Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.6% → 38.4%

Time: 1.7min

Alternatives: 34

Speedup: 2.6×

• 89.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.6% 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: 38.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y5 \cdot \left(y \cdot k - t \cdot j\right)\\ t_2 := \left(y3 \cdot y4 - x \cdot i\right) \cdot \left(y \cdot c\right)\\ t_3 := x \cdot j - z \cdot k\\ t_4 := b \cdot y4 - i \cdot y5\\ t_5 := y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\\ t_6 := i \cdot y1 - b \cdot y0\\ t_7 := j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot t_4\right) + x \cdot t_6\right)\\ t_8 := a \cdot b - c \cdot i\\ t_9 := x \cdot \left(\left(y \cdot t_8 + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_6\right)\\ \mathbf{if}\;y1 \leq -1.35 \cdot 10^{+99}:\\ \;\;\;\;y1 \cdot \left(i \cdot t_3 + t_5\right)\\ \mathbf{elif}\;y1 \leq -2.25 \cdot 10^{+17}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y1 \leq -5.6 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq -4.5 \cdot 10^{-170}:\\ \;\;\;\;i \cdot \left(y1 \cdot t_3 + \left(t_1 + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -3.4 \cdot 10^{-199}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t_8\\ \mathbf{elif}\;y1 \leq -5.6 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot t_4\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.6 \cdot 10^{-274}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq 4.2 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 4.3 \cdot 10^{-143}:\\ \;\;\;\;i \cdot t_1\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{-96}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{-91}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 5.6 \cdot 10^{+105}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;y1 \leq 1.06 \cdot 10^{+194}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y5 (- (* y k) (* t j))))
        (t_2 (* (- (* y3 y4) (* x i)) (* y c)))
        (t_3 (- (* x j) (* z k)))
        (t_4 (- (* b y4) (* i y5)))
        (t_5 (+ (* y4 (- (* k y2) (* j y3))) (* a (- (* z y3) (* x y2)))))
        (t_6 (- (* i y1) (* b y0)))
        (t_7 (* j (+ (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t t_4)) (* x t_6))))
        (t_8 (- (* a b) (* c i)))
        (t_9 (* x (+ (+ (* y t_8) (* y2 (- (* c y0) (* a y1)))) (* j t_6)))))
   (if (<= y1 -1.35e+99)
     (* y1 (+ (* i t_3) t_5))
     (if (<= y1 -2.25e+17)
       t_7
       (if (<= y1 -5.6e-83)
         t_2
         (if (<= y1 -4.5e-170)
           (* i (+ (* y1 t_3) (+ t_1 (* c (- (* z t) (* x y))))))
           (if (<= y1 -3.4e-199)
             (* (* x y) t_8)
             (if (<= y1 -5.6e-298)
               (*
                t
                (+
                 (+ (* z (- (* c i) (* a b))) (* j t_4))
                 (* y2 (- (* a y5) (* c y4)))))
               (if (<= y1 1.6e-274)
                 t_2
                 (if (<= y1 4.2e-215)
                   (* a (* b (- (* x y) (* z t))))
                   (if (<= y1 4.3e-143)
                     (* i t_1)
                     (if (<= y1 2.7e-96)
                       t_9
                       (if (<= y1 3.4e-91)
                         (*
                          y0
                          (+
                           (+
                            (* c (- (* x y2) (* z y3)))
                            (* y5 (- (* j y3) (* k y2))))
                           (* b (- (* z k) (* x j)))))
                         (if (<= y1 5.6e+105)
                           t_9
                           (if (<= y1 1.06e+194) t_7 (* y1 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 = y5 * ((y * k) - (t * j));
	double t_2 = ((y3 * y4) - (x * i)) * (y * c);
	double t_3 = (x * j) - (z * k);
	double t_4 = (b * y4) - (i * y5);
	double t_5 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)));
	double t_6 = (i * y1) - (b * y0);
	double t_7 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_4)) + (x * t_6));
	double t_8 = (a * b) - (c * i);
	double t_9 = x * (((y * t_8) + (y2 * ((c * y0) - (a * y1)))) + (j * t_6));
	double tmp;
	if (y1 <= -1.35e+99) {
		tmp = y1 * ((i * t_3) + t_5);
	} else if (y1 <= -2.25e+17) {
		tmp = t_7;
	} else if (y1 <= -5.6e-83) {
		tmp = t_2;
	} else if (y1 <= -4.5e-170) {
		tmp = i * ((y1 * t_3) + (t_1 + (c * ((z * t) - (x * y)))));
	} else if (y1 <= -3.4e-199) {
		tmp = (x * y) * t_8;
	} else if (y1 <= -5.6e-298) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * ((a * y5) - (c * y4))));
	} else if (y1 <= 1.6e-274) {
		tmp = t_2;
	} else if (y1 <= 4.2e-215) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 4.3e-143) {
		tmp = i * t_1;
	} else if (y1 <= 2.7e-96) {
		tmp = t_9;
	} else if (y1 <= 3.4e-91) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else if (y1 <= 5.6e+105) {
		tmp = t_9;
	} else if (y1 <= 1.06e+194) {
		tmp = t_7;
	} else {
		tmp = y1 * t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = y5 * ((y * k) - (t * j))
    t_2 = ((y3 * y4) - (x * i)) * (y * c)
    t_3 = (x * j) - (z * k)
    t_4 = (b * y4) - (i * y5)
    t_5 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)))
    t_6 = (i * y1) - (b * y0)
    t_7 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_4)) + (x * t_6))
    t_8 = (a * b) - (c * i)
    t_9 = x * (((y * t_8) + (y2 * ((c * y0) - (a * y1)))) + (j * t_6))
    if (y1 <= (-1.35d+99)) then
        tmp = y1 * ((i * t_3) + t_5)
    else if (y1 <= (-2.25d+17)) then
        tmp = t_7
    else if (y1 <= (-5.6d-83)) then
        tmp = t_2
    else if (y1 <= (-4.5d-170)) then
        tmp = i * ((y1 * t_3) + (t_1 + (c * ((z * t) - (x * y)))))
    else if (y1 <= (-3.4d-199)) then
        tmp = (x * y) * t_8
    else if (y1 <= (-5.6d-298)) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * ((a * y5) - (c * y4))))
    else if (y1 <= 1.6d-274) then
        tmp = t_2
    else if (y1 <= 4.2d-215) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y1 <= 4.3d-143) then
        tmp = i * t_1
    else if (y1 <= 2.7d-96) then
        tmp = t_9
    else if (y1 <= 3.4d-91) then
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    else if (y1 <= 5.6d+105) then
        tmp = t_9
    else if (y1 <= 1.06d+194) then
        tmp = t_7
    else
        tmp = y1 * 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 = y5 * ((y * k) - (t * j));
	double t_2 = ((y3 * y4) - (x * i)) * (y * c);
	double t_3 = (x * j) - (z * k);
	double t_4 = (b * y4) - (i * y5);
	double t_5 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)));
	double t_6 = (i * y1) - (b * y0);
	double t_7 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_4)) + (x * t_6));
	double t_8 = (a * b) - (c * i);
	double t_9 = x * (((y * t_8) + (y2 * ((c * y0) - (a * y1)))) + (j * t_6));
	double tmp;
	if (y1 <= -1.35e+99) {
		tmp = y1 * ((i * t_3) + t_5);
	} else if (y1 <= -2.25e+17) {
		tmp = t_7;
	} else if (y1 <= -5.6e-83) {
		tmp = t_2;
	} else if (y1 <= -4.5e-170) {
		tmp = i * ((y1 * t_3) + (t_1 + (c * ((z * t) - (x * y)))));
	} else if (y1 <= -3.4e-199) {
		tmp = (x * y) * t_8;
	} else if (y1 <= -5.6e-298) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * ((a * y5) - (c * y4))));
	} else if (y1 <= 1.6e-274) {
		tmp = t_2;
	} else if (y1 <= 4.2e-215) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 4.3e-143) {
		tmp = i * t_1;
	} else if (y1 <= 2.7e-96) {
		tmp = t_9;
	} else if (y1 <= 3.4e-91) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else if (y1 <= 5.6e+105) {
		tmp = t_9;
	} else if (y1 <= 1.06e+194) {
		tmp = t_7;
	} else {
		tmp = y1 * 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 = y5 * ((y * k) - (t * j))
	t_2 = ((y3 * y4) - (x * i)) * (y * c)
	t_3 = (x * j) - (z * k)
	t_4 = (b * y4) - (i * y5)
	t_5 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)))
	t_6 = (i * y1) - (b * y0)
	t_7 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_4)) + (x * t_6))
	t_8 = (a * b) - (c * i)
	t_9 = x * (((y * t_8) + (y2 * ((c * y0) - (a * y1)))) + (j * t_6))
	tmp = 0
	if y1 <= -1.35e+99:
		tmp = y1 * ((i * t_3) + t_5)
	elif y1 <= -2.25e+17:
		tmp = t_7
	elif y1 <= -5.6e-83:
		tmp = t_2
	elif y1 <= -4.5e-170:
		tmp = i * ((y1 * t_3) + (t_1 + (c * ((z * t) - (x * y)))))
	elif y1 <= -3.4e-199:
		tmp = (x * y) * t_8
	elif y1 <= -5.6e-298:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * ((a * y5) - (c * y4))))
	elif y1 <= 1.6e-274:
		tmp = t_2
	elif y1 <= 4.2e-215:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y1 <= 4.3e-143:
		tmp = i * t_1
	elif y1 <= 2.7e-96:
		tmp = t_9
	elif y1 <= 3.4e-91:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	elif y1 <= 5.6e+105:
		tmp = t_9
	elif y1 <= 1.06e+194:
		tmp = t_7
	else:
		tmp = y1 * 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(y5 * Float64(Float64(y * k) - Float64(t * j)))
	t_2 = Float64(Float64(Float64(y3 * y4) - Float64(x * i)) * Float64(y * c))
	t_3 = Float64(Float64(x * j) - Float64(z * k))
	t_4 = Float64(Float64(b * y4) - Float64(i * y5))
	t_5 = Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))
	t_6 = Float64(Float64(i * y1) - Float64(b * y0))
	t_7 = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * t_4)) + Float64(x * t_6)))
	t_8 = Float64(Float64(a * b) - Float64(c * i))
	t_9 = Float64(x * Float64(Float64(Float64(y * t_8) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_6)))
	tmp = 0.0
	if (y1 <= -1.35e+99)
		tmp = Float64(y1 * Float64(Float64(i * t_3) + t_5));
	elseif (y1 <= -2.25e+17)
		tmp = t_7;
	elseif (y1 <= -5.6e-83)
		tmp = t_2;
	elseif (y1 <= -4.5e-170)
		tmp = Float64(i * Float64(Float64(y1 * t_3) + Float64(t_1 + Float64(c * Float64(Float64(z * t) - Float64(x * y))))));
	elseif (y1 <= -3.4e-199)
		tmp = Float64(Float64(x * y) * t_8);
	elseif (y1 <= -5.6e-298)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * t_4)) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y1 <= 1.6e-274)
		tmp = t_2;
	elseif (y1 <= 4.2e-215)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 4.3e-143)
		tmp = Float64(i * t_1);
	elseif (y1 <= 2.7e-96)
		tmp = t_9;
	elseif (y1 <= 3.4e-91)
		tmp = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y1 <= 5.6e+105)
		tmp = t_9;
	elseif (y1 <= 1.06e+194)
		tmp = t_7;
	else
		tmp = Float64(y1 * 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 = y5 * ((y * k) - (t * j));
	t_2 = ((y3 * y4) - (x * i)) * (y * c);
	t_3 = (x * j) - (z * k);
	t_4 = (b * y4) - (i * y5);
	t_5 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)));
	t_6 = (i * y1) - (b * y0);
	t_7 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_4)) + (x * t_6));
	t_8 = (a * b) - (c * i);
	t_9 = x * (((y * t_8) + (y2 * ((c * y0) - (a * y1)))) + (j * t_6));
	tmp = 0.0;
	if (y1 <= -1.35e+99)
		tmp = y1 * ((i * t_3) + t_5);
	elseif (y1 <= -2.25e+17)
		tmp = t_7;
	elseif (y1 <= -5.6e-83)
		tmp = t_2;
	elseif (y1 <= -4.5e-170)
		tmp = i * ((y1 * t_3) + (t_1 + (c * ((z * t) - (x * y)))));
	elseif (y1 <= -3.4e-199)
		tmp = (x * y) * t_8;
	elseif (y1 <= -5.6e-298)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * ((a * y5) - (c * y4))));
	elseif (y1 <= 1.6e-274)
		tmp = t_2;
	elseif (y1 <= 4.2e-215)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y1 <= 4.3e-143)
		tmp = i * t_1;
	elseif (y1 <= 2.7e-96)
		tmp = t_9;
	elseif (y1 <= 3.4e-91)
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	elseif (y1 <= 5.6e+105)
		tmp = t_9;
	elseif (y1 <= 1.06e+194)
		tmp = t_7;
	else
		tmp = y1 * 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[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision] * N[(y * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(x * N[(N[(N[(y * t$95$8), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.35e+99], N[(y1 * N[(N[(i * t$95$3), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.25e+17], t$95$7, If[LessEqual[y1, -5.6e-83], t$95$2, If[LessEqual[y1, -4.5e-170], N[(i * N[(N[(y1 * t$95$3), $MachinePrecision] + N[(t$95$1 + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.4e-199], N[(N[(x * y), $MachinePrecision] * t$95$8), $MachinePrecision], If[LessEqual[y1, -5.6e-298], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.6e-274], t$95$2, If[LessEqual[y1, 4.2e-215], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.3e-143], N[(i * t$95$1), $MachinePrecision], If[LessEqual[y1, 2.7e-96], t$95$9, If[LessEqual[y1, 3.4e-91], N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.6e+105], t$95$9, If[LessEqual[y1, 1.06e+194], t$95$7, N[(y1 * t$95$5), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y1 < -1.34999999999999994e99

   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 67.6%

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

      1. mul-1-neg 67.6%

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

      2. *-commutative 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

   5. Simplified 67.6%

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

   if -1.34999999999999994e99 < y1 < -2.25e17 or 5.6000000000000003e105 < y1 < 1.0599999999999999e194

   1. Initial program 30.5%

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

   3. Taylor expanded in j around inf 69.7%

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

   if -2.25e17 < y1 < -5.6000000000000002e-83 or -5.59999999999999985e-298 < y1 < 1.59999999999999989e-274

   1. Initial program 27.2%

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

   3. Taylor expanded in c around inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

      4. *-commutative 58.3%

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

      5. *-commutative 58.3%

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

      6. *-commutative 58.3%

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

      7. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in y around -inf 69.8%

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

      1. *-commutative 69.8%

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

      2. *-commutative 69.8%

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

      3. associate-*l* 69.8%

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

      4. +-commutative 69.8%

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

      5. mul-1-neg 69.8%

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

      6. unsub-neg 69.8%

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

      7. *-commutative 69.8%

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

   8. Simplified 69.8%

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

   if -5.6000000000000002e-83 < y1 < -4.50000000000000002e-170

   1. Initial program 35.7%

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

   3. Taylor expanded in i around -inf 64.7%

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

   if -4.50000000000000002e-170 < y1 < -3.40000000000000006e-199

   1. Initial program 40.0%

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

   3. Taylor expanded in x around inf 79.7%

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

   4. Taylor expanded in y around inf 99.7%

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

      1. associate-*r* 100.0%

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

   6. Simplified 100.0%

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

   if -3.40000000000000006e-199 < y1 < -5.59999999999999985e-298

   1. Initial program 64.5%

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

   3. Taylor expanded in t around inf 76.9%

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

   if 1.59999999999999989e-274 < y1 < 4.2e-215

   1. Initial program 12.5%

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

   3. Taylor expanded in b around inf 62.5%

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

   4. Taylor expanded in a around inf 76.1%

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

   if 4.2e-215 < y1 < 4.29999999999999956e-143

   1. Initial program 12.5%

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

   3. Taylor expanded in i around -inf 62.7%

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

   4. Taylor expanded in y5 around inf 75.2%

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

   if 4.29999999999999956e-143 < y1 < 2.7e-96 or 3.40000000000000027e-91 < y1 < 5.6000000000000003e105

   1. Initial program 26.9%

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

   3. Taylor expanded in x around inf 59.7%

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

   if 2.7e-96 < y1 < 3.40000000000000027e-91

   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 y0 around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

      6. *-commutative 100.0%

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

      7. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 1.0599999999999999e194 < y1

   1. Initial program 20.8%

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

   3. Taylor expanded in y1 around -inf 50.3%

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

      1. mul-1-neg 50.3%

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

      2. *-commutative 50.3%

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

      3. distribute-rgt-neg-in 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in i around 0 59.1%

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

      1. associate-*r* 59.1%

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

      2. neg-mul-1 59.1%

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

      3. sub-neg 59.1%

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

      4. *-commutative 59.1%

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

      5. sub-neg 59.1%

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

      6. *-commutative 59.1%

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

   8. Simplified 59.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.35 \cdot 10^{+99}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -2.25 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -5.6 \cdot 10^{-83}:\\ \;\;\;\;\left(y3 \cdot y4 - x \cdot i\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y1 \leq -4.5 \cdot 10^{-170}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -3.4 \cdot 10^{-199}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)\\ \mathbf{elif}\;y1 \leq -5.6 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.6 \cdot 10^{-274}:\\ \;\;\;\;\left(y3 \cdot y4 - x \cdot i\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y1 \leq 4.2 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 4.3 \cdot 10^{-143}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{-91}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 5.6 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.06 \cdot 10^{+194}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in j around inf 42.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.6%

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

Alternative 3: 39.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x \cdot y\\ t_2 := z \cdot \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ t_3 := y \cdot y3 - t \cdot y2\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := a \cdot y5 - c \cdot y4\\ t_6 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_4\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_7 := y \cdot k - t \cdot j\\ \mathbf{if}\;z \leq -6 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-178}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-89}:\\ \;\;\;\;y4 \cdot \left(c \cdot t_3 - \left(y1 \cdot \left(j \cdot y3 - k \cdot y2\right) + b \cdot t_7\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;z \leq 180000:\\ \;\;\;\;t \cdot \left(y2 \cdot t_5\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+90}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{+176}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot t_1\right) + y4 \cdot t_3\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+199}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot t_7 + a \cdot t_1\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+271}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t_4\right) + t \cdot t_5\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z t) (* x y)))
        (t_2 (* z (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0))))))
        (t_3 (- (* y y3) (* t y2)))
        (t_4 (- (* c y0) (* a y1)))
        (t_5 (- (* a y5) (* c y4)))
        (t_6
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_4))
           (* j (- (* i y1) (* b y0))))))
        (t_7 (- (* y k) (* t j))))
   (if (<= z -6e+80)
     t_2
     (if (<= z 1.05e-178)
       t_6
       (if (<= z 9.2e-89)
         (* y4 (- (* c t_3) (+ (* y1 (- (* j y3) (* k y2))) (* b t_7))))
         (if (<= z 9.5e-20)
           (*
            a
            (+
             (* y5 (- (* t y2) (* y y3)))
             (+ (* b (- (* x y) (* z t))) (* y1 (- (* z y3) (* x y2))))))
           (if (<= z 180000.0)
             (* t (* y2 t_5))
             (if (<= z 1.6e+90)
               t_6
               (if (<= z 1.04e+176)
                 (*
                  c
                  (+ (+ (* y0 (- (* x y2) (* z y3))) (* i t_1)) (* y4 t_3)))
                 (if (<= z 2.6e+199)
                   (*
                    b
                    (- (* y0 (- (* z k) (* x j))) (+ (* y4 t_7) (* a t_1))))
                   (if (<= z 9.5e+271)
                     (*
                      y2
                      (+
                       (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_4))
                       (* t t_5)))
                     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 = (z * t) - (x * y);
	double t_2 = z * ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0))));
	double t_3 = (y * y3) - (t * y2);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (a * y5) - (c * y4);
	double t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	double t_7 = (y * k) - (t * j);
	double tmp;
	if (z <= -6e+80) {
		tmp = t_2;
	} else if (z <= 1.05e-178) {
		tmp = t_6;
	} else if (z <= 9.2e-89) {
		tmp = y4 * ((c * t_3) - ((y1 * ((j * y3) - (k * y2))) + (b * t_7)));
	} else if (z <= 9.5e-20) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) + (y1 * ((z * y3) - (x * y2)))));
	} else if (z <= 180000.0) {
		tmp = t * (y2 * t_5);
	} else if (z <= 1.6e+90) {
		tmp = t_6;
	} else if (z <= 1.04e+176) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * t_1)) + (y4 * t_3));
	} else if (z <= 2.6e+199) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_7) + (a * t_1)));
	} else if (z <= 9.5e+271) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * t_5));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (z * t) - (x * y)
    t_2 = z * ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0))))
    t_3 = (y * y3) - (t * y2)
    t_4 = (c * y0) - (a * y1)
    t_5 = (a * y5) - (c * y4)
    t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))))
    t_7 = (y * k) - (t * j)
    if (z <= (-6d+80)) then
        tmp = t_2
    else if (z <= 1.05d-178) then
        tmp = t_6
    else if (z <= 9.2d-89) then
        tmp = y4 * ((c * t_3) - ((y1 * ((j * y3) - (k * y2))) + (b * t_7)))
    else if (z <= 9.5d-20) then
        tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) + (y1 * ((z * y3) - (x * y2)))))
    else if (z <= 180000.0d0) then
        tmp = t * (y2 * t_5)
    else if (z <= 1.6d+90) then
        tmp = t_6
    else if (z <= 1.04d+176) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * t_1)) + (y4 * t_3))
    else if (z <= 2.6d+199) then
        tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_7) + (a * t_1)))
    else if (z <= 9.5d+271) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * t_5))
    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 = (z * t) - (x * y);
	double t_2 = z * ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0))));
	double t_3 = (y * y3) - (t * y2);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (a * y5) - (c * y4);
	double t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	double t_7 = (y * k) - (t * j);
	double tmp;
	if (z <= -6e+80) {
		tmp = t_2;
	} else if (z <= 1.05e-178) {
		tmp = t_6;
	} else if (z <= 9.2e-89) {
		tmp = y4 * ((c * t_3) - ((y1 * ((j * y3) - (k * y2))) + (b * t_7)));
	} else if (z <= 9.5e-20) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) + (y1 * ((z * y3) - (x * y2)))));
	} else if (z <= 180000.0) {
		tmp = t * (y2 * t_5);
	} else if (z <= 1.6e+90) {
		tmp = t_6;
	} else if (z <= 1.04e+176) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * t_1)) + (y4 * t_3));
	} else if (z <= 2.6e+199) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_7) + (a * t_1)));
	} else if (z <= 9.5e+271) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * t_5));
	} 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 = (z * t) - (x * y)
	t_2 = z * ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0))))
	t_3 = (y * y3) - (t * y2)
	t_4 = (c * y0) - (a * y1)
	t_5 = (a * y5) - (c * y4)
	t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))))
	t_7 = (y * k) - (t * j)
	tmp = 0
	if z <= -6e+80:
		tmp = t_2
	elif z <= 1.05e-178:
		tmp = t_6
	elif z <= 9.2e-89:
		tmp = y4 * ((c * t_3) - ((y1 * ((j * y3) - (k * y2))) + (b * t_7)))
	elif z <= 9.5e-20:
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) + (y1 * ((z * y3) - (x * y2)))))
	elif z <= 180000.0:
		tmp = t * (y2 * t_5)
	elif z <= 1.6e+90:
		tmp = t_6
	elif z <= 1.04e+176:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * t_1)) + (y4 * t_3))
	elif z <= 2.6e+199:
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_7) + (a * t_1)))
	elif z <= 9.5e+271:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * t_5))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * t) - Float64(x * y))
	t_2 = Float64(z * Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0)))))
	t_3 = Float64(Float64(y * y3) - Float64(t * y2))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(Float64(a * y5) - Float64(c * y4))
	t_6 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_4)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_7 = Float64(Float64(y * k) - Float64(t * j))
	tmp = 0.0
	if (z <= -6e+80)
		tmp = t_2;
	elseif (z <= 1.05e-178)
		tmp = t_6;
	elseif (z <= 9.2e-89)
		tmp = Float64(y4 * Float64(Float64(c * t_3) - Float64(Float64(y1 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(b * t_7))));
	elseif (z <= 9.5e-20)
		tmp = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))));
	elseif (z <= 180000.0)
		tmp = Float64(t * Float64(y2 * t_5));
	elseif (z <= 1.6e+90)
		tmp = t_6;
	elseif (z <= 1.04e+176)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * t_1)) + Float64(y4 * t_3)));
	elseif (z <= 2.6e+199)
		tmp = Float64(b * Float64(Float64(y0 * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y4 * t_7) + Float64(a * t_1))));
	elseif (z <= 9.5e+271)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_4)) + Float64(t * t_5)));
	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 = (z * t) - (x * y);
	t_2 = z * ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0))));
	t_3 = (y * y3) - (t * y2);
	t_4 = (c * y0) - (a * y1);
	t_5 = (a * y5) - (c * y4);
	t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	t_7 = (y * k) - (t * j);
	tmp = 0.0;
	if (z <= -6e+80)
		tmp = t_2;
	elseif (z <= 1.05e-178)
		tmp = t_6;
	elseif (z <= 9.2e-89)
		tmp = y4 * ((c * t_3) - ((y1 * ((j * y3) - (k * y2))) + (b * t_7)));
	elseif (z <= 9.5e-20)
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) + (y1 * ((z * y3) - (x * y2)))));
	elseif (z <= 180000.0)
		tmp = t * (y2 * t_5);
	elseif (z <= 1.6e+90)
		tmp = t_6;
	elseif (z <= 1.04e+176)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * t_1)) + (y4 * t_3));
	elseif (z <= 2.6e+199)
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_7) + (a * t_1)));
	elseif (z <= 9.5e+271)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * t_5));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+80], t$95$2, If[LessEqual[z, 1.05e-178], t$95$6, If[LessEqual[z, 9.2e-89], N[(y4 * N[(N[(c * t$95$3), $MachinePrecision] - N[(N[(y1 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-20], N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 180000.0], N[(t * N[(y2 * t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+90], t$95$6, If[LessEqual[z, 1.04e+176], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+199], N[(b * N[(N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * t$95$7), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+271], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if z < -5.99999999999999974e80 or 9.5e271 < z

