Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.5% → 41.0%

Time: 58.3s

Alternatives: 35

Speedup: 4.5×

• 88.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 41.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(\left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ t_2 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_3 := t \cdot j - y \cdot k\\ t_4 := x \cdot y - z \cdot t\\ t_5 := a \cdot \left(\left(b \cdot t\_4 + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_6 := b \cdot \left(\left(a \cdot t\_4 + y4 \cdot t\_3\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{+140}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+52}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;a \leq -4 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-217}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-179}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-131}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+126}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_3 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y
          (+
           (+ (* x (- (* a b) (* c i))) (* k (- (* i y5) (* b y4))))
           (* y3 (- (* c y4) (* a y5))))))
        (t_2
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4))))))
        (t_3 (- (* t j) (* y k)))
        (t_4 (- (* x y) (* z t)))
        (t_5
         (*
          a
          (+
           (+ (* b t_4) (* y1 (- (* z y3) (* x y2))))
           (* y5 (- (* t y2) (* y y3))))))
        (t_6 (* b (+ (+ (* a t_4) (* y4 t_3)) (* y0 (- (* z k) (* x j)))))))
   (if (<= a -7.6e+140)
     t_5
     (if (<= a -3.3e+98)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= a -3.5e+52)
         t_6
         (if (<= a -4e+21)
           t_1
           (if (<= a -2.1e-22)
             t_2
             (if (<= a -4e-83)
               t_1
               (if (<= a -4.6e-217)
                 t_2
                 (if (<= a 8.6e-179)
                   t_6
                   (if (<= a 1.85e-131)
                     (*
                      y1
                      (-
                       (* i (- (* x j) (* z k)))
                       (+
                        (* a (- (* x y2) (* z y3)))
                        (* y4 (- (* j y3) (* k y2))))))
                     (if (<= a 1.85e+25)
                       (*
                        j
                        (+
                         (+
                          (* t (- (* b y4) (* i y5)))
                          (* y3 (- (* y0 y5) (* y1 y4))))
                         (* x (- (* i y1) (* b y0)))))
                       (if (<= a 7.2e+126)
                         (*
                          y4
                          (+
                           (+ (* b t_3) (* y1 (- (* k y2) (* j y3))))
                           (* c (- (* y y3) (* t y2)))))
                         t_5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))));
	double t_2 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double t_3 = (t * j) - (y * k);
	double t_4 = (x * y) - (z * t);
	double t_5 = a * (((b * t_4) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	double t_6 = b * (((a * t_4) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (a <= -7.6e+140) {
		tmp = t_5;
	} else if (a <= -3.3e+98) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -3.5e+52) {
		tmp = t_6;
	} else if (a <= -4e+21) {
		tmp = t_1;
	} else if (a <= -2.1e-22) {
		tmp = t_2;
	} else if (a <= -4e-83) {
		tmp = t_1;
	} else if (a <= -4.6e-217) {
		tmp = t_2;
	} else if (a <= 8.6e-179) {
		tmp = t_6;
	} else if (a <= 1.85e-131) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * ((x * y2) - (z * y3))) + (y4 * ((j * y3) - (k * y2)))));
	} else if (a <= 1.85e+25) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (a <= 7.2e+126) {
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))))
    t_2 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    t_3 = (t * j) - (y * k)
    t_4 = (x * y) - (z * t)
    t_5 = a * (((b * t_4) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))))
    t_6 = b * (((a * t_4) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
    if (a <= (-7.6d+140)) then
        tmp = t_5
    else if (a <= (-3.3d+98)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (a <= (-3.5d+52)) then
        tmp = t_6
    else if (a <= (-4d+21)) then
        tmp = t_1
    else if (a <= (-2.1d-22)) then
        tmp = t_2
    else if (a <= (-4d-83)) then
        tmp = t_1
    else if (a <= (-4.6d-217)) then
        tmp = t_2
    else if (a <= 8.6d-179) then
        tmp = t_6
    else if (a <= 1.85d-131) then
        tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * ((x * y2) - (z * y3))) + (y4 * ((j * y3) - (k * y2)))))
