) then
        tmp = t_2
    else if (y4 <= (-6d-299)) then
        tmp = t_1
    else if (y4 <= 6.2d-247) then
        tmp = t_2
    else if (y4 <= 5.1d+225) then
        tmp = t_1
    else
        tmp = j * (y3 * (y1 * -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 * ((z * y3) - (x * y2)));
	double t_2 = (i * j) * (t * -y5);
	double tmp;
	if (y4 <= -2.3e+114) {
		tmp = c * (y * (y3 * y4));
	} else if (y4 <= -5300000.0) {
		tmp = t_2;
	} else if (y4 <= -6e-299) {
		tmp = t_1;
	} else if (y4 <= 6.2e-247) {
		tmp = t_2;
	} else if (y4 <= 5.1e+225) {
		tmp = t_1;
	} else {
		tmp = j * (y3 * (y1 * -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 * ((z * y3) - (x * y2)))
	t_2 = (i * j) * (t * -y5)
	tmp = 0
	if y4 <= -2.3e+114:
		tmp = c * (y * (y3 * y4))
	elif y4 <= -5300000.0:
		tmp = t_2
	elif y4 <= -6e-299:
		tmp = t_1
	elif y4 <= 6.2e-247:
		tmp = t_2
	elif y4 <= 5.1e+225:
		tmp = t_1
	else:
		tmp = j * (y3 * (y1 * -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(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	t_2 = Float64(Float64(i * j) * Float64(t * Float64(-y5)))
	tmp = 0.0
	if (y4 <= -2.3e+114)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y4 <= -5300000.0)
		tmp = t_2;
	elseif (y4 <= -6e-299)
		tmp = t_1;
	elseif (y4 <= 6.2e-247)
		tmp = t_2;
	elseif (y4 <= 5.1e+225)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(y3 * Float64(y1 * 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 * (y1 * ((z * y3) - (x * y2)));
	t_2 = (i * j) * (t * -y5);
	tmp = 0.0;
	if (y4 <= -2.3e+114)
		tmp = c * (y * (y3 * y4));
	elseif (y4 <= -5300000.0)
		tmp = t_2;
	elseif (y4 <= -6e-299)
		tmp = t_1;
	elseif (y4 <= 6.2e-247)
		tmp = t_2;
	elseif (y4 <= 5.1e+225)
		tmp = t_1;
	else
		tmp = j * (y3 * (y1 * -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[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * j), $MachinePrecision] * N[(t * (-y5)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.3e+114], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -5300000.0], t$95$2, If[LessEqual[y4, -6e-299], t$95$1, If[LessEqual[y4, 6.2e-247], t$95$2, If[LessEqual[y4, 5.1e+225], t$95$1, N[(j * N[(y3 * N[(y1 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -2.3e114

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 32.0%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 32.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 32.0%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 45.1%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 40.3%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if -2.3e114 < y4 < -5.3e6 or -5.99999999999999969e-299 < y4 < 6.20000000000000031e-247

   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 y5 around -inf 53.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 56.2%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 54.1%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 54.1%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 54.1%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around inf 41.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot \left(t \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 41.6%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot \left(t \cdot y5\right)\right)} \]

      2. *-commutative 41.6%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(j \cdot i\right)} \cdot \left(t \cdot y5\right)\right) \]

      3. *-commutative 41.6%

         \[\leadsto -1 \cdot \left(\left(j \cdot i\right) \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   9. Simplified 41.6%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot i\right) \cdot \left(y5 \cdot t\right)\right)} \]

   if -5.3e6 < y4 < -5.99999999999999969e-299 or 6.20000000000000031e-247 < y4 < 5.0999999999999999e225

   1. Initial program 37.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 42.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 42.1%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 42.1%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 42.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 42.1%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 42.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 42.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 42.1%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 42.1%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 35.0%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 5.0999999999999999e225 < y4

   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 j around inf 47.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 47.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 47.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 47.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 53.5%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 53.5%

         \[\leadsto j \cdot \left(y3 \cdot \left(\color{blue}{y5 \cdot y0} - y1 \cdot y4\right)\right) \]

      2. *-commutative 53.5%

         \[\leadsto j \cdot \left(y3 \cdot \left(y5 \cdot y0 - \color{blue}{y4 \cdot y1}\right)\right) \]

   8. Simplified 53.5%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0 - y4 \cdot y1\right)\right)} \]

   9. Taylor expanded in y5 around 0 53.9%

      \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

       1. neg-mul-1 53.9%

          \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(-y1 \cdot y4\right)}\right) \]

       2. distribute-rgt-neg-in 53.9%

          \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot \left(-y4\right)\right)}\right) \]