   1. Initial program 17.4%

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

   3. Taylor expanded in z around -inf 55.7%

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

   4. Taylor expanded in k around 0 62.1%

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

   if -5.99999999999999974e80 < z < 1.05e-178 or 1.8e5 < z < 1.59999999999999999e90

   1. Initial program 32.6%

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

   3. Taylor expanded in x around inf 54.7%

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

   if 1.05e-178 < z < 9.200000000000001e-89

   1. Initial program 42.1%

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

   3. Taylor expanded in y4 around inf 74.7%

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

   if 9.200000000000001e-89 < z < 9.5e-20

   1. Initial program 37.8%

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

   3. Taylor expanded in a around -inf 56.6%

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

      1. mul-1-neg 56.6%

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

      2. distribute-rgt-neg-in 56.6%

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

      3. +-commutative 56.6%

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

      4. mul-1-neg 56.6%

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

      5. unsub-neg 56.6%

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

      6. *-commutative 56.6%

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

      7. *-commutative 56.6%

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

      8. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   if 9.5e-20 < z < 1.8e5

   1. Initial program 20.0%

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

   3. Taylor expanded in y2 around inf 60.1%

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

   4. Taylor expanded in t around inf 80.4%

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

   if 1.59999999999999999e90 < z < 1.04e176

   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 c around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

      5. *-commutative 64.2%

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

      6. *-commutative 64.2%

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

      7. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   if 1.04e176 < z < 2.6000000000000001e199

   1. Initial program 49.7%

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

   3. Taylor expanded in b around inf 67.6%

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

   if 2.6000000000000001e199 < z < 9.5e271

   1. Initial program 21.4%

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

   3. Taylor expanded in y2 around inf 71.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+80}:\\ \;\;\;\;z \cdot \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-178}:\\ \;\;\;\;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}\;z \leq 9.2 \cdot 10^{-89}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right) - \left(y1 \cdot \left(j \cdot y3 - k \cdot y2\right) + b \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;z \leq 180000:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+90}:\\ \;\;\;\;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}\;z \leq 1.04 \cdot 10^{+176}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+199}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+271}:\\ \;\;\;\;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{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 34.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b - c \cdot i\\ t_2 := x \cdot \left(\left(y \cdot t_1 + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+120}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(j \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+30}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-210}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+197}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a b) (* c i)))
        (t_2
         (*
          x
          (+
           (+ (* y t_1) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= y -8.2e+204)
     t_2
     (if (<= y -4.1e+120)
       (* (* y1 y3) (* j (- y4)))
       (if (<= y -1.18e+73)
         t_2
         (if (<= y -7.5e+30)
           (* (* y0 y2) (- (* x c) (* k y5)))
           (if (<= y -1.36e-17)
             t_2
             (if (<= y 2.95e-210)
               (*
                y1
                (+ (* y4 (- (* k y2) (* j y3))) (* a (- (* z y3) (* x y2)))))
               (if (<= y 2.7e-11)
                 (*
                  b
                  (-
                   (* y0 (- (* z k) (* x j)))
                   (+ (* y4 (- (* y k) (* t j))) (* a (- (* z t) (* x y))))))
                 (if (<= y 7.2e+197) t_2 (* (* x y) 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 * b) - (c * i);
	double t_2 = x * (((y * t_1) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y <= -8.2e+204) {
		tmp = t_2;
	} else if (y <= -4.1e+120) {
		tmp = (y1 * y3) * (j * -y4);
	} else if (y <= -1.18e+73) {
		tmp = t_2;
	} else if (y <= -7.5e+30) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else if (y <= -1.36e-17) {
		tmp = t_2;
	} else if (y <= 2.95e-210) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	} else if (y <= 2.7e-11) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))));
	} else if (y <= 7.2e+197) {
		tmp = t_2;
	} else {
		tmp = (x * y) * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) - (c * i)
    t_2 = x * (((y * t_1) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    if (y <= (-8.2d+204)) then
        tmp = t_2
    else if (y <= (-4.1d+120)) then
        tmp = (y1 * y3) * (j * -y4)
    else if (y <= (-1.18d+73)) then
        tmp = t_2
    else if (y <= (-7.5d+30)) then
        tmp = (y0 * y2) * ((x * c) - (k * y5))
    else if (y <= (-1.36d-17)) then
        tmp = t_2
    else if (y <= 2.95d-210) then
        tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
    else if (y <= 2.7d-11) then
        tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))))
    else if (y <= 7.2d+197) then
        tmp = t_2
    else
        tmp = (x * y) * 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 * b) - (c * i);
	double t_2 = x * (((y * t_1) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y <= -8.2e+204) {
		tmp = t_2;
	} else if (y <= -4.1e+120) {
		tmp = (y1 * y3) * (j * -y4);
	} else if (y <= -1.18e+73) {
		tmp = t_2;
	} else if (y <= -7.5e+30) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else if (y <= -1.36e-17) {
		tmp = t_2;
	} else if (y <= 2.95e-210) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	} else if (y <= 2.7e-11) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))));
	} else if (y <= 7.2e+197) {
		tmp = t_2;
	} else {
		tmp = (x * y) * 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 * b) - (c * i)
	t_2 = x * (((y * t_1) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y <= -8.2e+204:
		tmp = t_2
	elif y <= -4.1e+120:
		tmp = (y1 * y3) * (j * -y4)
	elif y <= -1.18e+73:
		tmp = t_2
	elif y <= -7.5e+30:
		tmp = (y0 * y2) * ((x * c) - (k * y5))
	elif y <= -1.36e-17:
		tmp = t_2
	elif y <= 2.95e-210:
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
	elif y <= 2.7e-11:
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))))
	elif y <= 7.2e+197:
		tmp = t_2
	else:
		tmp = (x * y) * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * b) - Float64(c * i))
	t_2 = Float64(x * Float64(Float64(Float64(y * t_1) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y <= -8.2e+204)
		tmp = t_2;
	elseif (y <= -4.1e+120)
		tmp = Float64(Float64(y1 * y3) * Float64(j * Float64(-y4)));
	elseif (y <= -1.18e+73)
		tmp = t_2;
	elseif (y <= -7.5e+30)
		tmp = Float64(Float64(y0 * y2) * Float64(Float64(x * c) - Float64(k * y5)));
	elseif (y <= -1.36e-17)
		tmp = t_2;
	elseif (y <= 2.95e-210)
		tmp = Float64(y1 * Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (y <= 2.7e-11)
		tmp = Float64(b * Float64(Float64(y0 * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y4 * Float64(Float64(y * k) - Float64(t * j))) + Float64(a * Float64(Float64(z * t) - Float64(x * y))))));
	elseif (y <= 7.2e+197)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * y) * 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 * b) - (c * i);
	t_2 = x * (((y * t_1) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y <= -8.2e+204)
		tmp = t_2;
	elseif (y <= -4.1e+120)
		tmp = (y1 * y3) * (j * -y4);
	elseif (y <= -1.18e+73)
		tmp = t_2;
	elseif (y <= -7.5e+30)
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	elseif (y <= -1.36e-17)
		tmp = t_2;
	elseif (y <= 2.95e-210)
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	elseif (y <= 2.7e-11)
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))));
	elseif (y <= 7.2e+197)
		tmp = t_2;
	else
		tmp = (x * y) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[(y * t$95$1), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+204], t$95$2, If[LessEqual[y, -4.1e+120], N[(N[(y1 * y3), $MachinePrecision] * N[(j * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.18e+73], t$95$2, If[LessEqual[y, -7.5e+30], N[(N[(y0 * y2), $MachinePrecision] * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.36e-17], t$95$2, If[LessEqual[y, 2.95e-210], N[(y1 * N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-11], N[(b * N[(N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+197], t$95$2, N[(N[(x * y), $MachinePrecision] * t$95$1), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.19999999999999949e204 or -4.1e120 < y < -1.18000000000000004e73 or -7.49999999999999973e30 < y < -1.36e-17 or 2.70000000000000005e-11 < y < 7.19999999999999965e197

   1. Initial program 28.8%

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

   3. Taylor expanded in x around inf 64.9%

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

   if -8.19999999999999949e204 < y < -4.1e120

   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 30.8%

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

      1. mul-1-neg 30.8%

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

      2. *-commutative 30.8%

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

      3. distribute-rgt-neg-in 30.8%

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

   5. Simplified 30.8%

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

   6. Taylor expanded in y3 around -inf 50.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 50.1%

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

   8. Simplified 50.1%

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

   9. Taylor expanded in a around 0 50.7%

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

       1. neg-mul-1 50.7%

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

       2. distribute-rgt-neg-in 50.7%

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

   11. Simplified 50.7%

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

   if -1.18000000000000004e73 < y < -7.49999999999999973e30

   1. Initial program 7.1%

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

   3. Taylor expanded in y2 around inf 64.9%

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

   4. Taylor expanded in y0 around inf 38.3%

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

      1. associate-*r* 51.3%

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

      2. *-commutative 51.3%

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

      3. +-commutative 51.3%

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

      4. mul-1-neg 51.3%

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

      5. unsub-neg 51.3%

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

      6. *-commutative 51.3%

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

   6. Simplified 51.3%

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

   if -1.36e-17 < y < 2.9499999999999999e-210

   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 y1 around -inf 50.3%

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

      1. mul-1-neg 50.3%

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

      2. *-commutative 50.3%

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

      3. distribute-rgt-neg-in 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in i around 0 49.5%

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

      1. associate-*r* 49.5%

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

      2. neg-mul-1 49.5%

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

      3. sub-neg 49.5%

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

      4. *-commutative 49.5%

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

      5. sub-neg 49.5%

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

      6. *-commutative 49.5%

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

   8. Simplified 49.5%

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

   if 2.9499999999999999e-210 < y < 2.70000000000000005e-11

   1. Initial program 44.1%

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

   3. Taylor expanded in b around inf 59.2%

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

   if 7.19999999999999965e197 < y

   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 x around inf 41.7%

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

   4. Taylor expanded in y around inf 64.6%

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

      1. associate-*r* 64.6%

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

   6. Simplified 64.6%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+204}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+120}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(j \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+30}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-210}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 34.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-24}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-169}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-308}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-222}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          b
          (-
           (* y0 (- (* z k) (* x j)))
           (+ (* y4 (- (* y k) (* t j))) (* a (- (* z t) (* x y))))))))
   (if (<= x -4.6e+140)
     (* i (* j (* x y1)))
     (if (<= x -3.2e-24)
       (* (* x y) (- (* a b) (* c i)))
       (if (<= x -9.5e-169)
         (* i (* k (- (* y y5) (* z y1))))
         (if (<= x -2.6e-308)
           (* t (* y2 (- (* a y5) (* c y4))))
           (if (<= x 1.12e-250)
             t_1
             (if (<= x 7.4e-222)
               (* k (* y2 (- (* y1 y4) (* y0 y5))))
               (if (<= x 8.6e+114)
                 t_1
                 (* j (* x (- (* i y1) (* b y0)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))));
	double tmp;
	if (x <= -4.6e+140) {
		tmp = i * (j * (x * y1));
	} else if (x <= -3.2e-24) {
		tmp = (x * y) * ((a * b) - (c * i));
	} else if (x <= -9.5e-169) {
		tmp = i * (k * ((y * y5) - (z * y1)));
	} else if (x <= -2.6e-308) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 1.12e-250) {
		tmp = t_1;
	} else if (x <= 7.4e-222) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (x <= 8.6e+114) {
		tmp = t_1;
	} else {
		tmp = j * (x * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))))
    if (x <= (-4.6d+140)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-3.2d-24)) then
        tmp = (x * y) * ((a * b) - (c * i))
    else if (x <= (-9.5d-169)) then
        tmp = i * (k * ((y * y5) - (z * y1)))
    else if (x <= (-2.6d-308)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= 1.12d-250) then
        tmp = t_1
    else if (x <= 7.4d-222) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (x <= 8.6d+114) then
        tmp = t_1
    else
        tmp = j * (x * ((i * y1) - (b * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))));
	double tmp;
	if (x <= -4.6e+140) {
		tmp = i * (j * (x * y1));
	} else if (x <= -3.2e-24) {
		tmp = (x * y) * ((a * b) - (c * i));
	} else if (x <= -9.5e-169) {
		tmp = i * (k * ((y * y5) - (z * y1)));
	} else if (x <= -2.6e-308) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 1.12e-250) {
		tmp = t_1;
	} else if (x <= 7.4e-222) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (x <= 8.6e+114) {
		tmp = t_1;
	} else {
		tmp = j * (x * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))))
	tmp = 0
	if x <= -4.6e+140:
		tmp = i * (j * (x * y1))
	elif x <= -3.2e-24:
		tmp = (x * y) * ((a * b) - (c * i))
	elif x <= -9.5e-169:
		tmp = i * (k * ((y * y5) - (z * y1)))
	elif x <= -2.6e-308:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= 1.12e-250:
		tmp = t_1
	elif x <= 7.4e-222:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif x <= 8.6e+114:
		tmp = t_1
	else:
		tmp = j * (x * ((i * y1) - (b * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(Float64(y0 * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y4 * Float64(Float64(y * k) - Float64(t * j))) + Float64(a * Float64(Float64(z * t) - Float64(x * y))))))
	tmp = 0.0
	if (x <= -4.6e+140)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -3.2e-24)
		tmp = Float64(Float64(x * y) * Float64(Float64(a * b) - Float64(c * i)));
	elseif (x <= -9.5e-169)
		tmp = Float64(i * Float64(k * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (x <= -2.6e-308)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 1.12e-250)
		tmp = t_1;
	elseif (x <= 7.4e-222)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (x <= 8.6e+114)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))));
	tmp = 0.0;
	if (x <= -4.6e+140)
		tmp = i * (j * (x * y1));
	elseif (x <= -3.2e-24)
		tmp = (x * y) * ((a * b) - (c * i));
	elseif (x <= -9.5e-169)
		tmp = i * (k * ((y * y5) - (z * y1)));
	elseif (x <= -2.6e-308)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= 1.12e-250)
		tmp = t_1;
	elseif (x <= 7.4e-222)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (x <= 8.6e+114)
		tmp = t_1;
	else
		tmp = j * (x * ((i * y1) - (b * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.6e+140], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e-24], N[(N[(x * y), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.5e-169], N[(i * N[(k * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.6e-308], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e-250], t$95$1, If[LessEqual[x, 7.4e-222], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.6e+114], t$95$1, N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -4.59999999999999981e140

   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 x around inf 68.2%

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

   4. Taylor expanded in y1 around inf 52.0%

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

      1. distribute-lft-out-- 52.0%

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

      2. *-commutative 52.0%

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

      3. *-commutative 52.0%

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

   6. Simplified 52.0%

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

   7. Taylor expanded in y2 around 0 55.6%

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

      1. *-commutative 55.6%

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

   9. Simplified 55.6%

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

   if -4.59999999999999981e140 < x < -3.20000000000000012e-24

   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 x around inf 43.9%

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

   4. Taylor expanded in y around inf 54.1%

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

      1. associate-*r* 60.4%

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

   6. Simplified 60.4%

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

   if -3.20000000000000012e-24 < x < -9.5000000000000001e-169

   1. Initial program 37.6%

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

   3. Taylor expanded in i around -inf 50.7%

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

   4. Taylor expanded in k around inf 55.4%

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

      1. distribute-lft-out-- 55.4%

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

      2. *-commutative 55.4%

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

   6. Simplified 55.4%

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

   if -9.5000000000000001e-169 < x < -2.6e-308

   1. Initial program 22.5%

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

   3. Taylor expanded in y2 around inf 48.6%

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

   4. Taylor expanded in t around inf 58.5%

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

   if -2.6e-308 < x < 1.11999999999999996e-250 or 7.3999999999999997e-222 < x < 8.6000000000000001e114

   1. Initial program 34.3%

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

   3. Taylor expanded in b around inf 46.7%

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

   if 1.11999999999999996e-250 < x < 7.3999999999999997e-222

   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 y2 around inf 43.3%

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

   4. Taylor expanded in k around inf 86.1%

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

   if 8.6000000000000001e114 < x

   1. Initial program 31.4%

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

   3. Taylor expanded in x around inf 71.4%

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

   4. Taylor expanded in j around inf 63.7%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-24}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-169}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-308}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-222}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := a \cdot b - c \cdot i\\ t_3 := x \cdot \left(\left(y \cdot t_2 + y2 \cdot t_1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+204}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+120}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(j \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-44}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t_1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-210}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+197}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* a b) (* c i)))
        (t_3 (* x (+ (+ (* y t_2) (* y2 t_1)) (* j (- (* i y1) (* b y0)))))))
   (if (<= y -8.2e+204)
     t_3
     (if (<= y -4.1e+120)
       (* (* y1 y3) (* j (- y4)))
       (if (<= y -3.5e+76)
         t_3
         (if (<= y -2.8e-44)
           (*
            y2
            (+
             (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_1))
             (* t (- (* a y5) (* c y4)))))
           (if (<= y 4.4e-210)
             (*
              y1
              (+ (* y4 (- (* k y2) (* j y3))) (* a (- (* z y3) (* x y2)))))
             (if (<= y 2.65e-11)
               (*
                b
                (-
                 (* y0 (- (* z k) (* x j)))
                 (+ (* y4 (- (* y k) (* t j))) (* a (- (* z t) (* x y))))))
               (if (<= y 7.8e+197) t_3 (* (* x y) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (a * b) - (c * i);
	double t_3 = x * (((y * t_2) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y <= -8.2e+204) {
		tmp = t_3;
	} else if (y <= -4.1e+120) {
		tmp = (y1 * y3) * (j * -y4);
	} else if (y <= -3.5e+76) {
		tmp = t_3;
	} else if (y <= -2.8e-44) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 4.4e-210) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	} else if (y <= 2.65e-11) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))));
	} else if (y <= 7.8e+197) {
		tmp = t_3;
	} else {
		tmp = (x * y) * t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (a * b) - (c * i)
    t_3 = x * (((y * t_2) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
    if (y <= (-8.2d+204)) then
        tmp = t_3
    else if (y <= (-4.1d+120)) then
        tmp = (y1 * y3) * (j * -y4)
    else if (y <= (-3.5d+76)) then
        tmp = t_3
    else if (y <= (-2.8d-44)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
    else if (y <= 4.4d-210) then
        tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
    else if (y <= 2.65d-11) then
        tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))))
    else if (y <= 7.8d+197) then
        tmp = t_3
    else
        tmp = (x * y) * t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (a * b) - (c * i);
	double t_3 = x * (((y * t_2) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y <= -8.2e+204) {
		tmp = t_3;
	} else if (y <= -4.1e+120) {
		tmp = (y1 * y3) * (j * -y4);
	} else if (y <= -3.5e+76) {
		tmp = t_3;
	} else if (y <= -2.8e-44) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 4.4e-210) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	} else if (y <= 2.65e-11) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))));
	} else if (y <= 7.8e+197) {
		tmp = t_3;
	} else {
		tmp = (x * y) * t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (a * b) - (c * i)
	t_3 = x * (((y * t_2) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y <= -8.2e+204:
		tmp = t_3
	elif y <= -4.1e+120:
		tmp = (y1 * y3) * (j * -y4)
	elif y <= -3.5e+76:
		tmp = t_3
	elif y <= -2.8e-44:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
	elif y <= 4.4e-210:
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
	elif y <= 2.65e-11:
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))))
	elif y <= 7.8e+197:
		tmp = t_3
	else:
		tmp = (x * y) * t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(a * b) - Float64(c * i))
	t_3 = Float64(x * Float64(Float64(Float64(y * t_2) + Float64(y2 * t_1)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y <= -8.2e+204)
		tmp = t_3;
	elseif (y <= -4.1e+120)
		tmp = Float64(Float64(y1 * y3) * Float64(j * Float64(-y4)));
	elseif (y <= -3.5e+76)
		tmp = t_3;
	elseif (y <= -2.8e-44)
		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 (y <= 4.4e-210)
		tmp = Float64(y1 * Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (y <= 2.65e-11)
		tmp = Float64(b * Float64(Float64(y0 * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y4 * Float64(Float64(y * k) - Float64(t * j))) + Float64(a * Float64(Float64(z * t) - Float64(x * y))))));
	elseif (y <= 7.8e+197)
		tmp = t_3;
	else
		tmp = Float64(Float64(x * y) * t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (a * b) - (c * i);
	t_3 = x * (((y * t_2) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y <= -8.2e+204)
		tmp = t_3;
	elseif (y <= -4.1e+120)
		tmp = (y1 * y3) * (j * -y4);
	elseif (y <= -3.5e+76)
		tmp = t_3;
	elseif (y <= -2.8e-44)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	elseif (y <= 4.4e-210)
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	elseif (y <= 2.65e-11)
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * ((y * k) - (t * j))) + (a * ((z * t) - (x * y)))));
	elseif (y <= 7.8e+197)
		tmp = t_3;
	else
		tmp = (x * y) * t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * t$95$2), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+204], t$95$3, If[LessEqual[y, -4.1e+120], N[(N[(y1 * y3), $MachinePrecision] * N[(j * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e+76], t$95$3, If[LessEqual[y, -2.8e-44], 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[y, 4.4e-210], N[(y1 * N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e-11], N[(b * N[(N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+197], t$95$3, N[(N[(x * y), $MachinePrecision] * t$95$2), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.19999999999999949e204 or -4.1e120 < y < -3.5e76 or 2.6499999999999999e-11 < y < 7.8e197