    else if (a <= 1.85d+25) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else if (a <= 7.2d+126) then
        tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))));
	double t_2 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double t_3 = (t * j) - (y * k);
	double t_4 = (x * y) - (z * t);
	double t_5 = a * (((b * t_4) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	double t_6 = b * (((a * t_4) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (a <= -7.6e+140) {
		tmp = t_5;
	} else if (a <= -3.3e+98) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -3.5e+52) {
		tmp = t_6;
	} else if (a <= -4e+21) {
		tmp = t_1;
	} else if (a <= -2.1e-22) {
		tmp = t_2;
	} else if (a <= -4e-83) {
		tmp = t_1;
	} else if (a <= -4.6e-217) {
		tmp = t_2;
	} else if (a <= 8.6e-179) {
		tmp = t_6;
	} else if (a <= 1.85e-131) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * ((x * y2) - (z * y3))) + (y4 * ((j * y3) - (k * y2)))));
	} else if (a <= 1.85e+25) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (a <= 7.2e+126) {
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))))
	t_2 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	t_3 = (t * j) - (y * k)
	t_4 = (x * y) - (z * t)
	t_5 = a * (((b * t_4) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))))
	t_6 = b * (((a * t_4) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if a <= -7.6e+140:
		tmp = t_5
	elif a <= -3.3e+98:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif a <= -3.5e+52:
		tmp = t_6
	elif a <= -4e+21:
		tmp = t_1
	elif a <= -2.1e-22:
		tmp = t_2
	elif a <= -4e-83:
		tmp = t_1
	elif a <= -4.6e-217:
		tmp = t_2
	elif a <= 8.6e-179:
		tmp = t_6
	elif a <= 1.85e-131:
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * ((x * y2) - (z * y3))) + (y4 * ((j * y3) - (k * y2)))))
	elif a <= 1.85e+25:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	elif a <= 7.2e+126:
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(Float64(Float64(x * Float64(Float64(a * b) - Float64(c * i))) + Float64(k * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))))
	t_2 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	t_4 = Float64(Float64(x * y) - Float64(z * t))
	t_5 = Float64(a * Float64(Float64(Float64(b * t_4) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))))
	t_6 = Float64(b * Float64(Float64(Float64(a * t_4) + Float64(y4 * t_3)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (a <= -7.6e+140)
		tmp = t_5;
	elseif (a <= -3.3e+98)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (a <= -3.5e+52)
		tmp = t_6;
	elseif (a <= -4e+21)
		tmp = t_1;
	elseif (a <= -2.1e-22)
		tmp = t_2;
	elseif (a <= -4e-83)
		tmp = t_1;
	elseif (a <= -4.6e-217)
		tmp = t_2;
	elseif (a <= 8.6e-179)
		tmp = t_6;
	elseif (a <= 1.85e-131)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(a * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (a <= 1.85e+25)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (a <= 7.2e+126)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_3) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))));
	t_2 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	t_3 = (t * j) - (y * k);
	t_4 = (x * y) - (z * t);
	t_5 = a * (((b * t_4) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	t_6 = b * (((a * t_4) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (a <= -7.6e+140)
		tmp = t_5;
	elseif (a <= -3.3e+98)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (a <= -3.5e+52)
		tmp = t_6;
	elseif (a <= -4e+21)
		tmp = t_1;
	elseif (a <= -2.1e-22)
		tmp = t_2;
	elseif (a <= -4e-83)
		tmp = t_1;
	elseif (a <= -4.6e-217)
		tmp = t_2;
	elseif (a <= 8.6e-179)
		tmp = t_6;
	elseif (a <= 1.85e-131)
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * ((x * y2) - (z * y3))) + (y4 * ((j * y3) - (k * y2)))));
	elseif (a <= 1.85e+25)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	elseif (a <= 7.2e+126)
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(N[(N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(a * N[(N[(N[(b * t$95$4), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(b * N[(N[(N[(a * t$95$4), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.6e+140], t$95$5, If[LessEqual[a, -3.3e+98], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.5e+52], t$95$6, If[LessEqual[a, -4e+21], t$95$1, If[LessEqual[a, -2.1e-22], t$95$2, If[LessEqual[a, -4e-83], t$95$1, If[LessEqual[a, -4.6e-217], t$95$2, If[LessEqual[a, 8.6e-179], t$95$6, If[LessEqual[a, 1.85e-131], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+25], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+126], N[(y4 * N[(N[(N[(b * t$95$3), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -7.6000000000000002e140 or 7.2000000000000001e126 < a