   11. Simplified 53.9%

       \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot \left(-y4\right)\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.3 \cdot 10^{+114}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -5300000:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y4 \leq -6 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 6.2 \cdot 10^{-247}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(t \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y4 \leq 5.1 \cdot 10^{+225}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y1 \cdot \left(-y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 29.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -2.1 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 2.25 \cdot 10^{-139}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+79}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 4 \cdot 10^{+152}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 3.4 \cdot 10^{+281}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* t (- (* b y4) (* i y5))))))
   (if (<= y5 -2.1e-49)
     t_1
     (if (<= y5 2.25e-139)
       (* a (* y1 (- (* z y3) (* x y2))))
       (if (<= y5 2.5e+79)
         (* k (* y2 (- (* y1 y4) (* y0 y5))))
         (if (<= y5 4e+152)
           (* j (* y3 (- (* y0 y5) (* y1 y4))))
           (if (<= y5 3.4e+281) t_1 (* i (* k (* y 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 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (y5 <= -2.1e-49) {
		tmp = t_1;
	} else if (y5 <= 2.25e-139) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 2.5e+79) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y5 <= 4e+152) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y5 <= 3.4e+281) {
		tmp = t_1;
	} else {
		tmp = i * (k * (y * 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) :: tmp
    t_1 = j * (t * ((b * y4) - (i * y5)))
    if (y5 <= (-2.1d-49)) then
        tmp = t_1
    else if (y5 <= 2.25d-139) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y5 <= 2.5d+79) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (y5 <= 4d+152) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (y5 <= 3.4d+281) then
        tmp = t_1
    else
        tmp = i * (k * (y * 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 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (y5 <= -2.1e-49) {
		tmp = t_1;
	} else if (y5 <= 2.25e-139) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 2.5e+79) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y5 <= 4e+152) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y5 <= 3.4e+281) {
		tmp = t_1;
	} else {
		tmp = i * (k * (y * y5));
	}
	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 y5 <= -2.1e-49:
		tmp = t_1
	elif y5 <= 2.25e-139:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y5 <= 2.5e+79:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif y5 <= 4e+152:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif y5 <= 3.4e+281:
		tmp = t_1
	else:
		tmp = i * (k * (y * 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(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	tmp = 0.0
	if (y5 <= -2.1e-49)
		tmp = t_1;
	elseif (y5 <= 2.25e-139)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y5 <= 2.5e+79)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y5 <= 4e+152)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (y5 <= 3.4e+281)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(k * Float64(y * 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 = j * (t * ((b * y4) - (i * y5)));
	tmp = 0.0;
	if (y5 <= -2.1e-49)
		tmp = t_1;
	elseif (y5 <= 2.25e-139)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y5 <= 2.5e+79)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (y5 <= 4e+152)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (y5 <= 3.4e+281)
		tmp = t_1;
	else
		tmp = i * (k * (y * 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[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.1e-49], t$95$1, If[LessEqual[y5, 2.25e-139], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.5e+79], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4e+152], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.4e+281], t$95$1, N[(i * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -2.0999999999999999e-49 or 4.0000000000000002e152 < y5 < 3.40000000000000011e281

   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 j around inf 46.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 46.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 46.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 46.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 46.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 50.3%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto j \cdot \left(t \cdot \left(b \cdot y4 - \color{blue}{y5 \cdot i}\right)\right) \]

   8. Simplified 50.3%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - y5 \cdot i\right)\right)} \]

   if -2.0999999999999999e-49 < y5 < 2.25000000000000011e-139

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 43.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 43.6%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 43.6%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 43.6%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 43.6%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 43.6%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 43.6%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 43.6%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 43.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 38.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 2.25000000000000011e-139 < y5 < 2.5e79

   1. Initial program 48.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 54.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 54.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 54.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around inf 44.0%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 44.0%

         \[\leadsto k \cdot \left(y2 \cdot \left(\color{blue}{y4 \cdot y1} - y0 \cdot y5\right)\right) \]

      2. *-commutative 44.0%

         \[\leadsto k \cdot \left(y2 \cdot \left(y4 \cdot y1 - \color{blue}{y5 \cdot y0}\right)\right) \]

   8. Simplified 44.0%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   if 2.5e79 < y5 < 4.0000000000000002e152

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 22.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 22.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 22.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 22.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 22.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 22.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 43.3%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.3%

         \[\leadsto j \cdot \left(y3 \cdot \left(\color{blue}{y5 \cdot y0} - y1 \cdot y4\right)\right) \]

      2. *-commutative 43.3%

         \[\leadsto j \cdot \left(y3 \cdot \left(y5 \cdot y0 - \color{blue}{y4 \cdot y1}\right)\right) \]

   8. Simplified 43.3%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0 - y4 \cdot y1\right)\right)} \]

   if 3.40000000000000011e281 < y5

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 87.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 75.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 63.6%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 63.6%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 63.6%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around 0 77.6%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 77.6%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)} \]

      2. *-commutative 77.6%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(k \cdot \left(y \cdot y5\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 77.6%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

   9. Simplified 77.6%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.1 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 2.25 \cdot 10^{-139}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+79}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 4 \cdot 10^{+152}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 3.4 \cdot 10^{+281}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 29.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;y5 \leq -2 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 7.6 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 1.25 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (- (* z y3) (* x y2))))))
   (if (<= y5 -2e-49)
     (* j (* t (- (* b y4) (* i y5))))
     (if (<= y5 7.6e-174)
       t_1
       (if (<= y5 1.25e-104)
         (* y0 (* y2 (* x c)))
         (if (<= y5 2.5e+203) t_1 (* i (* k (* y 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 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y5 <= -2e-49) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y5 <= 7.6e-174) {
		tmp = t_1;
	} else if (y5 <= 1.25e-104) {
		tmp = y0 * (y2 * (x * c));
	} else if (y5 <= 2.5e+203) {
		tmp = t_1;
	} else {
		tmp = i * (k * (y * 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) :: tmp
    t_1 = a * (y1 * ((z * y3) - (x * y2)))
    if (y5 <= (-2d-49)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (y5 <= 7.6d-174) then
        tmp = t_1
    else if (y5 <= 1.25d-104) then
        tmp = y0 * (y2 * (x * c))
    else if (y5 <= 2.5d+203) then
        tmp = t_1
    else
        tmp = i * (k * (y * 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 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y5 <= -2e-49) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (y5 <= 7.6e-174) {
		tmp = t_1;
	} else if (y5 <= 1.25e-104) {
		tmp = y0 * (y2 * (x * c));
	} else if (y5 <= 2.5e+203) {
		tmp = t_1;
	} else {
		tmp = i * (k * (y * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * ((z * y3) - (x * y2)))
	tmp = 0
	if y5 <= -2e-49:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif y5 <= 7.6e-174:
		tmp = t_1
	elif y5 <= 1.25e-104:
		tmp = y0 * (y2 * (x * c))
	elif y5 <= 2.5e+203:
		tmp = t_1
	else:
		tmp = i * (k * (y * 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(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (y5 <= -2e-49)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (y5 <= 7.6e-174)
		tmp = t_1;
	elseif (y5 <= 1.25e-104)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (y5 <= 2.5e+203)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(k * Float64(y * 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 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (y5 <= -2e-49)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (y5 <= 7.6e-174)
		tmp = t_1;
	elseif (y5 <= 1.25e-104)
		tmp = y0 * (y2 * (x * c));
	elseif (y5 <= 2.5e+203)
		tmp = t_1;
	else
		tmp = i * (k * (y * 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[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2e-49], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.6e-174], t$95$1, If[LessEqual[y5, 1.25e-104], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.5e+203], t$95$1, N[(i * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -1.99999999999999987e-49