   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 x around inf 64.6%

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

   if -8.19999999999999949e204 < y < -4.1e120

   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 30.8%

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

      1. mul-1-neg 30.8%

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

      2. *-commutative 30.8%

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

      3. distribute-rgt-neg-in 30.8%

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

   5. Simplified 30.8%

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

   6. Taylor expanded in y3 around -inf 50.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 50.1%

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

   8. Simplified 50.1%

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

   9. Taylor expanded in a around 0 50.7%

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

       1. neg-mul-1 50.7%

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

       2. distribute-rgt-neg-in 50.7%

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

   11. Simplified 50.7%

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

   if -3.5e76 < y < -2.8e-44

   1. Initial program 18.1%

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

   3. Taylor expanded in y2 around inf 61.2%

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

   if -2.8e-44 < y < 4.39999999999999979e-210

   1. Initial program 31.0%

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

   3. Taylor expanded in y1 around -inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. *-commutative 51.1%

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

      3. distribute-rgt-neg-in 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in i around 0 48.5%

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

      1. associate-*r* 48.5%

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

      2. neg-mul-1 48.5%

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

      3. sub-neg 48.5%

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

      4. *-commutative 48.5%

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

      5. sub-neg 48.5%

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

      6. *-commutative 48.5%

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

   8. Simplified 48.5%

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

   if 4.39999999999999979e-210 < y < 2.6499999999999999e-11

   1. Initial program 44.1%

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

   3. Taylor expanded in b around inf 59.2%

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

   if 7.8e197 < y

   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 x around inf 41.7%

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

   4. Taylor expanded in y around inf 64.6%

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

      1. associate-*r* 64.6%

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

   6. Simplified 64.6%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+204}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+120}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(j \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-44}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-210}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := y \cdot k - t \cdot j\\ t_3 := x \cdot j - z \cdot k\\ t_4 := y4 \cdot t_1 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\\ t_5 := i \cdot y1 - b \cdot y0\\ t_6 := j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot t_5\right)\\ \mathbf{if}\;y1 \leq -3.6 \cdot 10^{+98}:\\ \;\;\;\;y1 \cdot \left(i \cdot t_3 + t_4\right)\\ \mathbf{elif}\;y1 \leq -4.5 \cdot 10^{+17}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y1 \leq -1.6 \cdot 10^{-83}:\\ \;\;\;\;\left(y3 \cdot y4 - x \cdot i\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y1 \leq -3.15 \cdot 10^{-204}:\\ \;\;\;\;i \cdot \left(y1 \cdot t_3 + \left(y5 \cdot t_2 + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.05 \cdot 10^{-145}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(y0 \cdot t_1 - i \cdot t_2\right)\right)\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_5\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{+194}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y1 \leq 1.22 \cdot 10^{+224}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* y k) (* t j)))
        (t_3 (- (* x j) (* z k)))
        (t_4 (+ (* y4 t_1) (* a (- (* z y3) (* x y2)))))
        (t_5 (- (* i y1) (* b y0)))
        (t_6
         (*
          j
          (+
           (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
           (* x t_5)))))
   (if (<= y1 -3.6e+98)
     (* y1 (+ (* i t_3) t_4))
     (if (<= y1 -4.5e+17)
       t_6
       (if (<= y1 -1.6e-83)
         (* (- (* y3 y4) (* x i)) (* y c))
         (if (<= y1 -3.15e-204)
           (* i (+ (* y1 t_3) (+ (* y5 t_2) (* c (- (* z t) (* x y))))))
           (if (<= y1 1.05e-145)
             (* y5 (- (* a (- (* t y2) (* y y3))) (- (* y0 t_1) (* i t_2))))
             (if (<= y1 3.8e+106)
               (*
                x
                (+
                 (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
                 (* j t_5)))
               (if (<= y1 3.5e+194)
                 t_6
                 (if (<= y1 1.22e+224)
                   (* y0 (* c (- (* x y2) (* z y3))))
                   (* y1 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 = (k * y2) - (j * y3);
	double t_2 = (y * k) - (t * j);
	double t_3 = (x * j) - (z * k);
	double t_4 = (y4 * t_1) + (a * ((z * y3) - (x * y2)));
	double t_5 = (i * y1) - (b * y0);
	double t_6 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5));
	double tmp;
	if (y1 <= -3.6e+98) {
		tmp = y1 * ((i * t_3) + t_4);
	} else if (y1 <= -4.5e+17) {
		tmp = t_6;
	} else if (y1 <= -1.6e-83) {
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	} else if (y1 <= -3.15e-204) {
		tmp = i * ((y1 * t_3) + ((y5 * t_2) + (c * ((z * t) - (x * y)))));
	} else if (y1 <= 1.05e-145) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((y0 * t_1) - (i * t_2)));
	} else if (y1 <= 3.8e+106) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5));
	} else if (y1 <= 3.5e+194) {
		tmp = t_6;
	} else if (y1 <= 1.22e+224) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else {
		tmp = y1 * t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (y * k) - (t * j)
    t_3 = (x * j) - (z * k)
    t_4 = (y4 * t_1) + (a * ((z * y3) - (x * y2)))
    t_5 = (i * y1) - (b * y0)
    t_6 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5))
    if (y1 <= (-3.6d+98)) then
        tmp = y1 * ((i * t_3) + t_4)
    else if (y1 <= (-4.5d+17)) then
        tmp = t_6
    else if (y1 <= (-1.6d-83)) then
        tmp = ((y3 * y4) - (x * i)) * (y * c)
    else if (y1 <= (-3.15d-204)) then
        tmp = i * ((y1 * t_3) + ((y5 * t_2) + (c * ((z * t) - (x * y)))))
    else if (y1 <= 1.05d-145) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((y0 * t_1) - (i * t_2)))
    else if (y1 <= 3.8d+106) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5))
    else if (y1 <= 3.5d+194) then
        tmp = t_6
    else if (y1 <= 1.22d+224) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else
        tmp = y1 * 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 = (k * y2) - (j * y3);
	double t_2 = (y * k) - (t * j);
	double t_3 = (x * j) - (z * k);
	double t_4 = (y4 * t_1) + (a * ((z * y3) - (x * y2)));
	double t_5 = (i * y1) - (b * y0);
	double t_6 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5));
	double tmp;
	if (y1 <= -3.6e+98) {
		tmp = y1 * ((i * t_3) + t_4);
	} else if (y1 <= -4.5e+17) {
		tmp = t_6;
	} else if (y1 <= -1.6e-83) {
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	} else if (y1 <= -3.15e-204) {
		tmp = i * ((y1 * t_3) + ((y5 * t_2) + (c * ((z * t) - (x * y)))));
	} else if (y1 <= 1.05e-145) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((y0 * t_1) - (i * t_2)));
	} else if (y1 <= 3.8e+106) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5));
	} else if (y1 <= 3.5e+194) {
		tmp = t_6;
	} else if (y1 <= 1.22e+224) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else {
		tmp = y1 * 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 = (k * y2) - (j * y3)
	t_2 = (y * k) - (t * j)
	t_3 = (x * j) - (z * k)
	t_4 = (y4 * t_1) + (a * ((z * y3) - (x * y2)))
	t_5 = (i * y1) - (b * y0)
	t_6 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5))
	tmp = 0
	if y1 <= -3.6e+98:
		tmp = y1 * ((i * t_3) + t_4)
	elif y1 <= -4.5e+17:
		tmp = t_6
	elif y1 <= -1.6e-83:
		tmp = ((y3 * y4) - (x * i)) * (y * c)
	elif y1 <= -3.15e-204:
		tmp = i * ((y1 * t_3) + ((y5 * t_2) + (c * ((z * t) - (x * y)))))
	elif y1 <= 1.05e-145:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((y0 * t_1) - (i * t_2)))
	elif y1 <= 3.8e+106:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5))
	elif y1 <= 3.5e+194:
		tmp = t_6
	elif y1 <= 1.22e+224:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	else:
		tmp = y1 * 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(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(y * k) - Float64(t * j))
	t_3 = Float64(Float64(x * j) - Float64(z * k))
	t_4 = Float64(Float64(y4 * t_1) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))
	t_5 = Float64(Float64(i * y1) - Float64(b * y0))
	t_6 = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * t_5)))
	tmp = 0.0
	if (y1 <= -3.6e+98)
		tmp = Float64(y1 * Float64(Float64(i * t_3) + t_4));
	elseif (y1 <= -4.5e+17)
		tmp = t_6;
	elseif (y1 <= -1.6e-83)
		tmp = Float64(Float64(Float64(y3 * y4) - Float64(x * i)) * Float64(y * c));
	elseif (y1 <= -3.15e-204)
		tmp = Float64(i * Float64(Float64(y1 * t_3) + Float64(Float64(y5 * t_2) + Float64(c * Float64(Float64(z * t) - Float64(x * y))))));
	elseif (y1 <= 1.05e-145)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(Float64(y0 * t_1) - Float64(i * t_2))));
	elseif (y1 <= 3.8e+106)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_5)));
	elseif (y1 <= 3.5e+194)
		tmp = t_6;
	elseif (y1 <= 1.22e+224)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	else
		tmp = Float64(y1 * 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 = (k * y2) - (j * y3);
	t_2 = (y * k) - (t * j);
	t_3 = (x * j) - (z * k);
	t_4 = (y4 * t_1) + (a * ((z * y3) - (x * y2)));
	t_5 = (i * y1) - (b * y0);
	t_6 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5));
	tmp = 0.0;
	if (y1 <= -3.6e+98)
		tmp = y1 * ((i * t_3) + t_4);
	elseif (y1 <= -4.5e+17)
		tmp = t_6;
	elseif (y1 <= -1.6e-83)
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	elseif (y1 <= -3.15e-204)
		tmp = i * ((y1 * t_3) + ((y5 * t_2) + (c * ((z * t) - (x * y)))));
	elseif (y1 <= 1.05e-145)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((y0 * t_1) - (i * t_2)));
	elseif (y1 <= 3.8e+106)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5));
	elseif (y1 <= 3.5e+194)
		tmp = t_6;
	elseif (y1 <= 1.22e+224)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	else
		tmp = y1 * 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[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y4 * t$95$1), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -3.6e+98], N[(y1 * N[(N[(i * t$95$3), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -4.5e+17], t$95$6, If[LessEqual[y1, -1.6e-83], N[(N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision] * N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.15e-204], N[(i * N[(N[(y1 * t$95$3), $MachinePrecision] + N[(N[(y5 * t$95$2), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.05e-145], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y0 * t$95$1), $MachinePrecision] - N[(i * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.8e+106], 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$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.5e+194], t$95$6, If[LessEqual[y1, 1.22e+224], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * t$95$4), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y1 < -3.59999999999999981e98

   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 67.6%

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

      1. mul-1-neg 67.6%

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

      2. *-commutative 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

   5. Simplified 67.6%

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

   if -3.59999999999999981e98 < y1 < -4.5e17 or 3.7999999999999998e106 < y1 < 3.4999999999999997e194

   1. Initial program 30.5%

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

   3. Taylor expanded in j around inf 69.7%

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

   if -4.5e17 < y1 < -1.6000000000000001e-83

   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 c around inf 67.3%

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

      1. +-commutative 67.3%

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

      2. mul-1-neg 67.3%

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

      3. unsub-neg 67.3%

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

      4. *-commutative 67.3%

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

      5. *-commutative 67.3%

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

      6. *-commutative 67.3%

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

      7. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in y around -inf 73.9%

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

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*l* 73.9%

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

      4. +-commutative 73.9%

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

      5. mul-1-neg 73.9%

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

      6. unsub-neg 73.9%

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

      7. *-commutative 73.9%

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

   8. Simplified 73.9%

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

   if -1.6000000000000001e-83 < y1 < -3.14999999999999996e-204

   1. Initial program 35.0%

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

   3. Taylor expanded in i around -inf 65.3%

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

   if -3.14999999999999996e-204 < y1 < 1.04999999999999996e-145

   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 y5 around -inf 54.3%

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

   if 1.04999999999999996e-145 < y1 < 3.7999999999999998e106

   1. Initial program 24.7%

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

   3. Taylor expanded in x around inf 56.5%

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

   if 3.4999999999999997e194 < y1 < 1.21999999999999997e224

   1. Initial program 18.2%

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

   3. Taylor expanded in c around inf 36.6%

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

      1. +-commutative 36.6%

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

      2. mul-1-neg 36.6%

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

      3. unsub-neg 36.6%

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

      4. *-commutative 36.6%

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

      5. *-commutative 36.6%

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

      6. *-commutative 36.6%

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

      7. *-commutative 36.6%

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

   5. Simplified 36.6%

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

   6. Taylor expanded in y0 around inf 46.8%

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

      1. *-commutative 46.8%

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

      2. *-commutative 46.8%

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

      3. *-commutative 46.8%

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

      4. fma-neg 46.8%

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

      5. distribute-lft-neg-out 46.8%

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

      6. associate-*l* 55.5%

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

      7. distribute-lft-neg-out 55.5%

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

      8. fma-neg 55.5%

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

      9. *-commutative 55.5%

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

      10. *-commutative 55.5%

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

   8. Simplified 55.5%

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

   if 1.21999999999999997e224 < y1

   1. Initial program 23.1%

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

   3. Taylor expanded in y1 around -inf 54.4%

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

      1. mul-1-neg 54.4%

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

      2. *-commutative 54.4%

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

      3. distribute-rgt-neg-in 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in i around 0 69.6%

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

      1. associate-*r* 69.6%

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

      2. neg-mul-1 69.6%

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

      3. sub-neg 69.6%

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

      4. *-commutative 69.6%

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

      5. sub-neg 69.6%

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

      6. *-commutative 69.6%

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

   8. Simplified 69.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.6 \cdot 10^{+98}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -4.5 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -1.6 \cdot 10^{-83}:\\ \;\;\;\;\left(y3 \cdot y4 - x \cdot i\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y1 \leq -3.15 \cdot 10^{-204}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.05 \cdot 10^{-145}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - i \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{+194}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.22 \cdot 10^{+224}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{if}\;y1 \leq -1.36 \cdot 10^{+15}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + t_2\right)\\ \mathbf{elif}\;y1 \leq -3.6 \cdot 10^{-207}:\\ \;\;\;\;\left(y3 \cdot y4 - x \cdot i\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{-264}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot t_1 + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7.8 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 9.5 \cdot 10^{-140}:\\ \;\;\;\;i \cdot \left(y5 \cdot t_1\right)\\ \mathbf{elif}\;y1 \leq 4.6 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j)))
        (t_2 (+ (* y4 (- (* k y2) (* j y3))) (* a (- (* z y3) (* x y2))))))
   (if (<= y1 -1.36e+15)
     (* y1 (+ (* i (- (* x j) (* z k))) t_2))
     (if (<= y1 -3.6e-207)
       (* (- (* y3 y4) (* x i)) (* y c))
       (if (<= y1 3.2e-264)
         (*
          b
          (-
           (* y0 (- (* z k) (* x j)))
           (+ (* y4 t_1) (* a (- (* z t) (* x y))))))
         (if (<= y1 7.8e-216)
           (* a (* b (- (* x y) (* z t))))
           (if (<= y1 9.5e-140)
             (* i (* y5 t_1))
             (if (<= y1 4.6e+183)
               (*
                x
                (+
                 (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
                 (* j (- (* i y1) (* b y0)))))
               (* y1 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 = (y * k) - (t * j);
	double t_2 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -1.36e+15) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + t_2);
	} else if (y1 <= -3.6e-207) {
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	} else if (y1 <= 3.2e-264) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	} else if (y1 <= 7.8e-216) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 9.5e-140) {
		tmp = i * (y5 * t_1);
	} else if (y1 <= 4.6e+183) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y1 * t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)))
    if (y1 <= (-1.36d+15)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + t_2)
    else if (y1 <= (-3.6d-207)) then
        tmp = ((y3 * y4) - (x * i)) * (y * c)
    else if (y1 <= 3.2d-264) then
        tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_1) + (a * ((z * t) - (x * y)))))
    else if (y1 <= 7.8d-216) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y1 <= 9.5d-140) then
        tmp = i * (y5 * t_1)
    else if (y1 <= 4.6d+183) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else
        tmp = y1 * 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 = (y * k) - (t * j);
	double t_2 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -1.36e+15) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + t_2);
	} else if (y1 <= -3.6e-207) {
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	} else if (y1 <= 3.2e-264) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	} else if (y1 <= 7.8e-216) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 9.5e-140) {
		tmp = i * (y5 * t_1);
	} else if (y1 <= 4.6e+183) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y1 * 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 = (y * k) - (t * j)
	t_2 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)))
	tmp = 0
	if y1 <= -1.36e+15:
		tmp = y1 * ((i * ((x * j) - (z * k))) + t_2)
	elif y1 <= -3.6e-207:
		tmp = ((y3 * y4) - (x * i)) * (y * c)
	elif y1 <= 3.2e-264:
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_1) + (a * ((z * t) - (x * y)))))
	elif y1 <= 7.8e-216:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y1 <= 9.5e-140:
		tmp = i * (y5 * t_1)
	elif y1 <= 4.6e+183:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	else:
		tmp = y1 * t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * k) - Float64(t * j))
	t_2 = Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (y1 <= -1.36e+15)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + t_2));
	elseif (y1 <= -3.6e-207)
		tmp = Float64(Float64(Float64(y3 * y4) - Float64(x * i)) * Float64(y * c));
	elseif (y1 <= 3.2e-264)
		tmp = Float64(b * Float64(Float64(y0 * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y4 * t_1) + Float64(a * Float64(Float64(z * t) - Float64(x * y))))));
	elseif (y1 <= 7.8e-216)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 9.5e-140)
		tmp = Float64(i * Float64(y5 * t_1));
	elseif (y1 <= 4.6e+183)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	else
		tmp = Float64(y1 * 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 = (y * k) - (t * j);
	t_2 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (y1 <= -1.36e+15)
		tmp = y1 * ((i * ((x * j) - (z * k))) + t_2);
	elseif (y1 <= -3.6e-207)
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	elseif (y1 <= 3.2e-264)
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	elseif (y1 <= 7.8e-216)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y1 <= 9.5e-140)
		tmp = i * (y5 * t_1);
	elseif (y1 <= 4.6e+183)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	else
		tmp = y1 * t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.36e+15], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.6e-207], N[(N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision] * N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.2e-264], N[(b * N[(N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * t$95$1), $MachinePrecision] + N[(a * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7.8e-216], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9.5e-140], N[(i * N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.6e+183], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * t$95$2), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -1.36e15

   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 61.8%

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

      1. mul-1-neg 61.8%

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

      2. *-commutative 61.8%

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

      3. distribute-rgt-neg-in 61.8%

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

   5. Simplified 61.8%

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

   if -1.36e15 < y1 < -3.5999999999999997e-207

   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 c around inf 50.3%

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

      1. +-commutative 50.3%

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

      2. mul-1-neg 50.3%

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

      3. unsub-neg 50.3%

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

      4. *-commutative 50.3%

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

      5. *-commutative 50.3%

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

      6. *-commutative 50.3%

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

      7. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in y around -inf 56.2%

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

      1. *-commutative 56.2%

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

      2. *-commutative 56.2%

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

      3. associate-*l* 53.6%

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

      4. +-commutative 53.6%

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

      5. mul-1-neg 53.6%

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

      6. unsub-neg 53.6%

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

      7. *-commutative 53.6%

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

   8. Simplified 53.6%

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

   if -3.5999999999999997e-207 < y1 < 3.19999999999999995e-264

   1. Initial program 43.0%

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

   3. Taylor expanded in b around inf 54.0%

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

   if 3.19999999999999995e-264 < y1 < 7.8000000000000002e-216

   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 b around inf 40.0%

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

   4. Taylor expanded in a around inf 80.9%

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

   if 7.8000000000000002e-216 < y1 < 9.50000000000000019e-140

   1. Initial program 12.5%

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

   3. Taylor expanded in i around -inf 62.7%

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

   4. Taylor expanded in y5 around inf 75.2%

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

   if 9.50000000000000019e-140 < y1 < 4.5999999999999996e183

   1. Initial program 23.9%

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

   3. Taylor expanded in x around inf 54.7%

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

   if 4.5999999999999996e183 < y1

   1. Initial program 21.4%

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

   3. Taylor expanded in y1 around -inf 46.7%

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

      1. mul-1-neg 46.7%

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

      2. *-commutative 46.7%

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

      3. distribute-rgt-neg-in 46.7%

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

   5. Simplified 46.7%

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

   6. Taylor expanded in i around 0 58.1%

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

      1. associate-*r* 58.1%

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

      2. neg-mul-1 58.1%

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

      3. sub-neg 58.1%

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

      4. *-commutative 58.1%

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

      5. sub-neg 58.1%

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

      6. *-commutative 58.1%

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

   8. Simplified 58.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.36 \cdot 10^{+15}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -3.6 \cdot 10^{-207}:\\ \;\;\;\;\left(y3 \cdot y4 - x \cdot i\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{-264}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7.8 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 9.5 \cdot 10^{-140}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 4.6 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 30.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-263}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-15}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+99}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* x (- (* i y1) (* b y0))))))
   (if (<= x -6.5e+126)
     (* i (* j (* x y1)))
     (if (<= x -2.25e-55)
       (* c (* i (- (* z t) (* x y))))
       (if (<= x 2.8e-263)
         (* t (* y2 (- (* a y5) (* c y4))))
         (if (<= x 5.2e-146)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= x 4.4e-15)
             (* k (* y2 (- (* y1 y4) (* y0 y5))))
             (if (<= x 5.5e+61)
               t_1
               (if (<= x 3.4e+76)
                 (* x (* a (- (* y b) (* y1 y2))))
                 (if (<= x 3.4e+99)
                   (* b (* y0 (- (* z k) (* x j))))
                   (if (<= x 4.8e+122)
                     (* a (* b (- (* x y) (* z t))))
                     t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (x * ((i * y1) - (b * y0)));
	double tmp;
	if (x <= -6.5e+126) {
		tmp = i * (j * (x * y1));
	} else if (x <= -2.25e-55) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 2.8e-263) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 5.2e-146) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (x <= 4.4e-15) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (x <= 5.5e+61) {
		tmp = t_1;
	} else if (x <= 3.4e+76) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (x <= 3.4e+99) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (x <= 4.8e+122) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (x * ((i * y1) - (b * y0)))
    if (x <= (-6.5d+126)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-2.25d-55)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (x <= 2.8d-263) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= 5.2d-146) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (x <= 4.4d-15) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (x <= 5.5d+61) then
        tmp = t_1
    else if (x <= 3.4d+76) then
        tmp = x * (a * ((y * b) - (y1 * y2)))
    else if (x <= 3.4d+99) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (x <= 4.8d+122) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (x * ((i * y1) - (b * y0)));
	double tmp;
	if (x <= -6.5e+126) {
		tmp = i * (j * (x * y1));
	} else if (x <= -2.25e-55) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 2.8e-263) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 5.2e-146) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (x <= 4.4e-15) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (x <= 5.5e+61) {
		tmp = t_1;
	} else if (x <= 3.4e+76) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (x <= 3.4e+99) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (x <= 4.8e+122) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (x * ((i * y1) - (b * y0)))
	tmp = 0
	if x <= -6.5e+126:
		tmp = i * (j * (x * y1))
	elif x <= -2.25e-55:
		tmp = c * (i * ((z * t) - (x * y)))
	elif x <= 2.8e-263:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= 5.2e-146:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif x <= 4.4e-15:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif x <= 5.5e+61:
		tmp = t_1
	elif x <= 3.4e+76:
		tmp = x * (a * ((y * b) - (y1 * y2)))
	elif x <= 3.4e+99:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif x <= 4.8e+122:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))))
	tmp = 0.0
	if (x <= -6.5e+126)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -2.25e-55)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (x <= 2.8e-263)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 5.2e-146)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (x <= 4.4e-15)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (x <= 5.5e+61)
		tmp = t_1;
	elseif (x <= 3.4e+76)
		tmp = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (x <= 3.4e+99)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (x <= 4.8e+122)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (x * ((i * y1) - (b * y0)));
	tmp = 0.0;
	if (x <= -6.5e+126)
		tmp = i * (j * (x * y1));
	elseif (x <= -2.25e-55)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (x <= 2.8e-263)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= 5.2e-146)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (x <= 4.4e-15)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (x <= 5.5e+61)
		tmp = t_1;
	elseif (x <= 3.4e+76)
		tmp = x * (a * ((y * b) - (y1 * y2)));
	elseif (x <= 3.4e+99)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (x <= 4.8e+122)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.5e+126], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.25e-55], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e-263], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e-146], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-15], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+61], t$95$1, If[LessEqual[x, 3.4e+76], N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+99], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+122], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -6.5000000000000005e126

   1. Initial program 28.7%

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

   3. Taylor expanded in x around inf 68.2%

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

   4. Taylor expanded in y1 around inf 51.2%

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

      1. distribute-lft-out-- 51.2%

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

      2. *-commutative 51.2%

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

      3. *-commutative 51.2%

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

   6. Simplified 51.2%

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

   7. Taylor expanded in y2 around 0 54.5%

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

      1. *-commutative 54.5%

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

   9. Simplified 54.5%

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

   if -6.5000000000000005e126 < x < -2.24999999999999985e-55

   1. Initial program 18.8%

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

   3. Taylor expanded in c around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

      5. *-commutative 50.4%

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

      6. *-commutative 50.4%

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

      7. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in i around inf 53.7%

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

      1. *-commutative 53.7%

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

   8. Simplified 53.7%

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

   if -2.24999999999999985e-55 < x < 2.8e-263

   1. Initial program 29.8%

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

   3. Taylor expanded in y2 around inf 47.9%

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

   4. Taylor expanded in t around inf 44.8%

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

   if 2.8e-263 < x < 5.19999999999999974e-146

   1. Initial program 36.2%

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

   3. Taylor expanded in b around inf 40.7%

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

   4. Taylor expanded in y4 around inf 52.4%

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

   if 5.19999999999999974e-146 < x < 4.39999999999999971e-15

   1. Initial program 27.8%

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

   3. Taylor expanded in y2 around inf 38.7%

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

   4. Taylor expanded in k around inf 39.5%

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

   if 4.39999999999999971e-15 < x < 5.50000000000000036e61 or 4.8000000000000004e122 < x

   1. Initial program 36.6%

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

   3. Taylor expanded in x around inf 65.9%

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

   4. Taylor expanded in j around inf 64.1%

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

   if 5.50000000000000036e61 < x < 3.3999999999999997e76

   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 x around inf 100.0%

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

   4. Taylor expanded in a around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

      4. *-commutative 75.6%

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

   6. Simplified 75.6%

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

   if 3.3999999999999997e76 < x < 3.39999999999999984e99

   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 b around inf 60.0%

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

   4. Taylor expanded in y0 around inf 60.1%

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

   if 3.39999999999999984e99 < x < 4.8000000000000004e122

   1. Initial program 28.6%

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

   3. Taylor expanded in b around inf 42.9%

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

   4. Taylor expanded in a around inf 57.9%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-263}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-15}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+99}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-53}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-142}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-17}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+58}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+117}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -6.2e+126)
   (* i (* j (* x y1)))
   (if (<= x -3.1e-53)
     (* c (* i (- (* z t) (* x y))))
     (if (<= x 2.4e-256)
       (* t (* y2 (- (* a y5) (* c y4))))
       (if (<= x 2.85e-142)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= x 1.15e-17)
           (* k (* y2 (- (* y1 y4) (* y0 y5))))
           (if (<= x 1.22e+58)
             (* y0 (* c (- (* x y2) (* z y3))))
             (if (<= x 2.4e+76)
               (* x (* a (- (* y b) (* y1 y2))))
               (if (<= x 9.5e+98)
                 (* b (* y0 (- (* z k) (* x j))))
                 (if (<= x 7.5e+117)
                   (* a (* b (- (* x y) (* z t))))
                   (* j (* x (- (* i y1) (* b y0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -6.2e+126) {
		tmp = i * (j * (x * y1));
	} else if (x <= -3.1e-53) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 2.4e-256) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 2.85e-142) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (x <= 1.15e-17) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (x <= 1.22e+58) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (x <= 2.4e+76) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (x <= 9.5e+98) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (x <= 7.5e+117) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = j * (x * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-6.2d+126)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-3.1d-53)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (x <= 2.4d-256) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= 2.85d-142) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (x <= 1.15d-17) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (x <= 1.22d+58) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (x <= 2.4d+76) then
        tmp = x * (a * ((y * b) - (y1 * y2)))
    else if (x <= 9.5d+98) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (x <= 7.5d+117) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = j * (x * ((i * y1) - (b * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -6.2e+126) {
		tmp = i * (j * (x * y1));
	} else if (x <= -3.1e-53) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 2.4e-256) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 2.85e-142) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (x <= 1.15e-17) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (x <= 1.22e+58) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (x <= 2.4e+76) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (x <= 9.5e+98) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (x <= 7.5e+117) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = j * (x * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -6.2e+126:
		tmp = i * (j * (x * y1))
	elif x <= -3.1e-53:
		tmp = c * (i * ((z * t) - (x * y)))
	elif x <= 2.4e-256:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= 2.85e-142:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif x <= 1.15e-17:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif x <= 1.22e+58:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif x <= 2.4e+76:
		tmp = x * (a * ((y * b) - (y1 * y2)))
	elif x <= 9.5e+98:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif x <= 7.5e+117:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = j * (x * ((i * y1) - (b * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -6.2e+126)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -3.1e-53)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (x <= 2.4e-256)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 2.85e-142)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (x <= 1.15e-17)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (x <= 1.22e+58)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (x <= 2.4e+76)
		tmp = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (x <= 9.5e+98)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (x <= 7.5e+117)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -6.2e+126)
		tmp = i * (j * (x * y1));
	elseif (x <= -3.1e-53)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (x <= 2.4e-256)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= 2.85e-142)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (x <= 1.15e-17)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (x <= 1.22e+58)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (x <= 2.4e+76)
		tmp = x * (a * ((y * b) - (y1 * y2)));
	elseif (x <= 9.5e+98)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (x <= 7.5e+117)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = j * (x * ((i * y1) - (b * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -6.2e+126], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e-53], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-256], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.85e-142], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-17], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.22e+58], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+76], N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+98], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+117], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if x < -6.2e126

   1. Initial program 28.7%

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

   3. Taylor expanded in x around inf 68.2%

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

   4. Taylor expanded in y1 around inf 51.2%

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

      1. distribute-lft-out-- 51.2%

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

      2. *-commutative 51.2%

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

      3. *-commutative 51.2%

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

   6. Simplified 51.2%

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

   7. Taylor expanded in y2 around 0 54.5%

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

      1. *-commutative 54.5%

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

   9. Simplified 54.5%

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

   if -6.2e126 < x < -3.10000000000000015e-53

   1. Initial program 18.8%

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

   3. Taylor expanded in c around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

      5. *-commutative 50.4%

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

      6. *-commutative 50.4%

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

      7. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in i around inf 53.7%

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

      1. *-commutative 53.7%

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

   8. Simplified 53.7%

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

   if -3.10000000000000015e-53 < x < 2.3999999999999999e-256

   1. Initial program 29.8%

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

   3. Taylor expanded in y2 around inf 47.9%

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

   4. Taylor expanded in t around inf 44.8%

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

   if 2.3999999999999999e-256 < x < 2.84999999999999997e-142

   1. Initial program 36.2%

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

   3. Taylor expanded in b around inf 40.7%

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

   4. Taylor expanded in y4 around inf 52.4%

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

   if 2.84999999999999997e-142 < x < 1.15000000000000004e-17

   1. Initial program 27.8%

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

   3. Taylor expanded in y2 around inf 38.7%

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

   4. Taylor expanded in k around inf 39.5%

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

   if 1.15000000000000004e-17 < x < 1.21999999999999995e58

   1. Initial program 57.1%

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

   3. Taylor expanded in c around inf 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. *-commutative 71.9%

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

      5. *-commutative 71.9%

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

      6. *-commutative 71.9%

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

      7. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in y0 around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. *-commutative 57.7%

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

      3. *-commutative 57.7%

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

      4. fma-neg 57.7%

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

      5. distribute-lft-neg-out 57.7%

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

      6. associate-*l* 57.7%

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

      7. distribute-lft-neg-out 57.7%

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

      8. fma-neg 57.7%

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

      9. *-commutative 57.7%

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

      10. *-commutative 57.7%

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

   8. Simplified 57.7%

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

   if 1.21999999999999995e58 < x < 2.4e76

   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 x around inf 100.0%

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

   4. Taylor expanded in a around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

      4. *-commutative 75.6%

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

   6. Simplified 75.6%

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

   if 2.4e76 < x < 9.5000000000000001e98

   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 b around inf 60.0%

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

   4. Taylor expanded in y0 around inf 60.1%

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

   if 9.5000000000000001e98 < x < 7.5e117

   1. Initial program 28.6%

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

   3. Taylor expanded in b around inf 42.9%

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

   4. Taylor expanded in a around inf 57.9%

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

   if 7.5e117 < x

   1. Initial program 32.4%

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

   3. Taylor expanded in x around inf 70.6%

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

   4. Taylor expanded in j around inf 65.5%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-53}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-142}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-17}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+58}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+117}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x \cdot y\\ t_2 := x \cdot j - z \cdot k\\ t_3 := y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\\ t_4 := y \cdot k - t \cdot j\\ \mathbf{if}\;y1 \leq -380000:\\ \;\;\;\;y1 \cdot \left(i \cdot t_2 + t_3\right)\\ \mathbf{elif}\;y1 \leq -5.5 \cdot 10^{-80}:\\ \;\;\;\;\left(y3 \cdot y4 - x \cdot i\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y1 \leq -1.1 \cdot 10^{-249}:\\ \;\;\;\;i \cdot \left(y1 \cdot t_2 + \left(y5 \cdot t_4 + c \cdot t_1\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-264}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot t_4 + a \cdot t_1\right)\right)\\ \mathbf{elif}\;y1 \leq 6.4 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z t) (* x y)))
        (t_2 (- (* x j) (* z k)))
        (t_3 (+ (* y4 (- (* k y2) (* j y3))) (* a (- (* z y3) (* x y2)))))
        (t_4 (- (* y k) (* t j))))
   (if (<= y1 -380000.0)
     (* y1 (+ (* i t_2) t_3))
     (if (<= y1 -5.5e-80)
       (* (- (* y3 y4) (* x i)) (* y c))
       (if (<= y1 -1.1e-249)
         (* i (+ (* y1 t_2) (+ (* y5 t_4) (* c t_1))))
         (if (<= y1 3.1e-264)
           (* b (- (* y0 (- (* z k) (* x j))) (+ (* y4 t_4) (* a t_1))))
           (if (<= y1 6.4e+184)
             (*
              x
              (+
               (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
               (* j (- (* i y1) (* b y0)))))
             (* y1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * t) - (x * y);
	double t_2 = (x * j) - (z * k);
	double t_3 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)));
	double t_4 = (y * k) - (t * j);
	double tmp;
	if (y1 <= -380000.0) {
		tmp = y1 * ((i * t_2) + t_3);
	} else if (y1 <= -5.5e-80) {
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	} else if (y1 <= -1.1e-249) {
		tmp = i * ((y1 * t_2) + ((y5 * t_4) + (c * t_1)));
	} else if (y1 <= 3.1e-264) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_4) + (a * t_1)));
	} else if (y1 <= 6.4e+184) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y1 * t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (z * t) - (x * y)
    t_2 = (x * j) - (z * k)
    t_3 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)))
    t_4 = (y * k) - (t * j)
    if (y1 <= (-380000.0d0)) then
        tmp = y1 * ((i * t_2) + t_3)
    else if (y1 <= (-5.5d-80)) then
        tmp = ((y3 * y4) - (x * i)) * (y * c)
    else if (y1 <= (-1.1d-249)) then
        tmp = i * ((y1 * t_2) + ((y5 * t_4) + (c * t_1)))
    else if (y1 <= 3.1d-264) then
        tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_4) + (a * t_1)))
    else if (y1 <= 6.4d+184) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else
        tmp = y1 * t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * t) - (x * y);
	double t_2 = (x * j) - (z * k);
	double t_3 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)));
	double t_4 = (y * k) - (t * j);
	double tmp;
	if (y1 <= -380000.0) {
		tmp = y1 * ((i * t_2) + t_3);
	} else if (y1 <= -5.5e-80) {
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	} else if (y1 <= -1.1e-249) {
		tmp = i * ((y1 * t_2) + ((y5 * t_4) + (c * t_1)));
	} else if (y1 <= 3.1e-264) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_4) + (a * t_1)));
	} else if (y1 <= 6.4e+184) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y1 * t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (z * t) - (x * y)
	t_2 = (x * j) - (z * k)
	t_3 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)))
	t_4 = (y * k) - (t * j)
	tmp = 0
	if y1 <= -380000.0:
		tmp = y1 * ((i * t_2) + t_3)
	elif y1 <= -5.5e-80:
		tmp = ((y3 * y4) - (x * i)) * (y * c)
	elif y1 <= -1.1e-249:
		tmp = i * ((y1 * t_2) + ((y5 * t_4) + (c * t_1)))
	elif y1 <= 3.1e-264:
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_4) + (a * t_1)))
	elif y1 <= 6.4e+184:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	else:
		tmp = y1 * t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * t) - Float64(x * y))
	t_2 = Float64(Float64(x * j) - Float64(z * k))
	t_3 = Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))
	t_4 = Float64(Float64(y * k) - Float64(t * j))
	tmp = 0.0
	if (y1 <= -380000.0)
		tmp = Float64(y1 * Float64(Float64(i * t_2) + t_3));
	elseif (y1 <= -5.5e-80)
		tmp = Float64(Float64(Float64(y3 * y4) - Float64(x * i)) * Float64(y * c));
	elseif (y1 <= -1.1e-249)
		tmp = Float64(i * Float64(Float64(y1 * t_2) + Float64(Float64(y5 * t_4) + Float64(c * t_1))));
	elseif (y1 <= 3.1e-264)
		tmp = Float64(b * Float64(Float64(y0 * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y4 * t_4) + Float64(a * t_1))));
	elseif (y1 <= 6.4e+184)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	else
		tmp = Float64(y1 * t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * t) - (x * y);
	t_2 = (x * j) - (z * k);
	t_3 = (y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)));
	t_4 = (y * k) - (t * j);
	tmp = 0.0;
	if (y1 <= -380000.0)
		tmp = y1 * ((i * t_2) + t_3);
	elseif (y1 <= -5.5e-80)
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	elseif (y1 <= -1.1e-249)
		tmp = i * ((y1 * t_2) + ((y5 * t_4) + (c * t_1)));
	elseif (y1 <= 3.1e-264)
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_4) + (a * t_1)));
	elseif (y1 <= 6.4e+184)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	else
		tmp = y1 * t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -380000.0], N[(y1 * N[(N[(i * t$95$2), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5.5e-80], N[(N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision] * N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.1e-249], N[(i * N[(N[(y1 * t$95$2), $MachinePrecision] + N[(N[(y5 * t$95$4), $MachinePrecision] + N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.1e-264], N[(b * N[(N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * t$95$4), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6.4e+184], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * t$95$3), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -3.8e5

   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 61.8%

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

      1. mul-1-neg 61.8%

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

      2. *-commutative 61.8%

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

      3. distribute-rgt-neg-in 61.8%

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

   5. Simplified 61.8%

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

   if -3.8e5 < y1 < -5.4999999999999997e-80

   1. Initial program 35.7%

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

   3. Taylor expanded in c around inf 71.8%

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

      1. +-commutative 71.8%

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

      2. mul-1-neg 71.8%

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

      3. unsub-neg 71.8%

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

      4. *-commutative 71.8%

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

      5. *-commutative 71.8%

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

      6. *-commutative 71.8%

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

      7. *-commutative 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in y around -inf 79.1%

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

      1. *-commutative 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-*l* 79.1%

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

      4. +-commutative 79.1%

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

      5. mul-1-neg 79.1%

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

      6. unsub-neg 79.1%

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

      7. *-commutative 79.1%

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

   8. Simplified 79.1%

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

   if -5.4999999999999997e-80 < y1 < -1.1e-249

   1. Initial program 43.7%

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

   3. Taylor expanded in i around -inf 62.9%

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

   if -1.1e-249 < y1 < 3.1000000000000002e-264

   1. Initial program 33.6%

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

   3. Taylor expanded in b around inf 56.1%

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

   if 3.1000000000000002e-264 < y1 < 6.39999999999999966e184

   1. Initial program 22.6%

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

   3. Taylor expanded in x around inf 52.5%

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

   if 6.39999999999999966e184 < y1

   1. Initial program 21.4%

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

   3. Taylor expanded in y1 around -inf 46.7%

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

      1. mul-1-neg 46.7%

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

      2. *-commutative 46.7%

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

      3. distribute-rgt-neg-in 46.7%

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

   5. Simplified 46.7%

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

   6. Taylor expanded in i around 0 58.1%

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

      1. associate-*r* 58.1%

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

      2. neg-mul-1 58.1%

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

      3. sub-neg 58.1%

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

      4. *-commutative 58.1%

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

      5. sub-neg 58.1%

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

      6. *-commutative 58.1%

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

   8. Simplified 58.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -380000:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -5.5 \cdot 10^{-80}:\\ \;\;\;\;\left(y3 \cdot y4 - x \cdot i\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y1 \leq -1.1 \cdot 10^{-249}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-264}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 6.4 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := x \cdot j - z \cdot k\\ t_3 := y4 \cdot t_1 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\\ t_4 := y \cdot k - t \cdot j\\ \mathbf{if}\;y1 \leq -13200000000000:\\ \;\;\;\;y1 \cdot \left(i \cdot t_2 + t_3\right)\\ \mathbf{elif}\;y1 \leq -1.25 \cdot 10^{-79}:\\ \;\;\;\;\left(y3 \cdot y4 - x \cdot i\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y1 \leq -5.5 \cdot 10^{-204}:\\ \;\;\;\;i \cdot \left(y1 \cdot t_2 + \left(y5 \cdot t_4 + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 9.5 \cdot 10^{-147}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(y0 \cdot t_1 - i \cdot t_4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.12 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* x j) (* z k)))
        (t_3 (+ (* y4 t_1) (* a (- (* z y3) (* x y2)))))
        (t_4 (- (* y k) (* t j))))
   (if (<= y1 -13200000000000.0)
     (* y1 (+ (* i t_2) t_3))
     (if (<= y1 -1.25e-79)
       (* (- (* y3 y4) (* x i)) (* y c))
       (if (<= y1 -5.5e-204)
         (* i (+ (* y1 t_2) (+ (* y5 t_4) (* c (- (* z t) (* x y))))))
         (if (<= y1 9.5e-147)
           (* y5 (- (* a (- (* t y2) (* y y3))) (- (* y0 t_1) (* i t_4))))
           (if (<= y1 1.12e+184)
             (*
              x
              (+
               (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
               (* j (- (* i y1) (* b y0)))))
             (* y1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (x * j) - (z * k);
	double t_3 = (y4 * t_1) + (a * ((z * y3) - (x * y2)));
	double t_4 = (y * k) - (t * j);
	double tmp;
	if (y1 <= -13200000000000.0) {
		tmp = y1 * ((i * t_2) + t_3);
	} else if (y1 <= -1.25e-79) {
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	} else if (y1 <= -5.5e-204) {
		tmp = i * ((y1 * t_2) + ((y5 * t_4) + (c * ((z * t) - (x * y)))));
	} else if (y1 <= 9.5e-147) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((y0 * t_1) - (i * t_4)));
	} else if (y1 <= 1.12e+184) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y1 * t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (x * j) - (z * k)
    t_3 = (y4 * t_1) + (a * ((z * y3) - (x * y2)))
    t_4 = (y * k) - (t * j)
    if (y1 <= (-13200000000000.0d0)) then
        tmp = y1 * ((i * t_2) + t_3)
    else if (y1 <= (-1.25d-79)) then
        tmp = ((y3 * y4) - (x * i)) * (y * c)
    else if (y1 <= (-5.5d-204)) then
        tmp = i * ((y1 * t_2) + ((y5 * t_4) + (c * ((z * t) - (x * y)))))
    else if (y1 <= 9.5d-147) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((y0 * t_1) - (i * t_4)))
    else if (y1 <= 1.12d+184) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else
        tmp = y1 * t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (x * j) - (z * k);
	double t_3 = (y4 * t_1) + (a * ((z * y3) - (x * y2)));
	double t_4 = (y * k) - (t * j);
	double tmp;
	if (y1 <= -13200000000000.0) {
		tmp = y1 * ((i * t_2) + t_3);
	} else if (y1 <= -1.25e-79) {
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	} else if (y1 <= -5.5e-204) {
		tmp = i * ((y1 * t_2) + ((y5 * t_4) + (c * ((z * t) - (x * y)))));
	} else if (y1 <= 9.5e-147) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((y0 * t_1) - (i * t_4)));
	} else if (y1 <= 1.12e+184) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y1 * t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = (x * j) - (z * k)
	t_3 = (y4 * t_1) + (a * ((z * y3) - (x * y2)))
	t_4 = (y * k) - (t * j)
	tmp = 0
	if y1 <= -13200000000000.0:
		tmp = y1 * ((i * t_2) + t_3)
	elif y1 <= -1.25e-79:
		tmp = ((y3 * y4) - (x * i)) * (y * c)
	elif y1 <= -5.5e-204:
		tmp = i * ((y1 * t_2) + ((y5 * t_4) + (c * ((z * t) - (x * y)))))
	elif y1 <= 9.5e-147:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((y0 * t_1) - (i * t_4)))
	elif y1 <= 1.12e+184:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	else:
		tmp = y1 * t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(x * j) - Float64(z * k))
	t_3 = Float64(Float64(y4 * t_1) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))
	t_4 = Float64(Float64(y * k) - Float64(t * j))
	tmp = 0.0
	if (y1 <= -13200000000000.0)
		tmp = Float64(y1 * Float64(Float64(i * t_2) + t_3));
	elseif (y1 <= -1.25e-79)
		tmp = Float64(Float64(Float64(y3 * y4) - Float64(x * i)) * Float64(y * c));
	elseif (y1 <= -5.5e-204)
		tmp = Float64(i * Float64(Float64(y1 * t_2) + Float64(Float64(y5 * t_4) + Float64(c * Float64(Float64(z * t) - Float64(x * y))))));
	elseif (y1 <= 9.5e-147)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(Float64(y0 * t_1) - Float64(i * t_4))));
	elseif (y1 <= 1.12e+184)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	else
		tmp = Float64(y1 * t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y2) - (j * y3);
	t_2 = (x * j) - (z * k);
	t_3 = (y4 * t_1) + (a * ((z * y3) - (x * y2)));
	t_4 = (y * k) - (t * j);
	tmp = 0.0;
	if (y1 <= -13200000000000.0)
		tmp = y1 * ((i * t_2) + t_3);
	elseif (y1 <= -1.25e-79)
		tmp = ((y3 * y4) - (x * i)) * (y * c);
	elseif (y1 <= -5.5e-204)
		tmp = i * ((y1 * t_2) + ((y5 * t_4) + (c * ((z * t) - (x * y)))));
	elseif (y1 <= 9.5e-147)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((y0 * t_1) - (i * t_4)));
	elseif (y1 <= 1.12e+184)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	else
		tmp = y1 * t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y4 * t$95$1), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -13200000000000.0], N[(y1 * N[(N[(i * t$95$2), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.25e-79], N[(N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision] * N[(y * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5.5e-204], N[(i * N[(N[(y1 * t$95$2), $MachinePrecision] + N[(N[(y5 * t$95$4), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9.5e-147], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y0 * t$95$1), $MachinePrecision] - N[(i * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.12e+184], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * t$95$3), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -1.32e13