   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 j around inf 49.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 49.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 49.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 49.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 49.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 46.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 46.2%

         \[\leadsto j \cdot \left(t \cdot \left(b \cdot y4 - \color{blue}{y5 \cdot i}\right)\right) \]

   8. Simplified 46.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - y5 \cdot i\right)\right)} \]

   if -1.99999999999999987e-49 < y5 < 7.60000000000000042e-174 or 1.24999999999999995e-104 < y5 < 2.49999999999999997e203

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 41.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 41.5%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 41.5%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 41.5%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 41.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 41.5%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 41.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 41.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 41.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 38.9%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 7.60000000000000042e-174 < y5 < 1.24999999999999995e-104

   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 y2 around inf 33.9%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 33.9%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 33.9%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 28.6%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 34.8%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 41.2%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

      2. *-commutative 41.2%

         \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   9. Simplified 41.2%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   if 2.49999999999999997e203 < y5

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf 80.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   4. Taylor expanded in i around inf 80.2%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 70.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-commutative 70.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y5 \cdot i\right)} \cdot \left(j \cdot t - k \cdot y\right)\right) \]

   6. Simplified 70.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot i\right) \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   7. Taylor expanded in j around 0 61.8%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 61.8%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)} \]

      2. *-commutative 61.8%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(k \cdot \left(y \cdot y5\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 61.8%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]

   9. Simplified 61.8%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y \cdot y5\right)\right) \cdot \left(-i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 7.6 \cdot 10^{-174}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.25 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+203}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 21.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-188}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(z \cdot \left(k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y4 (* c y3)))))
   (if (<= c -8.5e+203)
     t_1
     (if (<= c -2.4e+19)
       (* y0 (* y2 (* x c)))
       (if (<= c 6e-188)
         (* j (* y5 (* y0 y3)))
         (if (<= c 1.05e+64) (* i (* z (* k (- y1)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y4 * (c * y3));
	double tmp;
	if (c <= -8.5e+203) {
		tmp = t_1;
	} else if (c <= -2.4e+19) {
		tmp = y0 * (y2 * (x * c));
	} else if (c <= 6e-188) {
		tmp = j * (y5 * (y0 * y3));
	} else if (c <= 1.05e+64) {
		tmp = i * (z * (k * -y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (y4 * (c * y3))
    if (c <= (-8.5d+203)) then
        tmp = t_1
    else if (c <= (-2.4d+19)) then
        tmp = y0 * (y2 * (x * c))
    else if (c <= 6d-188) then
        tmp = j * (y5 * (y0 * y3))
    else if (c <= 1.05d+64) then
        tmp = i * (z * (k * -y1))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y4 * (c * y3));
	double tmp;
	if (c <= -8.5e+203) {
		tmp = t_1;
	} else if (c <= -2.4e+19) {
		tmp = y0 * (y2 * (x * c));
	} else if (c <= 6e-188) {
		tmp = j * (y5 * (y0 * y3));
	} else if (c <= 1.05e+64) {
		tmp = i * (z * (k * -y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (y4 * (c * y3))
	tmp = 0
	if c <= -8.5e+203:
		tmp = t_1
	elif c <= -2.4e+19:
		tmp = y0 * (y2 * (x * c))
	elif c <= 6e-188:
		tmp = j * (y5 * (y0 * y3))
	elif c <= 1.05e+64:
		tmp = i * (z * (k * -y1))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(y4 * Float64(c * y3)))
	tmp = 0.0
	if (c <= -8.5e+203)
		tmp = t_1;
	elseif (c <= -2.4e+19)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (c <= 6e-188)
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	elseif (c <= 1.05e+64)
		tmp = Float64(i * Float64(z * Float64(k * Float64(-y1))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (y4 * (c * y3));
	tmp = 0.0;
	if (c <= -8.5e+203)
		tmp = t_1;
	elseif (c <= -2.4e+19)
		tmp = y0 * (y2 * (x * c));
	elseif (c <= 6e-188)
		tmp = j * (y5 * (y0 * y3));
	elseif (c <= 1.05e+64)
		tmp = i * (z * (k * -y1));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.5e+203], t$95$1, If[LessEqual[c, -2.4e+19], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6e-188], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e+64], N[(i * N[(z * N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -8.50000000000000025e203 or 1.05e64 < c

   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 y2 around inf 33.0%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 33.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 33.0%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 39.4%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 39.6%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 46.0%

         \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   9. Simplified 46.0%

      \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   if -8.50000000000000025e203 < c < -2.4e19

   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 y2 around inf 45.4%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 45.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 45.4%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 34.2%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 30.3%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.0%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

      2. *-commutative 35.0%

         \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   9. Simplified 35.0%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   if -2.4e19 < c < 6.00000000000000033e-188

   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 y2 around inf 44.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 44.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 44.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 34.4%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y2 around 0 23.1%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 26.8%

         \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   9. Simplified 26.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   if 6.00000000000000033e-188 < c < 1.05e64