   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 61.8%

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

      1. mul-1-neg 61.8%

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

      2. *-commutative 61.8%

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

      3. distribute-rgt-neg-in 61.8%

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

   5. Simplified 61.8%

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

   if -1.32e13 < y1 < -1.25e-79

   1. Initial program 35.7%

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

   3. Taylor expanded in c around inf 71.8%

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

      1. +-commutative 71.8%

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

      2. mul-1-neg 71.8%

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

      3. unsub-neg 71.8%

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

      4. *-commutative 71.8%

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

      5. *-commutative 71.8%

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

      6. *-commutative 71.8%

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

      7. *-commutative 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in y around -inf 79.1%

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

      1. *-commutative 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-*l* 79.1%

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

      4. +-commutative 79.1%

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

      5. mul-1-neg 79.1%

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

      6. unsub-neg 79.1%

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

      7. *-commutative 79.1%

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

   8. Simplified 79.1%

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

   if -1.25e-79 < y1 < -5.4999999999999999e-204

   1. Initial program 35.0%

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

   3. Taylor expanded in i around -inf 65.3%

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

   if -5.4999999999999999e-204 < y1 < 9.49999999999999986e-147

   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 y5 around -inf 54.3%

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

   if 9.49999999999999986e-147 < y1 < 1.12000000000000007e184

   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 x around inf 54.6%

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

   if 1.12000000000000007e184 < y1

   1. Initial program 21.4%

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

   3. Taylor expanded in y1 around -inf 46.7%

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

      1. mul-1-neg 46.7%

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

      2. *-commutative 46.7%

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

      3. distribute-rgt-neg-in 46.7%

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

   5. Simplified 46.7%

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

   6. Taylor expanded in i around 0 58.1%

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

      1. associate-*r* 58.1%

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

      2. neg-mul-1 58.1%

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

      3. sub-neg 58.1%

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

      4. *-commutative 58.1%

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

      5. sub-neg 58.1%

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

      6. *-commutative 58.1%

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

   8. Simplified 58.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -13200000000000:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.25 \cdot 10^{-79}:\\ \;\;\;\;\left(y3 \cdot y4 - x \cdot i\right) \cdot \left(y \cdot c\right)\\ \mathbf{elif}\;y1 \leq -5.5 \cdot 10^{-204}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 9.5 \cdot 10^{-147}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - i \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.12 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_2 := k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{if}\;y4 \leq -1.15 \cdot 10^{+256}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -3.2 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -7 \cdot 10^{+162}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(j \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.05 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y4 \leq 4.2 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq 0.5:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y4 \leq 2.05 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq 9.5 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* x (- (* i y1) (* b y0)))))
        (t_2 (* k (* y2 (- (* y1 y4) (* y0 y5))))))
   (if (<= y4 -1.15e+256)
     (* t (* y2 (- (* a y5) (* c y4))))
     (if (<= y4 -3.2e+217)
       t_1
       (if (<= y4 -7e+162)
         (* (* y1 y3) (* j (- y4)))
         (if (<= y4 -1.05e-103)
           t_2
           (if (<= y4 4.2e-72)
             t_1
             (if (<= y4 0.5)
               (* i (* c (- (* z t) (* x y))))
               (if (<= y4 2.05e+35)
                 t_1
                 (if (<= y4 9.5e+194)
                   t_2
                   (* b (* y4 (- (* t j) (* y k))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (x * ((i * y1) - (b * y0)));
	double t_2 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (y4 <= -1.15e+256) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (y4 <= -3.2e+217) {
		tmp = t_1;
	} else if (y4 <= -7e+162) {
		tmp = (y1 * y3) * (j * -y4);
	} else if (y4 <= -1.05e-103) {
		tmp = t_2;
	} else if (y4 <= 4.2e-72) {
		tmp = t_1;
	} else if (y4 <= 0.5) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (y4 <= 2.05e+35) {
		tmp = t_1;
	} else if (y4 <= 9.5e+194) {
		tmp = t_2;
	} else {
		tmp = b * (y4 * ((t * j) - (y * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (x * ((i * y1) - (b * y0)))
    t_2 = k * (y2 * ((y1 * y4) - (y0 * y5)))
    if (y4 <= (-1.15d+256)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (y4 <= (-3.2d+217)) then
        tmp = t_1
    else if (y4 <= (-7d+162)) then
        tmp = (y1 * y3) * (j * -y4)
    else if (y4 <= (-1.05d-103)) then
        tmp = t_2
    else if (y4 <= 4.2d-72) then
        tmp = t_1
    else if (y4 <= 0.5d0) then
        tmp = i * (c * ((z * t) - (x * y)))
    else if (y4 <= 2.05d+35) then
        tmp = t_1
    else if (y4 <= 9.5d+194) then
        tmp = t_2
    else
        tmp = b * (y4 * ((t * j) - (y * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (x * ((i * y1) - (b * y0)));
	double t_2 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (y4 <= -1.15e+256) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (y4 <= -3.2e+217) {
		tmp = t_1;
	} else if (y4 <= -7e+162) {
		tmp = (y1 * y3) * (j * -y4);
	} else if (y4 <= -1.05e-103) {
		tmp = t_2;
	} else if (y4 <= 4.2e-72) {
		tmp = t_1;
	} else if (y4 <= 0.5) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (y4 <= 2.05e+35) {
		tmp = t_1;
	} else if (y4 <= 9.5e+194) {
		tmp = t_2;
	} else {
		tmp = b * (y4 * ((t * j) - (y * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (x * ((i * y1) - (b * y0)))
	t_2 = k * (y2 * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if y4 <= -1.15e+256:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif y4 <= -3.2e+217:
		tmp = t_1
	elif y4 <= -7e+162:
		tmp = (y1 * y3) * (j * -y4)
	elif y4 <= -1.05e-103:
		tmp = t_2
	elif y4 <= 4.2e-72:
		tmp = t_1
	elif y4 <= 0.5:
		tmp = i * (c * ((z * t) - (x * y)))
	elif y4 <= 2.05e+35:
		tmp = t_1
	elif y4 <= 9.5e+194:
		tmp = t_2
	else:
		tmp = b * (y4 * ((t * j) - (y * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))))
	t_2 = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (y4 <= -1.15e+256)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (y4 <= -3.2e+217)
		tmp = t_1;
	elseif (y4 <= -7e+162)
		tmp = Float64(Float64(y1 * y3) * Float64(j * Float64(-y4)));
	elseif (y4 <= -1.05e-103)
		tmp = t_2;
	elseif (y4 <= 4.2e-72)
		tmp = t_1;
	elseif (y4 <= 0.5)
		tmp = Float64(i * Float64(c * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y4 <= 2.05e+35)
		tmp = t_1;
	elseif (y4 <= 9.5e+194)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (x * ((i * y1) - (b * y0)));
	t_2 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (y4 <= -1.15e+256)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (y4 <= -3.2e+217)
		tmp = t_1;
	elseif (y4 <= -7e+162)
		tmp = (y1 * y3) * (j * -y4);
	elseif (y4 <= -1.05e-103)
		tmp = t_2;
	elseif (y4 <= 4.2e-72)
		tmp = t_1;
	elseif (y4 <= 0.5)
		tmp = i * (c * ((z * t) - (x * y)));
	elseif (y4 <= 2.05e+35)
		tmp = t_1;
	elseif (y4 <= 9.5e+194)
		tmp = t_2;
	else
		tmp = b * (y4 * ((t * j) - (y * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.15e+256], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -3.2e+217], t$95$1, If[LessEqual[y4, -7e+162], N[(N[(y1 * y3), $MachinePrecision] * N[(j * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.05e-103], t$95$2, If[LessEqual[y4, 4.2e-72], t$95$1, If[LessEqual[y4, 0.5], N[(i * N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.05e+35], t$95$1, If[LessEqual[y4, 9.5e+194], t$95$2, N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -1.1499999999999999e256

   1. Initial program 10.0%

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

   3. Taylor expanded in y2 around inf 50.1%

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

   4. Taylor expanded in t around inf 70.2%

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

   if -1.1499999999999999e256 < y4 < -3.2000000000000001e217 or -1.05000000000000002e-103 < y4 < 4.2e-72 or 0.5 < y4 < 2.0499999999999999e35

   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 x around inf 52.6%

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

   4. Taylor expanded in j around inf 49.6%

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

   if -3.2000000000000001e217 < y4 < -7.00000000000000036e162

   1. Initial program 18.8%

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

   3. Taylor expanded in y1 around -inf 31.6%

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

      1. mul-1-neg 31.6%

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

      2. *-commutative 31.6%

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

      3. distribute-rgt-neg-in 31.6%

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

   5. Simplified 31.6%

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

   6. Taylor expanded in y3 around -inf 62.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 62.6%

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

   8. Simplified 62.6%

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

   9. Taylor expanded in a around 0 62.7%

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

       1. neg-mul-1 62.7%

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

       2. distribute-rgt-neg-in 62.7%

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

   11. Simplified 62.7%

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

   if -7.00000000000000036e162 < y4 < -1.05000000000000002e-103 or 2.0499999999999999e35 < y4 < 9.5e194

   1. Initial program 30.1%

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

   3. Taylor expanded in y2 around inf 48.5%

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

   4. Taylor expanded in k around inf 45.8%

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

   if 4.2e-72 < y4 < 0.5

   1. Initial program 23.6%

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

   3. Taylor expanded in c around inf 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

      4. *-commutative 48.2%

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

      5. *-commutative 48.2%

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

      6. *-commutative 48.2%

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

      7. *-commutative 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in i around inf 40.2%

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

      1. *-commutative 40.2%

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

      2. associate-*l* 41.8%

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

      3. *-commutative 41.8%

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

   8. Simplified 41.8%

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

   if 9.5e194 < y4

   1. Initial program 30.8%

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

   3. Taylor expanded in b around inf 51.1%

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

   4. Taylor expanded in y4 around inf 58.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.15 \cdot 10^{+256}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -3.2 \cdot 10^{+217}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -7 \cdot 10^{+162}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(j \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.05 \cdot 10^{-103}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 4.2 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 0.5:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y4 \leq 2.05 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 9.5 \cdot 10^{+194}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ t_2 := x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-126}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq -3.55 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-296}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-111}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+60}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+254}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* z (* c (- (* t i) (* y0 y3)))))
        (t_2 (* x (* a (- (* y b) (* y1 y2))))))
   (if (<= a -1.1e+149)
     t_2
     (if (<= a -6.2e-8)
       t_1
       (if (<= a -5.8e-126)
         (* b (* y0 (- (* z k) (* x j))))
         (if (<= a -3.55e-191)
           t_1
           (if (<= a 2.4e-296)
             (* k (* y2 (- (* y1 y4) (* y0 y5))))
             (if (<= a 1.22e-111)
               (* i (* c (- (* z t) (* x y))))
               (if (<= a 2.25e+60)
                 (* i (* y1 (- (* x j) (* z k))))
                 (if (<= a 1.12e+254)
                   t_2
                   (* (* a b) (- (* x y) (* z t)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * (c * ((t * i) - (y0 * y3)));
	double t_2 = x * (a * ((y * b) - (y1 * y2)));
	double tmp;
	if (a <= -1.1e+149) {
		tmp = t_2;
	} else if (a <= -6.2e-8) {
		tmp = t_1;
	} else if (a <= -5.8e-126) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= -3.55e-191) {
		tmp = t_1;
	} else if (a <= 2.4e-296) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (a <= 1.22e-111) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (a <= 2.25e+60) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= 1.12e+254) {
		tmp = t_2;
	} else {
		tmp = (a * b) * ((x * y) - (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (c * ((t * i) - (y0 * y3)))
    t_2 = x * (a * ((y * b) - (y1 * y2)))
    if (a <= (-1.1d+149)) then
        tmp = t_2
    else if (a <= (-6.2d-8)) then
        tmp = t_1
    else if (a <= (-5.8d-126)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (a <= (-3.55d-191)) then
        tmp = t_1
    else if (a <= 2.4d-296) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (a <= 1.22d-111) then
        tmp = i * (c * ((z * t) - (x * y)))
    else if (a <= 2.25d+60) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (a <= 1.12d+254) then
        tmp = t_2
    else
        tmp = (a * b) * ((x * y) - (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * (c * ((t * i) - (y0 * y3)));
	double t_2 = x * (a * ((y * b) - (y1 * y2)));
	double tmp;
	if (a <= -1.1e+149) {
		tmp = t_2;
	} else if (a <= -6.2e-8) {
		tmp = t_1;
	} else if (a <= -5.8e-126) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= -3.55e-191) {
		tmp = t_1;
	} else if (a <= 2.4e-296) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (a <= 1.22e-111) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (a <= 2.25e+60) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= 1.12e+254) {
		tmp = t_2;
	} else {
		tmp = (a * b) * ((x * y) - (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = z * (c * ((t * i) - (y0 * y3)))
	t_2 = x * (a * ((y * b) - (y1 * y2)))
	tmp = 0
	if a <= -1.1e+149:
		tmp = t_2
	elif a <= -6.2e-8:
		tmp = t_1
	elif a <= -5.8e-126:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif a <= -3.55e-191:
		tmp = t_1
	elif a <= 2.4e-296:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif a <= 1.22e-111:
		tmp = i * (c * ((z * t) - (x * y)))
	elif a <= 2.25e+60:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif a <= 1.12e+254:
		tmp = t_2
	else:
		tmp = (a * b) * ((x * y) - (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))))
	t_2 = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))))
	tmp = 0.0
	if (a <= -1.1e+149)
		tmp = t_2;
	elseif (a <= -6.2e-8)
		tmp = t_1;
	elseif (a <= -5.8e-126)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (a <= -3.55e-191)
		tmp = t_1;
	elseif (a <= 2.4e-296)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (a <= 1.22e-111)
		tmp = Float64(i * Float64(c * Float64(Float64(z * t) - Float64(x * y))));
	elseif (a <= 2.25e+60)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (a <= 1.12e+254)
		tmp = t_2;
	else
		tmp = Float64(Float64(a * b) * Float64(Float64(x * y) - Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = z * (c * ((t * i) - (y0 * y3)));
	t_2 = x * (a * ((y * b) - (y1 * y2)));
	tmp = 0.0;
	if (a <= -1.1e+149)
		tmp = t_2;
	elseif (a <= -6.2e-8)
		tmp = t_1;
	elseif (a <= -5.8e-126)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (a <= -3.55e-191)
		tmp = t_1;
	elseif (a <= 2.4e-296)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (a <= 1.22e-111)
		tmp = i * (c * ((z * t) - (x * y)));
	elseif (a <= 2.25e+60)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (a <= 1.12e+254)
		tmp = t_2;
	else
		tmp = (a * b) * ((x * y) - (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e+149], t$95$2, If[LessEqual[a, -6.2e-8], t$95$1, If[LessEqual[a, -5.8e-126], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.55e-191], t$95$1, If[LessEqual[a, 2.4e-296], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e-111], N[(i * N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e+60], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e+254], t$95$2, N[(N[(a * b), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -1.1e149 or 2.25000000000000006e60 < a < 1.12e254

   1. Initial program 22.3%

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

   3. Taylor expanded in x around inf 47.5%

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

   4. Taylor expanded in a around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. unsub-neg 56.3%

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

      4. *-commutative 56.3%

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

   6. Simplified 56.3%

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

   if -1.1e149 < a < -6.2e-8 or -5.79999999999999975e-126 < a < -3.55000000000000013e-191

   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 z around -inf 44.4%

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

   4. Taylor expanded in c around inf 52.6%

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

      1. +-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

   6. Simplified 52.6%

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

   if -6.2e-8 < a < -5.79999999999999975e-126

   1. Initial program 7.2%

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

   3. Taylor expanded in b around inf 43.2%

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

   4. Taylor expanded in y0 around inf 57.5%

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

   if -3.55000000000000013e-191 < a < 2.39999999999999996e-296

   1. Initial program 39.4%

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

   3. Taylor expanded in y2 around inf 63.9%

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

   4. Taylor expanded in k around inf 55.2%

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

   if 2.39999999999999996e-296 < a < 1.22e-111

   1. Initial program 30.1%

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

   3. Taylor expanded in c around inf 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. unsub-neg 46.8%

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

      4. *-commutative 46.8%

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

      5. *-commutative 46.8%

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

      6. *-commutative 46.8%

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

      7. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in i around inf 39.5%

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

      1. *-commutative 39.5%

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

      2. associate-*l* 49.6%

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

      3. *-commutative 49.6%

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

   8. Simplified 49.6%

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

   if 1.22e-111 < a < 2.25000000000000006e60

   1. Initial program 31.5%

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

   3. Taylor expanded in 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. *-commutative 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in i around -inf 51.0%

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

   if 1.12e254 < a

   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 b around inf 58.8%

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

   4. Taylor expanded in a around inf 68.3%

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

      1. associate-*r* 76.1%

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

   6. Simplified 76.1%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-126}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq -3.55 \cdot 10^{-191}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-296}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-111}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+60}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+254}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ t_2 := z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-298}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-106}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+59}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+251}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \end{array} \]

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 (- (* k y2) (* j y3))) (* a (- (* z y3) (* x y2))))))
        (t_2 (* z (* c (- (* t i) (* y0 y3))))))
   (if (<= a -1e+150)
     t_1
     (if (<= a -3.8e+28)
       t_2
       (if (<= a -2.4e-126)
         t_1
         (if (<= a -4e-195)
           t_2
           (if (<= a 1.1e-298)
             (* k (* y2 (- (* y1 y4) (* y0 y5))))
             (if (<= a 6.2e-106)
               (* i (* c (- (* z t) (* x y))))
               (if (<= a 8.6e+59)
                 (* i (* y1 (- (* x j) (* z k))))
                 (if (<= a 4.2e+251)
                   (* x (* a (- (* y b) (* y1 y2))))
                   (* (* a b) (- (* x y) (* z t)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	double t_2 = z * (c * ((t * i) - (y0 * y3)));
	double tmp;
	if (a <= -1e+150) {
		tmp = t_1;
	} else if (a <= -3.8e+28) {
		tmp = t_2;
	} else if (a <= -2.4e-126) {
		tmp = t_1;
	} else if (a <= -4e-195) {
		tmp = t_2;
	} else if (a <= 1.1e-298) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (a <= 6.2e-106) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (a <= 8.6e+59) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= 4.2e+251) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else {
		tmp = (a * b) * ((x * y) - (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
    t_2 = z * (c * ((t * i) - (y0 * y3)))
    if (a <= (-1d+150)) then
        tmp = t_1
    else if (a <= (-3.8d+28)) then
        tmp = t_2
    else if (a <= (-2.4d-126)) then
        tmp = t_1
    else if (a <= (-4d-195)) then
        tmp = t_2
    else if (a <= 1.1d-298) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (a <= 6.2d-106) then
        tmp = i * (c * ((z * t) - (x * y)))
    else if (a <= 8.6d+59) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (a <= 4.2d+251) then
        tmp = x * (a * ((y * b) - (y1 * y2)))
    else
        tmp = (a * b) * ((x * y) - (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	double t_2 = z * (c * ((t * i) - (y0 * y3)));
	double tmp;
	if (a <= -1e+150) {
		tmp = t_1;
	} else if (a <= -3.8e+28) {
		tmp = t_2;
	} else if (a <= -2.4e-126) {
		tmp = t_1;
	} else if (a <= -4e-195) {
		tmp = t_2;
	} else if (a <= 1.1e-298) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (a <= 6.2e-106) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (a <= 8.6e+59) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= 4.2e+251) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else {
		tmp = (a * b) * ((x * y) - (z * t));
	}
	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 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
	t_2 = z * (c * ((t * i) - (y0 * y3)))
	tmp = 0
	if a <= -1e+150:
		tmp = t_1
	elif a <= -3.8e+28:
		tmp = t_2
	elif a <= -2.4e-126:
		tmp = t_1
	elif a <= -4e-195:
		tmp = t_2
	elif a <= 1.1e-298:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif a <= 6.2e-106:
		tmp = i * (c * ((z * t) - (x * y)))
	elif a <= 8.6e+59:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif a <= 4.2e+251:
		tmp = x * (a * ((y * b) - (y1 * y2)))
	else:
		tmp = (a * b) * ((x * y) - (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))))
	t_2 = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))))
	tmp = 0.0
	if (a <= -1e+150)
		tmp = t_1;
	elseif (a <= -3.8e+28)
		tmp = t_2;
	elseif (a <= -2.4e-126)
		tmp = t_1;
	elseif (a <= -4e-195)
		tmp = t_2;
	elseif (a <= 1.1e-298)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (a <= 6.2e-106)
		tmp = Float64(i * Float64(c * Float64(Float64(z * t) - Float64(x * y))));
	elseif (a <= 8.6e+59)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (a <= 4.2e+251)
		tmp = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))));
	else
		tmp = Float64(Float64(a * b) * Float64(Float64(x * y) - Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	t_2 = z * (c * ((t * i) - (y0 * y3)));
	tmp = 0.0;
	if (a <= -1e+150)
		tmp = t_1;
	elseif (a <= -3.8e+28)
		tmp = t_2;
	elseif (a <= -2.4e-126)
		tmp = t_1;
	elseif (a <= -4e-195)
		tmp = t_2;
	elseif (a <= 1.1e-298)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (a <= 6.2e-106)
		tmp = i * (c * ((z * t) - (x * y)));
	elseif (a <= 8.6e+59)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (a <= 4.2e+251)
		tmp = x * (a * ((y * b) - (y1 * y2)));
	else
		tmp = (a * b) * ((x * y) - (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+150], t$95$1, If[LessEqual[a, -3.8e+28], t$95$2, If[LessEqual[a, -2.4e-126], t$95$1, If[LessEqual[a, -4e-195], t$95$2, If[LessEqual[a, 1.1e-298], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-106], N[(i * N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e+59], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+251], N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -9.99999999999999981e149 or -3.7999999999999999e28 < a < -2.40000000000000007e-126

   1. Initial program 24.0%

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

   3. Taylor expanded in y1 around -inf 48.4%

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

      1. mul-1-neg 48.4%

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

      2. *-commutative 48.4%

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

      3. distribute-rgt-neg-in 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in i around 0 52.7%

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

      1. associate-*r* 52.7%

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

      2. neg-mul-1 52.7%

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

      3. sub-neg 52.7%

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

      4. *-commutative 52.7%

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

      5. sub-neg 52.7%

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

      6. *-commutative 52.7%

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

   8. Simplified 52.7%

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

   if -9.99999999999999981e149 < a < -3.7999999999999999e28 or -2.40000000000000007e-126 < a < -4.0000000000000004e-195

   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 z around -inf 48.0%

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

   4. Taylor expanded in c around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

   6. Simplified 59.9%

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

   if -4.0000000000000004e-195 < a < 1.1e-298

   1. Initial program 39.4%

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

   3. Taylor expanded in y2 around inf 63.9%

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

   4. Taylor expanded in k around inf 55.2%

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

   if 1.1e-298 < a < 6.19999999999999971e-106

   1. Initial program 30.1%

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

   3. Taylor expanded in c around inf 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. unsub-neg 46.8%

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

      4. *-commutative 46.8%

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

      5. *-commutative 46.8%

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

      6. *-commutative 46.8%

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

      7. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in i around inf 39.5%

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

      1. *-commutative 39.5%

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

      2. associate-*l* 49.6%

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

      3. *-commutative 49.6%

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

   8. Simplified 49.6%

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

   if 6.19999999999999971e-106 < a < 8.60000000000000049e59

   1. Initial program 31.5%

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

   3. Taylor expanded in 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. *-commutative 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in i around -inf 51.0%

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

   if 8.60000000000000049e59 < a < 4.2000000000000001e251

   1. Initial program 22.9%

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

   3. Taylor expanded in x around inf 48.1%

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

   4. Taylor expanded in a around inf 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. *-commutative 57.4%

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

   6. Simplified 57.4%

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

   if 4.2000000000000001e251 < a

   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 b around inf 58.8%

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

   4. Taylor expanded in a around inf 68.3%

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

      1. associate-*r* 76.1%

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

   6. Simplified 76.1%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+150}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-126}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-195}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-298}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-106}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+59}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+251}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;z \cdot \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-195}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-292}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-104}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+60}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \end{array} \]

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 (- (* k y2) (* j y3))) (* a (- (* z y3) (* x y2)))))))
   (if (<= a -3.8e+143)
     t_1
     (if (<= a -4.8e+70)
       (* z (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0)))))
       (if (<= a -7.2e-127)
         t_1
         (if (<= a -2.25e-195)
           (* z (* c (- (* t i) (* y0 y3))))
           (if (<= a 9e-292)
             (* k (* y2 (- (* y1 y4) (* y0 y5))))
             (if (<= a 6.4e-104)
               (* i (* c (- (* z t) (* x y))))
               (if (<= a 4.7e+60)
                 (* i (* y1 (- (* x j) (* z k))))
                 (if (<= a 5.8e+253)
                   (* x (* a (- (* y b) (* y1 y2))))
                   (* (* a b) (- (* x y) (* z t)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	double tmp;
	if (a <= -3.8e+143) {
		tmp = t_1;
	} else if (a <= -4.8e+70) {
		tmp = z * ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0))));
	} else if (a <= -7.2e-127) {
		tmp = t_1;
	} else if (a <= -2.25e-195) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (a <= 9e-292) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (a <= 6.4e-104) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (a <= 4.7e+60) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= 5.8e+253) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else {
		tmp = (a * b) * ((x * y) - (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
    if (a <= (-3.8d+143)) then
        tmp = t_1
    else if (a <= (-4.8d+70)) then
        tmp = z * ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0))))
    else if (a <= (-7.2d-127)) then
        tmp = t_1
    else if (a <= (-2.25d-195)) then
        tmp = z * (c * ((t * i) - (y0 * y3)))
    else if (a <= 9d-292) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (a <= 6.4d-104) then
        tmp = i * (c * ((z * t) - (x * y)))
    else if (a <= 4.7d+60) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (a <= 5.8d+253) then
        tmp = x * (a * ((y * b) - (y1 * y2)))
    else
        tmp = (a * b) * ((x * y) - (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	double tmp;
	if (a <= -3.8e+143) {
		tmp = t_1;
	} else if (a <= -4.8e+70) {
		tmp = z * ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0))));
	} else if (a <= -7.2e-127) {
		tmp = t_1;
	} else if (a <= -2.25e-195) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (a <= 9e-292) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (a <= 6.4e-104) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (a <= 4.7e+60) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= 5.8e+253) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else {
		tmp = (a * b) * ((x * y) - (z * t));
	}
	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 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))))
	tmp = 0
	if a <= -3.8e+143:
		tmp = t_1
	elif a <= -4.8e+70:
		tmp = z * ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0))))
	elif a <= -7.2e-127:
		tmp = t_1
	elif a <= -2.25e-195:
		tmp = z * (c * ((t * i) - (y0 * y3)))
	elif a <= 9e-292:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif a <= 6.4e-104:
		tmp = i * (c * ((z * t) - (x * y)))
	elif a <= 4.7e+60:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif a <= 5.8e+253:
		tmp = x * (a * ((y * b) - (y1 * y2)))
	else:
		tmp = (a * b) * ((x * y) - (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))))
	tmp = 0.0
	if (a <= -3.8e+143)
		tmp = t_1;
	elseif (a <= -4.8e+70)
		tmp = Float64(z * Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0)))));
	elseif (a <= -7.2e-127)
		tmp = t_1;
	elseif (a <= -2.25e-195)
		tmp = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (a <= 9e-292)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (a <= 6.4e-104)
		tmp = Float64(i * Float64(c * Float64(Float64(z * t) - Float64(x * y))));
	elseif (a <= 4.7e+60)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (a <= 5.8e+253)
		tmp = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))));
	else
		tmp = Float64(Float64(a * b) * Float64(Float64(x * y) - Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2))));
	tmp = 0.0;
	if (a <= -3.8e+143)
		tmp = t_1;
	elseif (a <= -4.8e+70)
		tmp = z * ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0))));
	elseif (a <= -7.2e-127)
		tmp = t_1;
	elseif (a <= -2.25e-195)
		tmp = z * (c * ((t * i) - (y0 * y3)));
	elseif (a <= 9e-292)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (a <= 6.4e-104)
		tmp = i * (c * ((z * t) - (x * y)));
	elseif (a <= 4.7e+60)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (a <= 5.8e+253)
		tmp = x * (a * ((y * b) - (y1 * y2)));
	else
		tmp = (a * b) * ((x * y) - (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+143], t$95$1, If[LessEqual[a, -4.8e+70], N[(z * N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.2e-127], t$95$1, If[LessEqual[a, -2.25e-195], N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-292], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e-104], N[(i * N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e+60], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e+253], N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -3.8e143 or -4.79999999999999974e70 < a < -7.1999999999999999e-127

   1. Initial program 25.8%

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

   3. Taylor expanded in y1 around -inf 48.8%

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

      1. mul-1-neg 48.8%

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

      2. *-commutative 48.8%

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

      3. distribute-rgt-neg-in 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in i around 0 52.5%

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

      1. associate-*r* 52.5%

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

      2. neg-mul-1 52.5%

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

      3. sub-neg 52.5%

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

      4. *-commutative 52.5%

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

      5. sub-neg 52.5%

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

      6. *-commutative 52.5%

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

   8. Simplified 52.5%

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

   if -3.8e143 < a < -4.79999999999999974e70

   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 z around -inf 53.5%

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

   4. Taylor expanded in k around 0 60.2%

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

   if -7.1999999999999999e-127 < a < -2.25e-195

   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 z around -inf 48.2%

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

   4. Taylor expanded in c around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

   6. Simplified 64.0%

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

   if -2.25e-195 < a < 8.99999999999999913e-292

   1. Initial program 39.4%

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

   3. Taylor expanded in y2 around inf 63.9%

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

   4. Taylor expanded in k around inf 55.2%

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

   if 8.99999999999999913e-292 < a < 6.39999999999999978e-104

   1. Initial program 30.1%

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

   3. Taylor expanded in c around inf 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. unsub-neg 46.8%

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

      4. *-commutative 46.8%

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

      5. *-commutative 46.8%

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

      6. *-commutative 46.8%

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

      7. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in i around inf 39.5%

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

      1. *-commutative 39.5%

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

      2. associate-*l* 49.6%

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

      3. *-commutative 49.6%

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

   8. Simplified 49.6%

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

   if 6.39999999999999978e-104 < a < 4.6999999999999998e60

   1. Initial program 31.5%

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

   3. Taylor expanded in 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. *-commutative 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in i around -inf 51.0%

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

   if 4.6999999999999998e60 < a < 5.79999999999999976e253

   1. Initial program 22.9%

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

   3. Taylor expanded in x around inf 48.1%

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

   4. Taylor expanded in a around inf 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. *-commutative 57.4%

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

   6. Simplified 57.4%

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

   if 5.79999999999999976e253 < a

   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 b around inf 58.8%

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

   4. Taylor expanded in a around inf 68.3%

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

      1. associate-*r* 76.1%

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

   6. Simplified 76.1%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+143}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;z \cdot \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-127}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-195}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-292}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-104}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+60}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{if}\;x \leq -8.4 \cdot 10^{+124}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-52}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-257}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.053:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+88} \lor \neg \left(x \leq 8.8 \cdot 10^{+117}\right):\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k))))))
   (if (<= x -8.4e+124)
     (* i (* j (* x y1)))
     (if (<= x -5.3e-52)
       (* c (* i (- (* z t) (* x y))))
       (if (<= x 1.15e-257)
         (* t (* y2 (- (* a y5) (* c y4))))
         (if (<= x 3.3e-152)
           t_1
           (if (<= x 0.053)
             (* y1 (* y4 (- (* k y2) (* j y3))))
             (if (or (<= x 7.8e+88) (not (<= x 8.8e+117)))
               (* j (* x (- (* i y1) (* b y0))))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (x <= -8.4e+124) {
		tmp = i * (j * (x * y1));
	} else if (x <= -5.3e-52) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 1.15e-257) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 3.3e-152) {
		tmp = t_1;
	} else if (x <= 0.053) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if ((x <= 7.8e+88) || !(x <= 8.8e+117)) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y4 * ((t * j) - (y * k)))
    if (x <= (-8.4d+124)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-5.3d-52)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (x <= 1.15d-257) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= 3.3d-152) then
        tmp = t_1
    else if (x <= 0.053d0) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if ((x <= 7.8d+88) .or. (.not. (x <= 8.8d+117))) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (x <= -8.4e+124) {
		tmp = i * (j * (x * y1));
	} else if (x <= -5.3e-52) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 1.15e-257) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 3.3e-152) {
		tmp = t_1;
	} else if (x <= 0.053) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if ((x <= 7.8e+88) || !(x <= 8.8e+117)) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * ((t * j) - (y * k)))
	tmp = 0
	if x <= -8.4e+124:
		tmp = i * (j * (x * y1))
	elif x <= -5.3e-52:
		tmp = c * (i * ((z * t) - (x * y)))
	elif x <= 1.15e-257:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= 3.3e-152:
		tmp = t_1
	elif x <= 0.053:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif (x <= 7.8e+88) or not (x <= 8.8e+117):
		tmp = j * (x * ((i * y1) - (b * y0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	tmp = 0.0
	if (x <= -8.4e+124)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -5.3e-52)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (x <= 1.15e-257)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 3.3e-152)
		tmp = t_1;
	elseif (x <= 0.053)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif ((x <= 7.8e+88) || !(x <= 8.8e+117))
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y4 * ((t * j) - (y * k)));
	tmp = 0.0;
	if (x <= -8.4e+124)
		tmp = i * (j * (x * y1));
	elseif (x <= -5.3e-52)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (x <= 1.15e-257)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= 3.3e-152)
		tmp = t_1;
	elseif (x <= 0.053)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif ((x <= 7.8e+88) || ~((x <= 8.8e+117)))
		tmp = j * (x * ((i * y1) - (b * y0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.4e+124], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.3e-52], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-257], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e-152], t$95$1, If[LessEqual[x, 0.053], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 7.8e+88], N[Not[LessEqual[x, 8.8e+117]], $MachinePrecision]], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -8.40000000000000046e124

   1. Initial program 28.7%

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

   3. Taylor expanded in x around inf 68.2%

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

   4. Taylor expanded in y1 around inf 51.2%

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

      1. distribute-lft-out-- 51.2%

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

      2. *-commutative 51.2%

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

      3. *-commutative 51.2%

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

   6. Simplified 51.2%

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

   7. Taylor expanded in y2 around 0 54.5%

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

      1. *-commutative 54.5%

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

   9. Simplified 54.5%

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

   if -8.40000000000000046e124 < x < -5.3000000000000003e-52

   1. Initial program 18.8%

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

   3. Taylor expanded in c around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

      5. *-commutative 50.4%

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

      6. *-commutative 50.4%

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

      7. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in i around inf 53.7%

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

      1. *-commutative 53.7%

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

   8. Simplified 53.7%

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

   if -5.3000000000000003e-52 < x < 1.15e-257

   1. Initial program 29.8%

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

   3. Taylor expanded in y2 around inf 47.9%

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

   4. Taylor expanded in t around inf 44.8%

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

   if 1.15e-257 < x < 3.29999999999999998e-152 or 7.8000000000000002e88 < x < 8.80000000000000056e117

   1. Initial program 33.5%

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

   3. Taylor expanded in b around inf 46.0%

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

   4. Taylor expanded in y4 around inf 49.3%

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

   if 3.29999999999999998e-152 < x < 0.0529999999999999985

   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 y1 around -inf 46.0%

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

      1. mul-1-neg 46.0%

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

      2. *-commutative 46.0%

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

      3. distribute-rgt-neg-in 46.0%

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

   5. Simplified 46.0%

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

   6. Taylor expanded in y4 around -inf 43.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

   if 0.0529999999999999985 < x < 7.8000000000000002e88 or 8.80000000000000056e117 < x

   1. Initial program 36.2%

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

   3. Taylor expanded in x around inf 72.3%

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

   4. Taylor expanded in j around inf 62.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+124}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-52}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-257}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-152}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 0.053:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+88} \lor \neg \left(x \leq 8.8 \cdot 10^{+117}\right):\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-67}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.0205:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+88} \lor \neg \left(x \leq 1.4 \cdot 10^{+119}\right):\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k))))))
   (if (<= x -6e+140)
     (* i (* j (* x y1)))
     (if (<= x -5.8e-67)
       (* (* x y) (- (* a b) (* c i)))
       (if (<= x 7.5e-259)
         (* t (* y2 (- (* a y5) (* c y4))))
         (if (<= x 3.3e-152)
           t_1
           (if (<= x 0.0205)
             (* y1 (* y4 (- (* k y2) (* j y3))))
             (if (or (<= x 5.5e+88) (not (<= x 1.4e+119)))
               (* j (* x (- (* i y1) (* b y0))))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (x <= -6e+140) {
		tmp = i * (j * (x * y1));
	} else if (x <= -5.8e-67) {
		tmp = (x * y) * ((a * b) - (c * i));
	} else if (x <= 7.5e-259) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 3.3e-152) {
		tmp = t_1;
	} else if (x <= 0.0205) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if ((x <= 5.5e+88) || !(x <= 1.4e+119)) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y4 * ((t * j) - (y * k)))
    if (x <= (-6d+140)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-5.8d-67)) then
        tmp = (x * y) * ((a * b) - (c * i))
    else if (x <= 7.5d-259) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= 3.3d-152) then
        tmp = t_1
    else if (x <= 0.0205d0) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if ((x <= 5.5d+88) .or. (.not. (x <= 1.4d+119))) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (x <= -6e+140) {
		tmp = i * (j * (x * y1));
	} else if (x <= -5.8e-67) {
		tmp = (x * y) * ((a * b) - (c * i));
	} else if (x <= 7.5e-259) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 3.3e-152) {
		tmp = t_1;
	} else if (x <= 0.0205) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if ((x <= 5.5e+88) || !(x <= 1.4e+119)) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * ((t * j) - (y * k)))
	tmp = 0
	if x <= -6e+140:
		tmp = i * (j * (x * y1))
	elif x <= -5.8e-67:
		tmp = (x * y) * ((a * b) - (c * i))
	elif x <= 7.5e-259:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= 3.3e-152:
		tmp = t_1
	elif x <= 0.0205:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif (x <= 5.5e+88) or not (x <= 1.4e+119):
		tmp = j * (x * ((i * y1) - (b * y0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	tmp = 0.0
	if (x <= -6e+140)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -5.8e-67)
		tmp = Float64(Float64(x * y) * Float64(Float64(a * b) - Float64(c * i)));
	elseif (x <= 7.5e-259)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 3.3e-152)
		tmp = t_1;
	elseif (x <= 0.0205)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif ((x <= 5.5e+88) || !(x <= 1.4e+119))
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y4 * ((t * j) - (y * k)));
	tmp = 0.0;
	if (x <= -6e+140)
		tmp = i * (j * (x * y1));
	elseif (x <= -5.8e-67)
		tmp = (x * y) * ((a * b) - (c * i));
	elseif (x <= 7.5e-259)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= 3.3e-152)
		tmp = t_1;
	elseif (x <= 0.0205)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif ((x <= 5.5e+88) || ~((x <= 1.4e+119)))
		tmp = j * (x * ((i * y1) - (b * y0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+140], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-67], N[(N[(x * y), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-259], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e-152], t$95$1, If[LessEqual[x, 0.0205], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 5.5e+88], N[Not[LessEqual[x, 1.4e+119]], $MachinePrecision]], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -5.99999999999999993e140

   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 x around inf 68.2%

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

   4. Taylor expanded in y1 around inf 52.0%

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

      1. distribute-lft-out-- 52.0%

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

      2. *-commutative 52.0%

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

      3. *-commutative 52.0%

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

   6. Simplified 52.0%

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

   7. Taylor expanded in y2 around 0 55.6%

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

      1. *-commutative 55.6%

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

   9. Simplified 55.6%

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

   if -5.99999999999999993e140 < x < -5.8000000000000001e-67

   1. Initial program 21.6%

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

   3. Taylor expanded in x around inf 43.9%

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

   4. Taylor expanded in y around inf 54.8%

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

      1. associate-*r* 59.9%

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

   6. Simplified 59.9%

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

   if -5.8000000000000001e-67 < x < 7.50000000000000052e-259

   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 47.9%

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

   4. Taylor expanded in t around inf 44.5%

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

   if 7.50000000000000052e-259 < x < 3.29999999999999998e-152 or 5.5e88 < x < 1.40000000000000007e119

   1. Initial program 33.5%

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

   3. Taylor expanded in b around inf 46.0%

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

   4. Taylor expanded in y4 around inf 49.3%

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

   if 3.29999999999999998e-152 < x < 0.0205000000000000009

   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 y1 around -inf 46.0%

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

      1. mul-1-neg 46.0%

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

      2. *-commutative 46.0%

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

      3. distribute-rgt-neg-in 46.0%

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

   5. Simplified 46.0%

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

   6. Taylor expanded in y4 around -inf 43.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

   if 0.0205000000000000009 < x < 5.5e88 or 1.40000000000000007e119 < x

   1. Initial program 36.2%

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

   3. Taylor expanded in x around inf 72.3%

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

   4. Taylor expanded in j around inf 62.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-67}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-152}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 0.0205:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+88} \lor \neg \left(x \leq 1.4 \cdot 10^{+119}\right):\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-68}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-254}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-12}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+88} \lor \neg \left(x \leq 1.25 \cdot 10^{+118}\right):\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k))))))
   (if (<= x -3.5e+140)
     (* i (* j (* x y1)))
     (if (<= x -3.5e-68)
       (* (* x y) (- (* a b) (* c i)))
       (if (<= x -4.2e-254)
         (* (* k y2) (- (* y1 y4) (* y0 y5)))
         (if (<= x 3.3e-152)
           t_1
           (if (<= x 4.6e-12)
             (* y1 (* y4 (- (* k y2) (* j y3))))
             (if (or (<= x 5.1e+88) (not (<= x 1.25e+118)))
               (* j (* x (- (* i y1) (* b y0))))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (x <= -3.5e+140) {
		tmp = i * (j * (x * y1));
	} else if (x <= -3.5e-68) {
		tmp = (x * y) * ((a * b) - (c * i));
	} else if (x <= -4.2e-254) {
		tmp = (k * y2) * ((y1 * y4) - (y0 * y5));
	} else if (x <= 3.3e-152) {
		tmp = t_1;
	} else if (x <= 4.6e-12) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if ((x <= 5.1e+88) || !(x <= 1.25e+118)) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y4 * ((t * j) - (y * k)))
    if (x <= (-3.5d+140)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-3.5d-68)) then
        tmp = (x * y) * ((a * b) - (c * i))
    else if (x <= (-4.2d-254)) then
        tmp = (k * y2) * ((y1 * y4) - (y0 * y5))
    else if (x <= 3.3d-152) then
        tmp = t_1
    else if (x <= 4.6d-12) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if ((x <= 5.1d+88) .or. (.not. (x <= 1.25d+118))) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (x <= -3.5e+140) {
		tmp = i * (j * (x * y1));
	} else if (x <= -3.5e-68) {
		tmp = (x * y) * ((a * b) - (c * i));
	} else if (x <= -4.2e-254) {
		tmp = (k * y2) * ((y1 * y4) - (y0 * y5));
	} else if (x <= 3.3e-152) {
		tmp = t_1;
	} else if (x <= 4.6e-12) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if ((x <= 5.1e+88) || !(x <= 1.25e+118)) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * ((t * j) - (y * k)))
	tmp = 0
	if x <= -3.5e+140:
		tmp = i * (j * (x * y1))
	elif x <= -3.5e-68:
		tmp = (x * y) * ((a * b) - (c * i))
	elif x <= -4.2e-254:
		tmp = (k * y2) * ((y1 * y4) - (y0 * y5))
	elif x <= 3.3e-152:
		tmp = t_1
	elif x <= 4.6e-12:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif (x <= 5.1e+88) or not (x <= 1.25e+118):
		tmp = j * (x * ((i * y1) - (b * y0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	tmp = 0.0
	if (x <= -3.5e+140)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -3.5e-68)
		tmp = Float64(Float64(x * y) * Float64(Float64(a * b) - Float64(c * i)));
	elseif (x <= -4.2e-254)
		tmp = Float64(Float64(k * y2) * Float64(Float64(y1 * y4) - Float64(y0 * y5)));
	elseif (x <= 3.3e-152)
		tmp = t_1;
	elseif (x <= 4.6e-12)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif ((x <= 5.1e+88) || !(x <= 1.25e+118))
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y4 * ((t * j) - (y * k)));
	tmp = 0.0;
	if (x <= -3.5e+140)
		tmp = i * (j * (x * y1));
	elseif (x <= -3.5e-68)
		tmp = (x * y) * ((a * b) - (c * i));
	elseif (x <= -4.2e-254)
		tmp = (k * y2) * ((y1 * y4) - (y0 * y5));
	elseif (x <= 3.3e-152)
		tmp = t_1;
	elseif (x <= 4.6e-12)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif ((x <= 5.1e+88) || ~((x <= 1.25e+118)))
		tmp = j * (x * ((i * y1) - (b * y0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+140], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e-68], N[(N[(x * y), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-254], N[(N[(k * y2), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e-152], t$95$1, If[LessEqual[x, 4.6e-12], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 5.1e+88], N[Not[LessEqual[x, 1.25e+118]], $MachinePrecision]], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.49999999999999989e140