   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 y1 around -inf 44.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 44.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 44.9%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 44.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 44.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 44.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 44.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 44.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 44.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z around -inf 30.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 30.1%

         \[\leadsto \color{blue}{-y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

      2. associate-*r* 33.6%

         \[\leadsto -\color{blue}{\left(y1 \cdot z\right) \cdot \left(i \cdot k - a \cdot y3\right)} \]

      3. *-commutative 33.6%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(\color{blue}{k \cdot i} - a \cdot y3\right) \]

      4. *-commutative 33.6%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(k \cdot i - \color{blue}{y3 \cdot a}\right) \]

   8. Simplified 33.6%

      \[\leadsto \color{blue}{-\left(y1 \cdot z\right) \cdot \left(k \cdot i - y3 \cdot a\right)} \]

   9. Taylor expanded in k around inf 24.3%

      \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. add0 24.3%

          \[\leadsto -\color{blue}{\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right) + 0\right)} \]

       2. associate-*r* 24.1%

          \[\leadsto -\left(\color{blue}{\left(i \cdot k\right) \cdot \left(y1 \cdot z\right)} + 0\right) \]

   11. Applied egg-rr 24.1%

       \[\leadsto -\color{blue}{\left(\left(i \cdot k\right) \cdot \left(y1 \cdot z\right) + 0\right)} \]
   12. Step-by-step derivation

       1. add0 24.1%

          \[\leadsto -\color{blue}{\left(i \cdot k\right) \cdot \left(y1 \cdot z\right)} \]

       2. associate-*l* 24.3%

          \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       3. associate-*r* 26.1%

          \[\leadsto -i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)} \]

       4. *-commutative 26.1%

          \[\leadsto -i \cdot \left(\color{blue}{\left(y1 \cdot k\right)} \cdot z\right) \]

   13. Simplified 26.1%

       \[\leadsto -\color{blue}{i \cdot \left(\left(y1 \cdot k\right) \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{+203}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-188}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(z \cdot \left(k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 20.8% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+252}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* c (* x y2)))))
   (if (<= x -7.8e-13)
     t_1
     (if (<= x 7.6e+47)
       (* y (* y4 (* c y3)))
       (if (<= x 6.2e+252) t_1 (* j (* y3 (* 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 = y0 * (c * (x * y2));
	double tmp;
	if (x <= -7.8e-13) {
		tmp = t_1;
	} else if (x <= 7.6e+47) {
		tmp = y * (y4 * (c * y3));
	} else if (x <= 6.2e+252) {
		tmp = t_1;
	} else {
		tmp = j * (y3 * (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) :: tmp
    t_1 = y0 * (c * (x * y2))
    if (x <= (-7.8d-13)) then
        tmp = t_1
    else if (x <= 7.6d+47) then
        tmp = y * (y4 * (c * y3))
    else if (x <= 6.2d+252) then
        tmp = t_1
    else
        tmp = j * (y3 * (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 = y0 * (c * (x * y2));
	double tmp;
	if (x <= -7.8e-13) {
		tmp = t_1;
	} else if (x <= 7.6e+47) {
		tmp = y * (y4 * (c * y3));
	} else if (x <= 6.2e+252) {
		tmp = t_1;
	} else {
		tmp = j * (y3 * (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 = y0 * (c * (x * y2))
	tmp = 0
	if x <= -7.8e-13:
		tmp = t_1
	elif x <= 7.6e+47:
		tmp = y * (y4 * (c * y3))
	elif x <= 6.2e+252:
		tmp = t_1
	else:
		tmp = j * (y3 * (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(y0 * Float64(c * Float64(x * y2)))
	tmp = 0.0
	if (x <= -7.8e-13)
		tmp = t_1;
	elseif (x <= 7.6e+47)
		tmp = Float64(y * Float64(y4 * Float64(c * y3)));
	elseif (x <= 6.2e+252)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(y3 * 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 = y0 * (c * (x * y2));
	tmp = 0.0;
	if (x <= -7.8e-13)
		tmp = t_1;
	elseif (x <= 7.6e+47)
		tmp = y * (y4 * (c * y3));
	elseif (x <= 6.2e+252)
		tmp = t_1;
	else
		tmp = j * (y3 * (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[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e-13], t$95$1, If[LessEqual[x, 7.6e+47], N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+252], t$95$1, N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.80000000000000009e-13 or 7.6000000000000007e47 < x < 6.19999999999999964e252

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 36.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 36.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 36.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 37.4%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 35.1%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]

   if -7.80000000000000009e-13 < x < 7.6000000000000007e47

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 41.5%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 41.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.5%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 27.3%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 19.4%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 20.2%

         \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   9. Simplified 20.2%

      \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   if 6.19999999999999964e252 < x

   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 j around inf 58.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 58.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 58.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 58.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 58.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 58.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 42.7%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 42.7%

         \[\leadsto j \cdot \left(y3 \cdot \left(\color{blue}{y5 \cdot y0} - y1 \cdot y4\right)\right) \]

      2. *-commutative 42.7%

         \[\leadsto j \cdot \left(y3 \cdot \left(y5 \cdot y0 - \color{blue}{y4 \cdot y1}\right)\right) \]