   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 x around inf 68.2%

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

   4. Taylor expanded in y1 around inf 52.0%

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

      1. distribute-lft-out-- 52.0%

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

      2. *-commutative 52.0%

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

      3. *-commutative 52.0%

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

   6. Simplified 52.0%

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

   7. Taylor expanded in y2 around 0 55.6%

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

      1. *-commutative 55.6%

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

   9. Simplified 55.6%

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

   if -3.49999999999999989e140 < x < -3.50000000000000013e-68

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 43.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 54.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 59.9%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   6. Simplified 59.9%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   if -3.50000000000000013e-68 < x < -4.19999999999999993e-254

   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 50.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 38.5%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 43.3%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

      2. *-commutative 43.3%

         \[\leadsto \color{blue}{\left(y2 \cdot k\right)} \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   6. Simplified 43.3%

      \[\leadsto \color{blue}{\left(y2 \cdot k\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   if -4.19999999999999993e-254 < x < 3.29999999999999998e-152 or 5.0999999999999997e88 < x < 1.24999999999999993e118

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 48.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 48.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 3.29999999999999998e-152 < x < 4.59999999999999979e-12

   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 y1 around -inf 46.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 46.0%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 46.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 46.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 46.0%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y4 around -inf 43.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.7%

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot k} - j \cdot y3\right)\right) \]

   8. Simplified 43.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]

   if 4.59999999999999979e-12 < x < 5.0999999999999997e88 or 1.24999999999999993e118 < x

   1. Initial program 36.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 62.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-68}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(a \cdot b - c \cdot i\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-254}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-152}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-12}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+88} \lor \neg \left(x \leq 1.25 \cdot 10^{+118}\right):\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_2 := k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{if}\;y4 \leq -1.16 \cdot 10^{+163}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(j \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq 0.55:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq 3.4 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* x (- (* i y1) (* b y0)))))
        (t_2 (* k (* y2 (- (* y1 y4) (* y0 y5))))))
   (if (<= y4 -1.16e+163)
     (* (* y1 y3) (* j (- y4)))
     (if (<= y4 -1.02e-103)
       t_2
       (if (<= y4 4e-74)
         t_1
         (if (<= y4 0.55)
           (* i (* c (- (* z t) (* x y))))
           (if (<= y4 4e+34)
             t_1
             (if (<= y4 3.4e+186) t_2 (* b (* y4 (- (* t j) (* y k))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (x * ((i * y1) - (b * y0)));
	double t_2 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (y4 <= -1.16e+163) {
		tmp = (y1 * y3) * (j * -y4);
	} else if (y4 <= -1.02e-103) {
		tmp = t_2;
	} else if (y4 <= 4e-74) {
		tmp = t_1;
	} else if (y4 <= 0.55) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (y4 <= 4e+34) {
		tmp = t_1;
	} else if (y4 <= 3.4e+186) {
		tmp = t_2;
	} else {
		tmp = b * (y4 * ((t * j) - (y * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (x * ((i * y1) - (b * y0)))
    t_2 = k * (y2 * ((y1 * y4) - (y0 * y5)))
    if (y4 <= (-1.16d+163)) then
        tmp = (y1 * y3) * (j * -y4)
    else if (y4 <= (-1.02d-103)) then
        tmp = t_2
    else if (y4 <= 4d-74) then
        tmp = t_1
    else if (y4 <= 0.55d0) then
        tmp = i * (c * ((z * t) - (x * y)))
    else if (y4 <= 4d+34) then
        tmp = t_1
    else if (y4 <= 3.4d+186) then
        tmp = t_2
    else
        tmp = b * (y4 * ((t * j) - (y * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (x * ((i * y1) - (b * y0)));
	double t_2 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (y4 <= -1.16e+163) {
		tmp = (y1 * y3) * (j * -y4);
	} else if (y4 <= -1.02e-103) {
		tmp = t_2;
	} else if (y4 <= 4e-74) {
		tmp = t_1;
	} else if (y4 <= 0.55) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (y4 <= 4e+34) {
		tmp = t_1;
	} else if (y4 <= 3.4e+186) {
		tmp = t_2;
	} else {
		tmp = b * (y4 * ((t * j) - (y * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (x * ((i * y1) - (b * y0)))
	t_2 = k * (y2 * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if y4 <= -1.16e+163:
		tmp = (y1 * y3) * (j * -y4)
	elif y4 <= -1.02e-103:
		tmp = t_2
	elif y4 <= 4e-74:
		tmp = t_1
	elif y4 <= 0.55:
		tmp = i * (c * ((z * t) - (x * y)))
	elif y4 <= 4e+34:
		tmp = t_1
	elif y4 <= 3.4e+186:
		tmp = t_2
	else:
		tmp = b * (y4 * ((t * j) - (y * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))))
	t_2 = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (y4 <= -1.16e+163)
		tmp = Float64(Float64(y1 * y3) * Float64(j * Float64(-y4)));
	elseif (y4 <= -1.02e-103)
		tmp = t_2;
	elseif (y4 <= 4e-74)
		tmp = t_1;
	elseif (y4 <= 0.55)
		tmp = Float64(i * Float64(c * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y4 <= 4e+34)
		tmp = t_1;
	elseif (y4 <= 3.4e+186)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (x * ((i * y1) - (b * y0)));
	t_2 = k * (y2 * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (y4 <= -1.16e+163)
		tmp = (y1 * y3) * (j * -y4);
	elseif (y4 <= -1.02e-103)
		tmp = t_2;
	elseif (y4 <= 4e-74)
		tmp = t_1;
	elseif (y4 <= 0.55)
		tmp = i * (c * ((z * t) - (x * y)));
	elseif (y4 <= 4e+34)
		tmp = t_1;
	elseif (y4 <= 3.4e+186)
		tmp = t_2;
	else
		tmp = b * (y4 * ((t * j) - (y * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.16e+163], N[(N[(y1 * y3), $MachinePrecision] * N[(j * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.02e-103], t$95$2, If[LessEqual[y4, 4e-74], t$95$1, If[LessEqual[y4, 0.55], N[(i * N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4e+34], t$95$1, If[LessEqual[y4, 3.4e+186], t$95$2, N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -1.16000000000000002e163

   1. Initial program 15.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 27.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 27.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 27.6%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 27.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 27.6%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 57.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 55.1%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   8. Simplified 55.1%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   9. Taylor expanded in a around 0 52.0%

      \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 52.0%

          \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-j \cdot y4\right)} \]

       2. distribute-rgt-neg-in 52.0%

          \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(j \cdot \left(-y4\right)\right)} \]

   11. Simplified 52.0%

       \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(j \cdot \left(-y4\right)\right)} \]

   if -1.16000000000000002e163 < y4 < -1.01999999999999998e-103 or 3.99999999999999978e34 < y4 < 3.40000000000000005e186

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 48.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in k around inf 45.8%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if -1.01999999999999998e-103 < y4 < 3.99999999999999983e-74 or 0.55000000000000004 < y4 < 3.99999999999999978e34

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 51.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 47.1%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 3.99999999999999983e-74 < y4 < 0.55000000000000004

   1. Initial program 23.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 48.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 48.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 48.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 48.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 48.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 48.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 48.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 48.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 40.2%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z - x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z - x \cdot y\right)\right) \cdot c} \]

      2. associate-*l* 41.8%

         \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z - x \cdot y\right) \cdot c\right)} \]

      3. *-commutative 41.8%

         \[\leadsto i \cdot \left(\left(\color{blue}{z \cdot t} - x \cdot y\right) \cdot c\right) \]

   8. Simplified 41.8%

      \[\leadsto \color{blue}{i \cdot \left(\left(z \cdot t - x \cdot y\right) \cdot c\right)} \]

   if 3.40000000000000005e186 < y4

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 51.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 58.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.16 \cdot 10^{+163}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(j \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{-103}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{-74}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 0.55:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 3.4 \cdot 10^{+186}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ t_2 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y2 \leq -1.75 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq -2.8 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -2.1 \cdot 10^{-208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 4.6 \cdot 10^{-239}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k)))))
        (t_2 (* a (* b (- (* x y) (* z t))))))
   (if (<= y2 -1.75e-79)
     t_2
     (if (<= y2 -2.8e-133)
       t_1
       (if (<= y2 -2.1e-208)
         t_2
         (if (<= y2 4.6e-239)
           (* b (* y0 (- (* z k) (* x j))))
           (if (<= y2 7.5e+108) t_1 (* x (* a (* y1 (- y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y2 <= -1.75e-79) {
		tmp = t_2;
	} else if (y2 <= -2.8e-133) {
		tmp = t_1;
	} else if (y2 <= -2.1e-208) {
		tmp = t_2;
	} else if (y2 <= 4.6e-239) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= 7.5e+108) {
		tmp = t_1;
	} else {
		tmp = x * (a * (y1 * -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 = b * (y4 * ((t * j) - (y * k)))
    t_2 = a * (b * ((x * y) - (z * t)))
    if (y2 <= (-1.75d-79)) then
        tmp = t_2
    else if (y2 <= (-2.8d-133)) then
        tmp = t_1
    else if (y2 <= (-2.1d-208)) then
        tmp = t_2
    else if (y2 <= 4.6d-239) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y2 <= 7.5d+108) then
        tmp = t_1
    else
        tmp = x * (a * (y1 * -y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y2 <= -1.75e-79) {
		tmp = t_2;
	} else if (y2 <= -2.8e-133) {
		tmp = t_1;
	} else if (y2 <= -2.1e-208) {
		tmp = t_2;
	} else if (y2 <= 4.6e-239) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= 7.5e+108) {
		tmp = t_1;
	} else {
		tmp = x * (a * (y1 * -y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * ((t * j) - (y * k)))
	t_2 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y2 <= -1.75e-79:
		tmp = t_2
	elif y2 <= -2.8e-133:
		tmp = t_1
	elif y2 <= -2.1e-208:
		tmp = t_2
	elif y2 <= 4.6e-239:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y2 <= 7.5e+108:
		tmp = t_1
	else:
		tmp = x * (a * (y1 * -y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	t_2 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y2 <= -1.75e-79)
		tmp = t_2;
	elseif (y2 <= -2.8e-133)
		tmp = t_1;
	elseif (y2 <= -2.1e-208)
		tmp = t_2;
	elseif (y2 <= 4.6e-239)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y2 <= 7.5e+108)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(a * Float64(y1 * Float64(-y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y4 * ((t * j) - (y * k)));
	t_2 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y2 <= -1.75e-79)
		tmp = t_2;
	elseif (y2 <= -2.8e-133)
		tmp = t_1;
	elseif (y2 <= -2.1e-208)
		tmp = t_2;
	elseif (y2 <= 4.6e-239)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y2 <= 7.5e+108)
		tmp = t_1;
	else
		tmp = x * (a * (y1 * -y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.75e-79], t$95$2, If[LessEqual[y2, -2.8e-133], t$95$1, If[LessEqual[y2, -2.1e-208], t$95$2, If[LessEqual[y2, 4.6e-239], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.5e+108], t$95$1, N[(x * N[(a * N[(y1 * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.75000000000000015e-79 or -2.7999999999999999e-133 < y2 < -2.10000000000000012e-208

   1. Initial program 32.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 38.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.75000000000000015e-79 < y2 < -2.7999999999999999e-133 or 4.5999999999999998e-239 < y2 < 7.50000000000000039e108

   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 b around inf 42.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -2.10000000000000012e-208 < y2 < 4.5999999999999998e-239

   1. Initial program 30.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 33.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 46.3%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 7.50000000000000039e108 < y2

   1. Initial program 19.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 42.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in a around inf 46.2%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(y1 \cdot y2\right) + b \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 46.2%

         \[\leadsto x \cdot \left(a \cdot \color{blue}{\left(b \cdot y + -1 \cdot \left(y1 \cdot y2\right)\right)}\right) \]

      2. mul-1-neg 46.2%

         \[\leadsto x \cdot \left(a \cdot \left(b \cdot y + \color{blue}{\left(-y1 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 46.2%

         \[\leadsto x \cdot \left(a \cdot \color{blue}{\left(b \cdot y - y1 \cdot y2\right)}\right) \]

      4. *-commutative 46.2%

         \[\leadsto x \cdot \left(a \cdot \left(b \cdot y - \color{blue}{y2 \cdot y1}\right)\right) \]

   6. Simplified 46.2%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(b \cdot y - y2 \cdot y1\right)\right)} \]

   7. Taylor expanded in b around 0 45.8%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 45.8%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot \left(y1 \cdot y2\right)\right)} \]

      2. distribute-rgt-neg-in 45.8%

         \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(-y1 \cdot y2\right)\right)} \]

      3. *-commutative 45.8%

         \[\leadsto x \cdot \left(a \cdot \left(-\color{blue}{y2 \cdot y1}\right)\right) \]

      4. distribute-rgt-neg-in 45.8%

         \[\leadsto x \cdot \left(a \cdot \color{blue}{\left(y2 \cdot \left(-y1\right)\right)}\right) \]

   9. Simplified 45.8%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(y2 \cdot \left(-y1\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.75 \cdot 10^{-79}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq -2.8 \cdot 10^{-133}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -2.1 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 4.6 \cdot 10^{-239}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+111}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-62}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+88}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k))))))
   (if (<= x -8.2e+111)
     (* i (* j (* x y1)))
     (if (<= x -5.1e-62)
       (* c (* i (- (* z t) (* x y))))
       (if (<= x 1.7e-138)
         t_1
         (if (<= x 8e+88)
           (* i (* y1 (- (* x j) (* z k))))
           (if (<= x 2.9e+103) t_1 (* b (* y0 (- (* z k) (* x j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (x <= -8.2e+111) {
		tmp = i * (j * (x * y1));
	} else if (x <= -5.1e-62) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 1.7e-138) {
		tmp = t_1;
	} else if (x <= 8e+88) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (x <= 2.9e+103) {
		tmp = t_1;
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y4 * ((t * j) - (y * k)))
    if (x <= (-8.2d+111)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-5.1d-62)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (x <= 1.7d-138) then
        tmp = t_1
    else if (x <= 8d+88) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (x <= 2.9d+103) then
        tmp = t_1
    else
        tmp = b * (y0 * ((z * k) - (x * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (x <= -8.2e+111) {
		tmp = i * (j * (x * y1));
	} else if (x <= -5.1e-62) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 1.7e-138) {
		tmp = t_1;
	} else if (x <= 8e+88) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (x <= 2.9e+103) {
		tmp = t_1;
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * ((t * j) - (y * k)))
	tmp = 0
	if x <= -8.2e+111:
		tmp = i * (j * (x * y1))
	elif x <= -5.1e-62:
		tmp = c * (i * ((z * t) - (x * y)))
	elif x <= 1.7e-138:
		tmp = t_1
	elif x <= 8e+88:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif x <= 2.9e+103:
		tmp = t_1
	else:
		tmp = b * (y0 * ((z * k) - (x * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	tmp = 0.0
	if (x <= -8.2e+111)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -5.1e-62)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (x <= 1.7e-138)
		tmp = t_1;
	elseif (x <= 8e+88)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (x <= 2.9e+103)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y4 * ((t * j) - (y * k)));
	tmp = 0.0;
	if (x <= -8.2e+111)
		tmp = i * (j * (x * y1));
	elseif (x <= -5.1e-62)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (x <= 1.7e-138)
		tmp = t_1;
	elseif (x <= 8e+88)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (x <= 2.9e+103)
		tmp = t_1;
	else
		tmp = b * (y0 * ((z * k) - (x * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.2e+111], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.1e-62], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e-138], t$95$1, If[LessEqual[x, 8e+88], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+103], t$95$1, N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.19999999999999973e111

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 51.2%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 51.2%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 51.2%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 51.2%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 51.2%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y2 around 0 54.5%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 54.5%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 54.5%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -8.19999999999999973e111 < x < -5.1e-62

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 51.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 51.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 51.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 55.1%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z - x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 55.1%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - x \cdot y\right)\right) \]

   8. Simplified 55.1%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   if -5.1e-62 < x < 1.7000000000000001e-138 or 7.99999999999999968e88 < x < 2.8999999999999998e103

   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 b around inf 36.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.4%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 1.7000000000000001e-138 < x < 7.99999999999999968e88

   1. Initial program 37.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 45.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 45.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 45.7%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 45.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 45.7%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in i around -inf 36.1%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 2.8999999999999998e103 < 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 b around inf 49.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 59.3%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+111}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-62}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+88}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+123}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -3.65 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+55}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -3.4e+123)
   (* i (* j (* x y1)))
   (if (<= x -3.65e-59)
     (* c (* i (- (* z t) (* x y))))
     (if (<= x 1.8e-138)
       (* b (* y4 (- (* t j) (* y k))))
       (if (<= x 1.65e+55)
         (* i (* y1 (- (* x j) (* z k))))
         (if (<= x 1.75e+121)
           (* a (* b (- (* x y) (* z t))))
           (* j (* x (- (* i y1) (* b y0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.4e+123) {
		tmp = i * (j * (x * y1));
	} else if (x <= -3.65e-59) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 1.8e-138) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (x <= 1.65e+55) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (x <= 1.75e+121) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = j * (x * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-3.4d+123)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-3.65d-59)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (x <= 1.8d-138) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (x <= 1.65d+55) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (x <= 1.75d+121) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = j * (x * ((i * y1) - (b * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.4e+123) {
		tmp = i * (j * (x * y1));
	} else if (x <= -3.65e-59) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 1.8e-138) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (x <= 1.65e+55) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (x <= 1.75e+121) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = j * (x * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -3.4e+123:
		tmp = i * (j * (x * y1))
	elif x <= -3.65e-59:
		tmp = c * (i * ((z * t) - (x * y)))
	elif x <= 1.8e-138:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif x <= 1.65e+55:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif x <= 1.75e+121:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = j * (x * ((i * y1) - (b * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -3.4e+123)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -3.65e-59)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (x <= 1.8e-138)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (x <= 1.65e+55)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (x <= 1.75e+121)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -3.4e+123)
		tmp = i * (j * (x * y1));
	elseif (x <= -3.65e-59)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (x <= 1.8e-138)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (x <= 1.65e+55)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (x <= 1.75e+121)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = j * (x * ((i * y1) - (b * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -3.4e+123], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.65e-59], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e-138], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e+55], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e+121], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.40000000000000001e123

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 51.2%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 51.2%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 51.2%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 51.2%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 51.2%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y2 around 0 54.5%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 54.5%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 54.5%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -3.40000000000000001e123 < x < -3.6500000000000002e-59

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 51.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 51.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 51.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 55.1%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z - x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 55.1%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - x \cdot y\right)\right) \]

   8. Simplified 55.1%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   if -3.6500000000000002e-59 < x < 1.80000000000000009e-138

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 34.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 35.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 1.80000000000000009e-138 < x < 1.65e55

   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 y1 around -inf 47.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 47.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 47.7%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 47.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 47.7%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in i around -inf 38.4%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 1.65e55 < x < 1.75e121

   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 b around inf 47.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 41.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 1.75e121 < x

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 65.5%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+123}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -3.65 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+55}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 28.2% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{if}\;y1 \leq -1.6 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq -2.9 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(a \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.35 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{+203}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* j (* x y1)))))
   (if (<= y1 -1.6e+120)
     t_1
     (if (<= y1 -2.9e+95)
       (* x (* y1 (* a (- y2))))
       (if (<= y1 -1.35e+15)
         t_1
         (if (<= y1 2.7e+203)
           (* a (* b (- (* x y) (* z t))))
           (* j (* i (* x y1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (j * (x * y1));
	double tmp;
	if (y1 <= -1.6e+120) {
		tmp = t_1;
	} else if (y1 <= -2.9e+95) {
		tmp = x * (y1 * (a * -y2));
	} else if (y1 <= -1.35e+15) {
		tmp = t_1;
	} else if (y1 <= 2.7e+203) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = j * (i * (x * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (j * (x * y1))
    if (y1 <= (-1.6d+120)) then
        tmp = t_1
    else if (y1 <= (-2.9d+95)) then
        tmp = x * (y1 * (a * -y2))
    else if (y1 <= (-1.35d+15)) then
        tmp = t_1
    else if (y1 <= 2.7d+203) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = j * (i * (x * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (j * (x * y1));
	double tmp;
	if (y1 <= -1.6e+120) {
		tmp = t_1;
	} else if (y1 <= -2.9e+95) {
		tmp = x * (y1 * (a * -y2));
	} else if (y1 <= -1.35e+15) {
		tmp = t_1;
	} else if (y1 <= 2.7e+203) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = j * (i * (x * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (j * (x * y1))
	tmp = 0
	if y1 <= -1.6e+120:
		tmp = t_1
	elif y1 <= -2.9e+95:
		tmp = x * (y1 * (a * -y2))
	elif y1 <= -1.35e+15:
		tmp = t_1
	elif y1 <= 2.7e+203:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = j * (i * (x * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(j * Float64(x * y1)))
	tmp = 0.0
	if (y1 <= -1.6e+120)
		tmp = t_1;
	elseif (y1 <= -2.9e+95)
		tmp = Float64(x * Float64(y1 * Float64(a * Float64(-y2))));
	elseif (y1 <= -1.35e+15)
		tmp = t_1;
	elseif (y1 <= 2.7e+203)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (j * (x * y1));
	tmp = 0.0;
	if (y1 <= -1.6e+120)
		tmp = t_1;
	elseif (y1 <= -2.9e+95)
		tmp = x * (y1 * (a * -y2));
	elseif (y1 <= -1.35e+15)
		tmp = t_1;
	elseif (y1 <= 2.7e+203)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = j * (i * (x * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.6e+120], t$95$1, If[LessEqual[y1, -2.9e+95], N[(x * N[(y1 * N[(a * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.35e+15], t$95$1, If[LessEqual[y1, 2.7e+203], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -1.59999999999999991e120 or -2.90000000000000013e95 < y1 < -1.35e15

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 41.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 48.1%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 48.1%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 48.1%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 48.1%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 48.1%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y2 around 0 44.9%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.9%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 44.9%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -1.59999999999999991e120 < y1 < -2.90000000000000013e95

   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 x around inf 34.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 55.9%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 55.9%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 55.9%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 55.9%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 55.9%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y1 around 0 55.9%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 55.9%

         \[\leadsto x \cdot \color{blue}{\left(-y1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]

      2. distribute-rgt-neg-out 55.9%

         \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-\left(a \cdot y2 - i \cdot j\right)\right)\right)} \]

   9. Simplified 55.9%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-\left(a \cdot y2 - i \cdot j\right)\right)\right)} \]