   8. Simplified 42.7%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0 - y4 \cdot y1\right)\right)} \]

   9. Taylor expanded in y5 around inf 42.3%

      \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+252}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 20.7% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+252}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -7.5e-13)
   (* y0 (* c (* x y2)))
   (if (<= x 5.5e+47)
     (* y (* y4 (* c y3)))
     (if (<= x 6.2e+252) (* y0 (* y2 (* x c))) (* j (* y3 (* 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 tmp;
	if (x <= -7.5e-13) {
		tmp = y0 * (c * (x * y2));
	} else if (x <= 5.5e+47) {
		tmp = y * (y4 * (c * y3));
	} else if (x <= 6.2e+252) {
		tmp = y0 * (y2 * (x * c));
	} else {
		tmp = j * (y3 * (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) :: tmp
    if (x <= (-7.5d-13)) then
        tmp = y0 * (c * (x * y2))
    else if (x <= 5.5d+47) then
        tmp = y * (y4 * (c * y3))
    else if (x <= 6.2d+252) then
        tmp = y0 * (y2 * (x * c))
    else
        tmp = j * (y3 * (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 tmp;
	if (x <= -7.5e-13) {
		tmp = y0 * (c * (x * y2));
	} else if (x <= 5.5e+47) {
		tmp = y * (y4 * (c * y3));
	} else if (x <= 6.2e+252) {
		tmp = y0 * (y2 * (x * c));
	} else {
		tmp = j * (y3 * (y0 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -7.5e-13:
		tmp = y0 * (c * (x * y2))
	elif x <= 5.5e+47:
		tmp = y * (y4 * (c * y3))
	elif x <= 6.2e+252:
		tmp = y0 * (y2 * (x * c))
	else:
		tmp = j * (y3 * (y0 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -7.5e-13)
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	elseif (x <= 5.5e+47)
		tmp = Float64(y * Float64(y4 * Float64(c * y3)));
	elseif (x <= 6.2e+252)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	else
		tmp = Float64(j * Float64(y3 * 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)
	tmp = 0.0;
	if (x <= -7.5e-13)
		tmp = y0 * (c * (x * y2));
	elseif (x <= 5.5e+47)
		tmp = y * (y4 * (c * y3));
	elseif (x <= 6.2e+252)
		tmp = y0 * (y2 * (x * c));
	else
		tmp = j * (y3 * (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_] := If[LessEqual[x, -7.5e-13], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+47], N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+252], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.5000000000000004e-13

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 35.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 35.6%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 35.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 34.7%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 31.9%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]

   if -7.5000000000000004e-13 < x < 5.4999999999999998e47

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 41.5%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 41.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.5%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 27.3%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 19.4%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 20.2%

         \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   9. Simplified 20.2%

      \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   if 5.4999999999999998e47 < x < 6.19999999999999964e252

   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 y2 around inf 36.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 36.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 36.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 41.5%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 39.8%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.9%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

      2. *-commutative 39.9%

         \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   9. Simplified 39.9%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   if 6.19999999999999964e252 < x

   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 j around inf 58.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 58.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 58.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 58.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 58.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 58.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 42.7%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 42.7%

         \[\leadsto j \cdot \left(y3 \cdot \left(\color{blue}{y5 \cdot y0} - y1 \cdot y4\right)\right) \]

      2. *-commutative 42.7%

         \[\leadsto j \cdot \left(y3 \cdot \left(y5 \cdot y0 - \color{blue}{y4 \cdot y1}\right)\right) \]

   8. Simplified 42.7%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0 - y4 \cdot y1\right)\right)} \]

   9. Taylor expanded in y5 around inf 42.3%

      \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 27.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+252}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 18.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -2.8 \cdot 10^{+60}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 2.05 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -2.8e+60)
   (* y0 (* y2 (* x c)))
   (if (<= y1 6e-254)
     (* y (* y4 (* c y3)))
     (if (<= y1 2.05e+96) (* j (* y5 (* y0 y3))) (* (* a y1) (* z y3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -2.8e+60) {
		tmp = y0 * (y2 * (x * c));
	} else if (y1 <= 6e-254) {
		tmp = y * (y4 * (c * y3));
	} else if (y1 <= 2.05e+96) {
		tmp = j * (y5 * (y0 * y3));
	} else {
		tmp = (a * y1) * (z * y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-2.8d+60)) then
        tmp = y0 * (y2 * (x * c))
    else if (y1 <= 6d-254) then
        tmp = y * (y4 * (c * y3))
    else if (y1 <= 2.05d+96) then
        tmp = j * (y5 * (y0 * y3))
    else
        tmp = (a * y1) * (z * y3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -2.8e+60) {
		tmp = y0 * (y2 * (x * c));
	} else if (y1 <= 6e-254) {
		tmp = y * (y4 * (c * y3));
	} else if (y1 <= 2.05e+96) {
		tmp = j * (y5 * (y0 * y3));
	} else {
		tmp = (a * y1) * (z * y3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -2.8e+60:
		tmp = y0 * (y2 * (x * c))
	elif y1 <= 6e-254:
		tmp = y * (y4 * (c * y3))
	elif y1 <= 2.05e+96:
		tmp = j * (y5 * (y0 * y3))
	else:
		tmp = (a * y1) * (z * y3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -2.8e+60)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (y1 <= 6e-254)
		tmp = Float64(y * Float64(y4 * Float64(c * y3)));
	elseif (y1 <= 2.05e+96)
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	else
		tmp = Float64(Float64(a * y1) * Float64(z * y3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -2.8e+60)
		tmp = y0 * (y2 * (x * c));
	elseif (y1 <= 6e-254)
		tmp = y * (y4 * (c * y3));
	elseif (y1 <= 2.05e+96)
		tmp = j * (y5 * (y0 * y3));
	else
		tmp = (a * y1) * (z * y3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -2.8e+60], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6e-254], N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.05e+96], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * y1), $MachinePrecision] * N[(z * y3), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -2.8e60

   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 y2 around inf 36.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 36.6%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 36.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 35.5%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y5 around 0 23.9%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 25.6%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

      2. *-commutative 25.6%

         \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   9. Simplified 25.6%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(c \cdot x\right)\right)} \]

   if -2.8e60 < y1 < 6.00000000000000023e-254

   1. Initial program 29.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 37.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 37.6%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 37.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 34.7%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 26.8%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 29.4%

         \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   9. Simplified 29.4%

      \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   if 6.00000000000000023e-254 < y1 < 2.04999999999999999e96