   10. Taylor expanded in a around inf 67.0%

       \[\leadsto x \cdot \left(y1 \cdot \left(-\color{blue}{a \cdot y2}\right)\right) \]
   11. Step-by-step derivation

       1. *-commutative 67.0%

          \[\leadsto x \cdot \left(y1 \cdot \left(-\color{blue}{y2 \cdot a}\right)\right) \]

   12. Simplified 67.0%

       \[\leadsto x \cdot \left(y1 \cdot \left(-\color{blue}{y2 \cdot a}\right)\right) \]

   if -1.35e15 < y1 < 2.7e203

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 34.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 2.7e203 < y1

   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 x around inf 40.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 50.6%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   5. Taylor expanded in i around inf 60.3%

      \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(x \cdot y1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.6 \cdot 10^{+120}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -2.9 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(a \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.35 \cdot 10^{+15}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{+203}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+119}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-17}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -2.2e+119)
   (* i (* j (* x y1)))
   (if (<= x -4.7e-59)
     (* c (* i (- (* z t) (* x y))))
     (if (<= x 3.4e-17)
       (* b (* y4 (- (* t j) (* y k))))
       (* b (* y0 (- (* z k) (* x j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.2e+119) {
		tmp = i * (j * (x * y1));
	} else if (x <= -4.7e-59) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 3.4e-17) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-2.2d+119)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-4.7d-59)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (x <= 3.4d-17) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else
        tmp = b * (y0 * ((z * k) - (x * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.2e+119) {
		tmp = i * (j * (x * y1));
	} else if (x <= -4.7e-59) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 3.4e-17) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -2.2e+119:
		tmp = i * (j * (x * y1))
	elif x <= -4.7e-59:
		tmp = c * (i * ((z * t) - (x * y)))
	elif x <= 3.4e-17:
		tmp = b * (y4 * ((t * j) - (y * k)))
	else:
		tmp = b * (y0 * ((z * k) - (x * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -2.2e+119)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -4.7e-59)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (x <= 3.4e-17)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	else
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -2.2e+119)
		tmp = i * (j * (x * y1));
	elseif (x <= -4.7e-59)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (x <= 3.4e-17)
		tmp = b * (y4 * ((t * j) - (y * k)));
	else
		tmp = b * (y0 * ((z * k) - (x * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -2.2e+119], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.7e-59], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e-17], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.2000000000000001e119

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 51.2%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 51.2%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 51.2%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 51.2%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 51.2%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y2 around 0 54.5%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 54.5%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 54.5%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -2.2000000000000001e119 < x < -4.6999999999999999e-59

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 51.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 51.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 51.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 55.1%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z - x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 55.1%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - x \cdot y\right)\right) \]

   8. Simplified 55.1%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   if -4.6999999999999999e-59 < x < 3.3999999999999998e-17

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 36.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 32.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 3.3999999999999998e-17 < x

   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 b around inf 47.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 51.3%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+119}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-17}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+15}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 0.0132:\\ \;\;\;\;\left(-j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -3.5e+15)
   (* i (* j (* x y1)))
   (if (<= x 1.95e-113)
     (* a (* y3 (* z y1)))
     (if (<= x 0.0132) (* (- j) (* y1 (* y3 y4))) (* j (* b (* x (- y0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.5e+15) {
		tmp = i * (j * (x * y1));
	} else if (x <= 1.95e-113) {
		tmp = a * (y3 * (z * y1));
	} else if (x <= 0.0132) {
		tmp = -j * (y1 * (y3 * y4));
	} else {
		tmp = j * (b * (x * -y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-3.5d+15)) then
        tmp = i * (j * (x * y1))
    else if (x <= 1.95d-113) then
        tmp = a * (y3 * (z * y1))
    else if (x <= 0.0132d0) then
        tmp = -j * (y1 * (y3 * y4))
    else
        tmp = j * (b * (x * -y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.5e+15) {
		tmp = i * (j * (x * y1));
	} else if (x <= 1.95e-113) {
		tmp = a * (y3 * (z * y1));
	} else if (x <= 0.0132) {
		tmp = -j * (y1 * (y3 * y4));
	} else {
		tmp = j * (b * (x * -y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -3.5e+15:
		tmp = i * (j * (x * y1))
	elif x <= 1.95e-113:
		tmp = a * (y3 * (z * y1))
	elif x <= 0.0132:
		tmp = -j * (y1 * (y3 * y4))
	else:
		tmp = j * (b * (x * -y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -3.5e+15)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= 1.95e-113)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (x <= 0.0132)
		tmp = Float64(Float64(-j) * Float64(y1 * Float64(y3 * y4)));
	else
		tmp = Float64(j * Float64(b * Float64(x * Float64(-y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -3.5e+15)
		tmp = i * (j * (x * y1));
	elseif (x <= 1.95e-113)
		tmp = a * (y3 * (z * y1));
	elseif (x <= 0.0132)
		tmp = -j * (y1 * (y3 * y4));
	else
		tmp = j * (b * (x * -y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -3.5e+15], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e-113], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0132], N[((-j) * N[(y1 * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.5e15

   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 x around inf 62.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 45.8%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 45.8%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y2 around 0 48.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 48.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -3.5e15 < x < 1.9499999999999999e-113

   1. Initial program 29.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 33.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 33.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 33.7%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 33.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 33.7%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 27.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 27.8%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   8. Simplified 27.8%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   9. Taylor expanded in a around inf 21.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 21.1%

          \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   11. Simplified 21.1%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]

   12. Taylor expanded in y1 around 0 21.1%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 21.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

       2. associate-*r* 22.1%

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   14. Simplified 22.1%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   if 1.9499999999999999e-113 < x < 0.0132

   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 y1 around -inf 42.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 42.8%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 42.8%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 42.8%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 42.8%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 31.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 34.1%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   8. Simplified 34.1%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   9. Taylor expanded in a around 0 27.3%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 27.3%

          \[\leadsto \color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

       2. neg-mul-1 27.3%

          \[\leadsto \color{blue}{\left(-j\right)} \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right) \]

   11. Simplified 27.3%

       \[\leadsto \color{blue}{\left(-j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

   if 0.0132 < x

   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 x around inf 66.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 52.6%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   5. Taylor expanded in i around 0 47.2%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 47.2%

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y0\right)\right)} \]

      2. neg-mul-1 47.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(-b\right)} \cdot \left(x \cdot y0\right)\right) \]

      3. *-commutative 47.2%

         \[\leadsto j \cdot \left(\left(-b\right) \cdot \color{blue}{\left(y0 \cdot x\right)}\right) \]

   7. Simplified 47.2%

      \[\leadsto j \cdot \color{blue}{\left(\left(-b\right) \cdot \left(y0 \cdot x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+15}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 0.0132:\\ \;\;\;\;\left(-j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 22.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -320000000:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-115}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(j \cdot \left(-y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -320000000.0)
   (* i (* j (* x y1)))
   (if (<= x 1.55e-115)
     (* a (* y3 (* z y1)))
     (if (<= x 7.5e-11) (* (* y1 y3) (* j (- y4))) (* j (* b (* x (- y0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -320000000.0) {
		tmp = i * (j * (x * y1));
	} else if (x <= 1.55e-115) {
		tmp = a * (y3 * (z * y1));
	} else if (x <= 7.5e-11) {
		tmp = (y1 * y3) * (j * -y4);
	} else {
		tmp = j * (b * (x * -y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-320000000.0d0)) then
        tmp = i * (j * (x * y1))
    else if (x <= 1.55d-115) then
        tmp = a * (y3 * (z * y1))
    else if (x <= 7.5d-11) then
        tmp = (y1 * y3) * (j * -y4)
    else
        tmp = j * (b * (x * -y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -320000000.0) {
		tmp = i * (j * (x * y1));
	} else if (x <= 1.55e-115) {
		tmp = a * (y3 * (z * y1));
	} else if (x <= 7.5e-11) {
		tmp = (y1 * y3) * (j * -y4);
	} else {
		tmp = j * (b * (x * -y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -320000000.0:
		tmp = i * (j * (x * y1))
	elif x <= 1.55e-115:
		tmp = a * (y3 * (z * y1))
	elif x <= 7.5e-11:
		tmp = (y1 * y3) * (j * -y4)
	else:
		tmp = j * (b * (x * -y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -320000000.0)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= 1.55e-115)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (x <= 7.5e-11)
		tmp = Float64(Float64(y1 * y3) * Float64(j * Float64(-y4)));
	else
		tmp = Float64(j * Float64(b * Float64(x * Float64(-y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -320000000.0)
		tmp = i * (j * (x * y1));
	elseif (x <= 1.55e-115)
		tmp = a * (y3 * (z * y1));
	elseif (x <= 7.5e-11)
		tmp = (y1 * y3) * (j * -y4);
	else
		tmp = j * (b * (x * -y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -320000000.0], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e-115], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-11], N[(N[(y1 * y3), $MachinePrecision] * N[(j * (-y4)), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.2e8

   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 x around inf 62.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 45.8%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 45.8%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y2 around 0 48.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 48.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -3.2e8 < x < 1.55000000000000003e-115

   1. Initial program 29.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 33.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 33.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 33.7%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 33.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 33.7%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 27.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 27.8%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   8. Simplified 27.8%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   9. Taylor expanded in a around inf 21.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 21.1%

          \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   11. Simplified 21.1%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]

   12. Taylor expanded in y1 around 0 21.1%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 21.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

       2. associate-*r* 22.1%

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   14. Simplified 22.1%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   if 1.55000000000000003e-115 < x < 7.5e-11

   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 y1 around -inf 42.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 42.8%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 42.8%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 42.8%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 42.8%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 31.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 34.1%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   8. Simplified 34.1%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   9. Taylor expanded in a around 0 34.2%

      \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 34.2%

          \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-j \cdot y4\right)} \]

       2. distribute-rgt-neg-in 34.2%

          \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(j \cdot \left(-y4\right)\right)} \]

   11. Simplified 34.2%

       \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(j \cdot \left(-y4\right)\right)} \]

   if 7.5e-11 < x

   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 x around inf 66.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 52.6%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   5. Taylor expanded in i around 0 47.2%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 47.2%

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y0\right)\right)} \]

      2. neg-mul-1 47.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(-b\right)} \cdot \left(x \cdot y0\right)\right) \]

      3. *-commutative 47.2%

         \[\leadsto j \cdot \left(\left(-b\right) \cdot \color{blue}{\left(y0 \cdot x\right)}\right) \]

   7. Simplified 47.2%

      \[\leadsto j \cdot \color{blue}{\left(\left(-b\right) \cdot \left(y0 \cdot x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -320000000:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-115}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(j \cdot \left(-y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 25.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -6 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 6.5 \cdot 10^{+182}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(a \cdot \left(-y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -6e-208)
   (* a (* b (- (* x y) (* z t))))
   (if (<= y2 1.35e-54)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= y2 6.5e+182) (* i (* j (* x y1))) (* x (* y1 (* a (- y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -6e-208) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 1.35e-54) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= 6.5e+182) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = x * (y1 * (a * -y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-6d-208)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y2 <= 1.35d-54) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y2 <= 6.5d+182) then
        tmp = i * (j * (x * y1))
    else
        tmp = x * (y1 * (a * -y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -6e-208) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y2 <= 1.35e-54) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= 6.5e+182) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = x * (y1 * (a * -y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -6e-208:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y2 <= 1.35e-54:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y2 <= 6.5e+182:
		tmp = i * (j * (x * y1))
	else:
		tmp = x * (y1 * (a * -y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -6e-208)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y2 <= 1.35e-54)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y2 <= 6.5e+182)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = Float64(x * Float64(y1 * Float64(a * Float64(-y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -6e-208)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y2 <= 1.35e-54)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y2 <= 6.5e+182)
		tmp = i * (j * (x * y1));
	else
		tmp = x * (y1 * (a * -y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -6e-208], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.35e-54], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.5e+182], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y1 * N[(a * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -5.99999999999999972e-208

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 36.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -5.99999999999999972e-208 < y2 < 1.35000000000000013e-54

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y0 around inf 39.6%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 1.35000000000000013e-54 < y2 < 6.4999999999999998e182

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 47.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 38.1%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 38.1%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 38.1%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 38.1%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 38.1%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y2 around 0 36.1%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.1%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 36.1%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if 6.4999999999999998e182 < y2

   1. Initial program 26.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 43.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 52.5%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 52.5%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 52.5%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 52.5%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 52.5%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y1 around 0 52.5%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 52.5%

         \[\leadsto x \cdot \color{blue}{\left(-y1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]

      2. distribute-rgt-neg-out 52.5%

         \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-\left(a \cdot y2 - i \cdot j\right)\right)\right)} \]

   9. Simplified 52.5%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-\left(a \cdot y2 - i \cdot j\right)\right)\right)} \]

   10. Taylor expanded in a around inf 52.5%

       \[\leadsto x \cdot \left(y1 \cdot \left(-\color{blue}{a \cdot y2}\right)\right) \]
   11. Step-by-step derivation

       1. *-commutative 52.5%

          \[\leadsto x \cdot \left(y1 \cdot \left(-\color{blue}{y2 \cdot a}\right)\right) \]

   12. Simplified 52.5%

       \[\leadsto x \cdot \left(y1 \cdot \left(-\color{blue}{y2 \cdot a}\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -6 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 6.5 \cdot 10^{+182}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(a \cdot \left(-y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 21.4% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-133}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(b \cdot \left(-y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -7.5e+20)
   (* i (* j (* x y1)))
   (if (<= x 8e-133) (* a (* y3 (* z y1))) (* j (* x (* b (- y0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -7.5e+20) {
		tmp = i * (j * (x * y1));
	} else if (x <= 8e-133) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = j * (x * (b * -y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-7.5d+20)) then
        tmp = i * (j * (x * y1))
    else if (x <= 8d-133) then
        tmp = a * (y3 * (z * y1))
    else
        tmp = j * (x * (b * -y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -7.5e+20) {
		tmp = i * (j * (x * y1));
	} else if (x <= 8e-133) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = j * (x * (b * -y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -7.5e+20:
		tmp = i * (j * (x * y1))
	elif x <= 8e-133:
		tmp = a * (y3 * (z * y1))
	else:
		tmp = j * (x * (b * -y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -7.5e+20)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= 8e-133)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	else
		tmp = Float64(j * Float64(x * Float64(b * Float64(-y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -7.5e+20)
		tmp = i * (j * (x * y1));
	elseif (x <= 8e-133)
		tmp = a * (y3 * (z * y1));
	else
		tmp = j * (x * (b * -y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -7.5e+20], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-133], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(x * N[(b * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5e20

   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 x around inf 62.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 45.8%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 45.8%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y2 around 0 48.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 48.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -7.5e20 < x < 8.0000000000000005e-133

   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 y1 around -inf 32.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 32.4%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 32.4%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 32.4%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 27.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 27.3%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   8. Simplified 27.3%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   9. Taylor expanded in a around inf 20.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 20.5%

          \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   11. Simplified 20.5%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]

   12. Taylor expanded in y1 around 0 20.5%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 20.5%

          \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

       2. associate-*r* 21.5%

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   14. Simplified 21.5%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   if 8.0000000000000005e-133 < x

   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 x around inf 56.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 42.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   5. Taylor expanded in i around 0 31.8%

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot y0\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 31.8%

         \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(-b \cdot y0\right)}\right) \]

      2. distribute-lft-neg-out 31.8%

         \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(\left(-b\right) \cdot y0\right)}\right) \]

      3. *-commutative 31.8%

         \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(y0 \cdot \left(-b\right)\right)}\right) \]

   7. Simplified 31.8%

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(y0 \cdot \left(-b\right)\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-133}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(b \cdot \left(-y0\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 21.9% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+14}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-132}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -3.3e+14)
   (* i (* j (* x y1)))
   (if (<= x 2.8e-132) (* a (* y3 (* z y1))) (* j (* b (* x (- y0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.3e+14) {
		tmp = i * (j * (x * y1));
	} else if (x <= 2.8e-132) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = j * (b * (x * -y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-3.3d+14)) then
        tmp = i * (j * (x * y1))
    else if (x <= 2.8d-132) then
        tmp = a * (y3 * (z * y1))
    else
        tmp = j * (b * (x * -y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.3e+14) {
		tmp = i * (j * (x * y1));
	} else if (x <= 2.8e-132) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = j * (b * (x * -y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -3.3e+14:
		tmp = i * (j * (x * y1))
	elif x <= 2.8e-132:
		tmp = a * (y3 * (z * y1))
	else:
		tmp = j * (b * (x * -y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -3.3e+14)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= 2.8e-132)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	else
		tmp = Float64(j * Float64(b * Float64(x * Float64(-y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -3.3e+14)
		tmp = i * (j * (x * y1));
	elseif (x <= 2.8e-132)
		tmp = a * (y3 * (z * y1));
	else
		tmp = j * (b * (x * -y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -3.3e+14], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e-132], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.3e14

   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 x around inf 62.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 45.8%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 45.8%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y2 around 0 48.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 48.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -3.3e14 < x < 2.80000000000000002e-132

   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 y1 around -inf 32.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 32.4%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 32.4%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 32.4%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 27.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 27.3%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   8. Simplified 27.3%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   9. Taylor expanded in a around inf 20.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 20.5%

          \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   11. Simplified 20.5%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]

   12. Taylor expanded in y1 around 0 20.5%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 20.5%

          \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

       2. associate-*r* 21.5%

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   14. Simplified 21.5%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   if 2.80000000000000002e-132 < x

   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 x around inf 56.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 42.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   5. Taylor expanded in i around 0 36.4%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.4%

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y0\right)\right)} \]

      2. neg-mul-1 36.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(-b\right)} \cdot \left(x \cdot y0\right)\right) \]

      3. *-commutative 36.4%

         \[\leadsto j \cdot \left(\left(-b\right) \cdot \color{blue}{\left(y0 \cdot x\right)}\right) \]

   7. Simplified 36.4%

      \[\leadsto j \cdot \color{blue}{\left(\left(-b\right) \cdot \left(y0 \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+14}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-132}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 22.9% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -2.9 \cdot 10^{+28} \lor \neg \left(y1 \leq 2.6\right):\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y1 -2.9e+28) (not (<= y1 2.6)))
   (* a (* y3 (* z y1)))
   (* a (* (* x y) b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -2.9e+28) || !(y1 <= 2.6)) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y1 <= (-2.9d+28)) .or. (.not. (y1 <= 2.6d0))) then
        tmp = a * (y3 * (z * y1))
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -2.9e+28) || !(y1 <= 2.6)) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y1 <= -2.9e+28) or not (y1 <= 2.6):
		tmp = a * (y3 * (z * y1))
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y1 <= -2.9e+28) || !(y1 <= 2.6))
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y1 <= -2.9e+28) || ~((y1 <= 2.6)))
		tmp = a * (y3 * (z * y1));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y1, -2.9e+28], N[Not[LessEqual[y1, 2.6]], $MachinePrecision]], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y1 < -2.9000000000000001e28 or 2.60000000000000009 < y1

   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 y1 around -inf 53.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 53.8%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 53.8%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 53.8%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 53.8%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 38.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.0%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   8. Simplified 42.0%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   9. Taylor expanded in a around inf 27.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 27.8%

          \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   11. Simplified 27.8%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]

   12. Taylor expanded in y1 around 0 27.8%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 27.8%

          \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

       2. associate-*r* 32.1%

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   14. Simplified 32.1%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   if -2.9000000000000001e28 < y1 < 2.60000000000000009

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 42.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 33.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 26.5%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 26.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

      2. *-commutative 26.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   7. Simplified 26.5%

      \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.9 \cdot 10^{+28} \lor \neg \left(y1 \leq 2.6\right):\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 22.4% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -1.7e+18)
   (* i (* j (* x y1)))
   (if (<= x 7e-51) (* a (* y3 (* z y1))) (* a (* (* x y) b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.7e+18) {
		tmp = i * (j * (x * y1));
	} else if (x <= 7e-51) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-1.7d+18)) then
        tmp = i * (j * (x * y1))
    else if (x <= 7d-51) then
        tmp = a * (y3 * (z * y1))
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.7e+18) {
		tmp = i * (j * (x * y1));
	} else if (x <= 7e-51) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -1.7e+18:
		tmp = i * (j * (x * y1))
	elif x <= 7e-51:
		tmp = a * (y3 * (z * y1))
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -1.7e+18)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= 7e-51)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -1.7e+18)
		tmp = i * (j * (x * y1));
	elseif (x <= 7e-51)
		tmp = a * (y3 * (z * y1));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -1.7e+18], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-51], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7e18

   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 x around inf 62.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 45.8%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot y2 - i \cdot j\right)\right)}\right) \]

      2. *-commutative 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot a} - i \cdot j\right)\right)\right) \]

      3. *-commutative 45.8%

         \[\leadsto x \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - \color{blue}{j \cdot i}\right)\right)\right) \]

   6. Simplified 45.8%

      \[\leadsto x \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot a - j \cdot i\right)\right)\right)} \]

   7. Taylor expanded in y2 around 0 48.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 48.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -1.7e18 < x < 6.9999999999999995e-51

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 35.5%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 35.5%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 35.5%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 35.5%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 27.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 28.8%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   8. Simplified 28.8%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   9. Taylor expanded in a around inf 19.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 19.8%

          \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   11. Simplified 19.8%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]

   12. Taylor expanded in y1 around 0 19.8%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 19.8%

          \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

       2. associate-*r* 20.6%

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   14. Simplified 20.6%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   if 6.9999999999999995e-51 < x

   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 b around inf 47.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 41.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 36.7%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

      2. *-commutative 36.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \]

   7. Simplified 36.7%

      \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 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 29.8%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in y1 around -inf 39.6%

   \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
4. Step-by-step derivation

   1. mul-1-neg 39.6%

      \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   2. *-commutative 39.6%

      \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

   3. distribute-rgt-neg-in 39.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

5. Simplified 39.6%

   \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

6. Taylor expanded in y3 around -inf 30.0%

   \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
7. Step-by-step derivation

   1. associate-*r* 29.5%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

8. Simplified 29.5%

   \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

9. Taylor expanded in a around inf 18.5%

   \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
10. Step-by-step derivation

    1. *-commutative 18.5%

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

11. Simplified 18.5%

    \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]

12. Final simplification 18.5%

    \[\leadsto a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \]
13. Add Preprocessing

Alternative 34: 17.3% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y3 (* z y1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y3 * (z * y1));
}

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 * (y3 * (z * y1))
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 * (y3 * (z * y1));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y3 * (z * y1))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y3 * Float64(z * y1)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y3 * (z * y1));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 29.8%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in y1 around -inf 39.6%

   \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
4. Step-by-step derivation

   1. mul-1-neg 39.6%

      \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   2. *-commutative 39.6%

      \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

   3. distribute-rgt-neg-in 39.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

5. Simplified 39.6%

   \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

6. Taylor expanded in y3 around -inf 30.0%

   \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
7. Step-by-step derivation

   1. associate-*r* 29.5%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

8. Simplified 29.5%

   \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

9. Taylor expanded in a around inf 18.5%

   \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
10. Step-by-step derivation

    1. *-commutative 18.5%

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

11. Simplified 18.5%

    \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]

12. Taylor expanded in y1 around 0 18.5%

    \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
13. Step-by-step derivation

    1. *-commutative 18.5%

       \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

    2. associate-*r* 19.2%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

14. Simplified 19.2%

    \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

15. Final simplification 19.2%

    \[\leadsto a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right) \]
16. Add Preprocessing

Developer target: 27.3% 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 2024020 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))