   1. Initial program 41.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 46.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 46.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 46.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 36.5%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y2 around 0 21.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.4%

         \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   9. Simplified 28.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   if 2.04999999999999999e96 < y1

   1. Initial program 33.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 47.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 47.4%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 47.4%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 47.4%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 47.4%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 47.4%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 47.4%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 47.4%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 47.4%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 47.4%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 47.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around inf 29.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 34.7%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

      2. *-commutative 34.7%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z\right) \]

   9. Simplified 34.7%

      \[\leadsto \color{blue}{\left(y1 \cdot a\right) \cdot \left(y3 \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.8 \cdot 10^{+60}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 2.05 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 21.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -3.1 \cdot 10^{+70}:\\ \;\;\;\;i \cdot \left(\left(-k\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 2.8 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 10^{+96}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -3.1e+70)
   (* i (* (- k) (* z y1)))
   (if (<= y1 2.8e-253)
     (* y (* y4 (* c y3)))
     (if (<= y1 1e+96) (* j (* y5 (* y0 y3))) (* (* a y1) (* z y3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -3.1e+70) {
		tmp = i * (-k * (z * y1));
	} else if (y1 <= 2.8e-253) {
		tmp = y * (y4 * (c * y3));
	} else if (y1 <= 1e+96) {
		tmp = j * (y5 * (y0 * y3));
	} else {
		tmp = (a * y1) * (z * y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-3.1d+70)) then
        tmp = i * (-k * (z * y1))
    else if (y1 <= 2.8d-253) then
        tmp = y * (y4 * (c * y3))
    else if (y1 <= 1d+96) then
        tmp = j * (y5 * (y0 * y3))
    else
        tmp = (a * y1) * (z * y3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -3.1e+70) {
		tmp = i * (-k * (z * y1));
	} else if (y1 <= 2.8e-253) {
		tmp = y * (y4 * (c * y3));
	} else if (y1 <= 1e+96) {
		tmp = j * (y5 * (y0 * y3));
	} else {
		tmp = (a * y1) * (z * y3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -3.1e+70:
		tmp = i * (-k * (z * y1))
	elif y1 <= 2.8e-253:
		tmp = y * (y4 * (c * y3))
	elif y1 <= 1e+96:
		tmp = j * (y5 * (y0 * y3))
	else:
		tmp = (a * y1) * (z * y3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -3.1e+70)
		tmp = Float64(i * Float64(Float64(-k) * Float64(z * y1)));
	elseif (y1 <= 2.8e-253)
		tmp = Float64(y * Float64(y4 * Float64(c * y3)));
	elseif (y1 <= 1e+96)
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	else
		tmp = Float64(Float64(a * y1) * Float64(z * y3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -3.1e+70)
		tmp = i * (-k * (z * y1));
	elseif (y1 <= 2.8e-253)
		tmp = y * (y4 * (c * y3));
	elseif (y1 <= 1e+96)
		tmp = j * (y5 * (y0 * y3));
	else
		tmp = (a * y1) * (z * y3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -3.1e+70], N[(i * N[((-k) * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.8e-253], N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1e+96], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * y1), $MachinePrecision] * N[(z * y3), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -3.1000000000000003e70

   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 y1 around -inf 55.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 55.5%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 55.5%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 55.5%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 55.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 55.5%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 55.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 55.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 55.5%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 55.5%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z around -inf 34.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 34.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

      2. associate-*r* 36.5%

         \[\leadsto -\color{blue}{\left(y1 \cdot z\right) \cdot \left(i \cdot k - a \cdot y3\right)} \]

      3. *-commutative 36.5%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(\color{blue}{k \cdot i} - a \cdot y3\right) \]

      4. *-commutative 36.5%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(k \cdot i - \color{blue}{y3 \cdot a}\right) \]

   8. Simplified 36.5%

      \[\leadsto \color{blue}{-\left(y1 \cdot z\right) \cdot \left(k \cdot i - y3 \cdot a\right)} \]

   9. Taylor expanded in k around inf 31.4%

      \[\leadsto -\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

   if -3.1000000000000003e70 < y1 < 2.80000000000000006e-253

   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 y2 around inf 39.3%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 39.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 39.3%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 35.1%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 26.2%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.7%

         \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   9. Simplified 28.7%

      \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   if 2.80000000000000006e-253 < y1 < 1.00000000000000005e96

   1. Initial program 41.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 46.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 46.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 46.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 36.5%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y2 around 0 21.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.4%

         \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   9. Simplified 28.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   if 1.00000000000000005e96 < y1

   1. Initial program 33.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 47.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 47.4%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 47.4%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 47.4%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 47.4%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 47.4%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 47.4%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 47.4%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 47.4%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 47.4%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 47.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around inf 29.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 34.7%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z\right)} \]

      2. *-commutative 34.7%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z\right) \]

   9. Simplified 34.7%

      \[\leadsto \color{blue}{\left(y1 \cdot a\right) \cdot \left(y3 \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.1 \cdot 10^{+70}:\\ \;\;\;\;i \cdot \left(\left(-k\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 2.8 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 10^{+96}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 20.9% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -7 \cdot 10^{+78} \lor \neg \left(y1 \leq 9.5 \cdot 10^{+96}\right):\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y1 -7e+78) (not (<= y1 9.5e+96)))
   (* a (* y1 (* z y3)))
   (* c (* y (* y3 y4)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -7e+78) || !(y1 <= 9.5e+96)) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y1 <= (-7d+78)) .or. (.not. (y1 <= 9.5d+96))) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = c * (y * (y3 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -7e+78) || !(y1 <= 9.5e+96)) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y1 <= -7e+78) or not (y1 <= 9.5e+96):
		tmp = a * (y1 * (z * y3))
	else:
		tmp = c * (y * (y3 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y1 <= -7e+78) || !(y1 <= 9.5e+96))
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y1 <= -7e+78) || ~((y1 <= 9.5e+96)))
		tmp = a * (y1 * (z * y3));
	else
		tmp = c * (y * (y3 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y1, -7e+78], N[Not[LessEqual[y1, 9.5e+96]], $MachinePrecision]], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y1 < -7.0000000000000003e78 or 9.50000000000000089e96 < y1

   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 y1 around -inf 52.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 52.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 52.7%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 52.7%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 52.7%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 52.7%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 52.7%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 52.7%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 52.7%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 52.7%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 48.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around inf 27.0%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -7.0000000000000003e78 < y1 < 9.50000000000000089e96

   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 y2 around inf 41.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 41.6%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 27.3%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 21.0%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -7 \cdot 10^{+78} \lor \neg \left(y1 \leq 9.5 \cdot 10^{+96}\right):\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 19.4% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.6 \cdot 10^{+133} \lor \neg \left(c \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= c -7.6e+133) (not (<= c 2.2e-71)))
   (* c (* y (* y3 y4)))
   (* j (* y0 (* y3 y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((c <= -7.6e+133) || !(c <= 2.2e-71)) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((c <= (-7.6d+133)) .or. (.not. (c <= 2.2d-71))) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = j * (y0 * (y3 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((c <= -7.6e+133) || !(c <= 2.2e-71)) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (c <= -7.6e+133) or not (c <= 2.2e-71):
		tmp = c * (y * (y3 * y4))
	else:
		tmp = j * (y0 * (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((c <= -7.6e+133) || !(c <= 2.2e-71))
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((c <= -7.6e+133) || ~((c <= 2.2e-71)))
		tmp = c * (y * (y3 * y4));
	else
		tmp = j * (y0 * (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[c, -7.6e+133], N[Not[LessEqual[c, 2.2e-71]], $MachinePrecision]], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -7.6000000000000004e133 or 2.19999999999999997e-71 < c

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 34.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 34.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 33.8%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 26.9%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if -7.6000000000000004e133 < c < 2.19999999999999997e-71

   1. Initial program 34.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 43.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 43.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 43.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 33.0%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y2 around 0 20.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.6 \cdot 10^{+133} \lor \neg \left(c \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 20.7% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.08 \cdot 10^{+219} \lor \neg \left(y1 \leq 10^{+96}\right):\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y1 -1.08e+219) (not (<= y1 1e+96)))
   (* a (* y1 (* z y3)))
   (* j (* y3 (* 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 tmp;
	if ((y1 <= -1.08e+219) || !(y1 <= 1e+96)) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = j * (y3 * (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) :: tmp
    if ((y1 <= (-1.08d+219)) .or. (.not. (y1 <= 1d+96))) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = j * (y3 * (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 tmp;
	if ((y1 <= -1.08e+219) || !(y1 <= 1e+96)) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = j * (y3 * (y0 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y1 <= -1.08e+219) or not (y1 <= 1e+96):
		tmp = a * (y1 * (z * y3))
	else:
		tmp = j * (y3 * (y0 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y1 <= -1.08e+219) || !(y1 <= 1e+96))
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = Float64(j * Float64(y3 * 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)
	tmp = 0.0;
	if ((y1 <= -1.08e+219) || ~((y1 <= 1e+96)))
		tmp = a * (y1 * (z * y3));
	else
		tmp = j * (y3 * (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_] := If[Or[LessEqual[y1, -1.08e+219], N[Not[LessEqual[y1, 1e+96]], $MachinePrecision]], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y1 < -1.08000000000000005e219 or 1.00000000000000005e96 < y1

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 50.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 50.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 50.9%

         \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. +-commutative 50.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. mul-1-neg 50.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. unsub-neg 50.9%

         \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 50.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. *-commutative 50.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      8. *-commutative 50.9%

         \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. Simplified 50.9%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf 55.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   7. Taylor expanded in y3 around inf 33.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -1.08000000000000005e219 < y1 < 1.00000000000000005e96

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 37.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 37.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 37.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 37.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 37.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 28.6%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 28.6%

         \[\leadsto j \cdot \left(y3 \cdot \left(\color{blue}{y5 \cdot y0} - y1 \cdot y4\right)\right) \]

      2. *-commutative 28.6%

         \[\leadsto j \cdot \left(y3 \cdot \left(y5 \cdot y0 - \color{blue}{y4 \cdot y1}\right)\right) \]

   8. Simplified 28.6%

      \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0 - y4 \cdot y1\right)\right)} \]

   9. Taylor expanded in y5 around inf 20.7%

      \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 24.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.08 \cdot 10^{+219} \lor \neg \left(y1 \leq 10^{+96}\right):\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 39: 19.4% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+130} \lor \neg \left(c \leq 2.7 \cdot 10^{-71}\right):\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= c -6.5e+130) (not (<= c 2.7e-71)))
   (* c (* y (* y3 y4)))
   (* j (* y5 (* y0 y3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((c <= -6.5e+130) || !(c <= 2.7e-71)) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = j * (y5 * (y0 * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((c <= (-6.5d+130)) .or. (.not. (c <= 2.7d-71))) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = j * (y5 * (y0 * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((c <= -6.5e+130) || !(c <= 2.7e-71)) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = j * (y5 * (y0 * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (c <= -6.5e+130) or not (c <= 2.7e-71):
		tmp = c * (y * (y3 * y4))
	else:
		tmp = j * (y5 * (y0 * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((c <= -6.5e+130) || !(c <= 2.7e-71))
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((c <= -6.5e+130) || ~((c <= 2.7e-71)))
		tmp = c * (y * (y3 * y4));
	else
		tmp = j * (y5 * (y0 * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[c, -6.5e+130], N[Not[LessEqual[c, 2.7e-71]], $MachinePrecision]], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.5e130 or 2.7000000000000001e-71 < c

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 34.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 34.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 33.8%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 26.9%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if -6.5e130 < c < 2.7000000000000001e-71

   1. Initial program 34.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 43.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 43.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 43.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 33.0%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y2 around 0 20.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 24.1%

         \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   9. Simplified 24.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot y3\right) \cdot y5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+130} \lor \neg \left(c \leq 2.7 \cdot 10^{-71}\right):\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 40: 21.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+131} \lor \neg \left(c \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= c -1.05e+131) (not (<= c 2.2e-71)))
   (* y (* y3 (* c y4)))
   (* j (* y5 (* y0 y3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((c <= -1.05e+131) || !(c <= 2.2e-71)) {
		tmp = y * (y3 * (c * y4));
	} else {
		tmp = j * (y5 * (y0 * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((c <= (-1.05d+131)) .or. (.not. (c <= 2.2d-71))) then
        tmp = y * (y3 * (c * y4))
    else
        tmp = j * (y5 * (y0 * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((c <= -1.05e+131) || !(c <= 2.2e-71)) {
		tmp = y * (y3 * (c * y4));
	} else {
		tmp = j * (y5 * (y0 * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (c <= -1.05e+131) or not (c <= 2.2e-71):
		tmp = y * (y3 * (c * y4))
	else:
		tmp = j * (y5 * (y0 * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((c <= -1.05e+131) || !(c <= 2.2e-71))
		tmp = Float64(y * Float64(y3 * Float64(c * y4)));
	else
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((c <= -1.05e+131) || ~((c <= 2.2e-71)))
		tmp = y * (y3 * (c * y4));
	else
		tmp = j * (y5 * (y0 * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[c, -1.05e+131], N[Not[LessEqual[c, 2.2e-71]], $MachinePrecision]], N[(y * N[(y3 * N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.04999999999999993e131 or 2.19999999999999997e-71 < c

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 34.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 34.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 33.8%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 31.3%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(c \cdot y4\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 31.3%

         \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y4 \cdot c\right)}\right) \]

   9. Simplified 31.3%

      \[\leadsto y \cdot \left(y3 \cdot \color{blue}{\left(y4 \cdot c\right)}\right) \]

   if -1.04999999999999993e131 < c < 2.19999999999999997e-71

   1. Initial program 34.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 43.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 43.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 43.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 33.0%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y2 around 0 20.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 24.1%

         \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   9. Simplified 24.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot y3\right) \cdot y5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+131} \lor \neg \left(c \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 41: 21.1% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.02 \cdot 10^{+130} \lor \neg \left(c \leq 2.4 \cdot 10^{-71}\right):\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= c -2.02e+130) (not (<= c 2.4e-71)))
   (* y (* y4 (* c y3)))
   (* j (* y5 (* y0 y3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((c <= -2.02e+130) || !(c <= 2.4e-71)) {
		tmp = y * (y4 * (c * y3));
	} else {
		tmp = j * (y5 * (y0 * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((c <= (-2.02d+130)) .or. (.not. (c <= 2.4d-71))) then
        tmp = y * (y4 * (c * y3))
    else
        tmp = j * (y5 * (y0 * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((c <= -2.02e+130) || !(c <= 2.4e-71)) {
		tmp = y * (y4 * (c * y3));
	} else {
		tmp = j * (y5 * (y0 * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (c <= -2.02e+130) or not (c <= 2.4e-71):
		tmp = y * (y4 * (c * y3))
	else:
		tmp = j * (y5 * (y0 * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((c <= -2.02e+130) || !(c <= 2.4e-71))
		tmp = Float64(y * Float64(y4 * Float64(c * y3)));
	else
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((c <= -2.02e+130) || ~((c <= 2.4e-71)))
		tmp = y * (y4 * (c * y3));
	else
		tmp = j * (y5 * (y0 * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[c, -2.02e+130], N[Not[LessEqual[c, 2.4e-71]], $MachinePrecision]], N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.0199999999999999e130 or 2.4e-71 < c

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 34.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 34.7%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around inf 33.8%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 31.2%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 34.9%

         \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   9. Simplified 34.9%

      \[\leadsto y \cdot \color{blue}{\left(\left(c \cdot y3\right) \cdot y4\right)} \]

   if -2.0199999999999999e130 < c < 2.4e-71

   1. Initial program 34.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 43.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. *-commutative 43.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 43.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y0 around inf 33.0%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2\right)\right)} \]

   7. Taylor expanded in y2 around 0 20.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 24.1%

         \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   9. Simplified 24.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot y3\right) \cdot y5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.02 \cdot 10^{+130} \lor \neg \left(c \leq 2.4 \cdot 10^{-71}\right):\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 42: 17.2% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y1 (* z y3))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y1 * (z * y3));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y1 * (z * y3))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y1 * (z * y3));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y1 * (z * y3))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y1 * Float64(z * y3)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y1 * (z * y3));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 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 y1 around -inf 39.5%

   \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
4. Step-by-step derivation

   1. mul-1-neg 39.5%

      \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   2. distribute-rgt-neg-in 39.5%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   3. +-commutative 39.5%

      \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   4. mul-1-neg 39.5%

      \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   5. unsub-neg 39.5%

      \[\leadsto y1 \cdot \left(-\left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   6. *-commutative 39.5%

      \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   7. *-commutative 39.5%

      \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   8. *-commutative 39.5%

      \[\leadsto y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

5. Simplified 39.5%

   \[\leadsto \color{blue}{y1 \cdot \left(-\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

6. Taylor expanded in a around inf 29.7%

   \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

7. Taylor expanded in y3 around inf 15.1%

   \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

8. Final simplification 15.1%

   \[\leadsto a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \]
9. 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 2024046 
(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)))))