   1. Initial program 22.0%

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

   3. Taylor expanded in a around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

      4. *-commutative 74.2%

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

      5. *-commutative 74.2%

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

      6. *-commutative 74.2%

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

      7. mul-1-neg 74.2%

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

      8. *-commutative 74.2%

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

   5. Simplified 74.2%

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

   if -7.6000000000000002e140 < a < -3.30000000000000028e98

   1. Initial program 19.5%

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

   3. Taylor expanded in b around inf 19.0%

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

   4. Taylor expanded in x around inf 62.9%

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

   if -3.30000000000000028e98 < a < -3.5e52 or -4.6000000000000001e-217 < a < 8.60000000000000052e-179

   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 b around inf 53.4%

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

   if -3.5e52 < a < -4e21 or -2.10000000000000008e-22 < a < -4.0000000000000001e-83

   1. Initial program 21.0%

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

   3. Taylor expanded in y around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. mul-1-neg 76.5%

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

      3. unsub-neg 76.5%

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

      4. *-commutative 76.5%

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

      5. *-commutative 76.5%

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

      6. mul-1-neg 76.5%

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

   5. Simplified 76.5%

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

   if -4e21 < a < -2.10000000000000008e-22 or -4.0000000000000001e-83 < a < -4.6000000000000001e-217

   1. Initial program 21.5%

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

   3. Taylor expanded in y2 around inf 68.0%

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

   if 8.60000000000000052e-179 < a < 1.8500000000000001e-131

   1. Initial program 16.0%

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

   3. Taylor expanded in y1 around -inf 62.2%

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

      1. associate-*r* 62.2%

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

      2. neg-mul-1 62.2%

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

      3. +-commutative 62.2%

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

      4. mul-1-neg 62.2%

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

      5. unsub-neg 62.2%

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

      6. *-commutative 62.2%

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

      7. *-commutative 62.2%

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

      8. *-commutative 62.2%

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

      9. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   if 1.8500000000000001e-131 < a < 1.8499999999999999e25

   1. Initial program 24.2%

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

   3. Taylor expanded in j around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   if 1.8499999999999999e25 < a < 7.2000000000000001e126

   1. Initial program 58.2%

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

   3. Taylor expanded in y4 around inf 75.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+140}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(\left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;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}\;a \leq -4 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(\left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-217}:\\ \;\;\;\;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}\;a \leq 8.6 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-131}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+126}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 53.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(a * N[(N[(N[(b * t$95$2), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$1), $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 91.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf 41.6%

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

      1. +-commutative 41.6%

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

      2. mul-1-neg 41.6%

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

      3. unsub-neg 41.6%

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

      4. *-commutative 41.6%

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

      5. *-commutative 41.6%

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

      6. *-commutative 41.6%

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

      7. mul-1-neg 41.6%

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

      8. *-commutative 41.6%

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

   5. Simplified 41.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.9%

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

Alternative 3: 39.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t\_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := a \cdot y5 - c \cdot y4\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := y \cdot y3 - t \cdot y2\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+187}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+22}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - \left(i \cdot y1 + \frac{y5 \cdot \left(y0 \cdot y2 - y \cdot i\right)}{z}\right)\right)\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-66}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq -1.38 \cdot 10^{-211}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t\_5\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-246}:\\ \;\;\;\;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)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-284}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-100}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t\_4\right) + t \cdot t\_3\right)\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{-42}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot t\_5\right)\\ \mathbf{elif}\;b \leq 10^{+172}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot t\_3\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 (- (* t j) (* y k)))
        (t_2
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 t_1))
           (* y0 (- (* z k) (* x j))))))
        (t_3 (- (* a y5) (* c y4)))
        (t_4 (- (* c y0) (* a y1)))
        (t_5 (- (* y y3) (* t y2))))
   (if (<= b -6.8e+187)
     t_2
     (if (<= b -2.3e+106)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= b -1.45e+22)
         (*
          k
          (* z (- (* b y0) (+ (* i y1) (/ (* y5 (- (* y0 y2) (* y i))) z)))))
         (if (<= b -1.12e-66)
           (* a (* y1 (- (* z y3) (* x y2))))
           (if (<= b -1.38e-211)
             (* y4 (+ (+ (* b t_1) (* y1 (- (* k y2) (* j y3)))) (* c t_5)))
             (if (<= b -2.2e-246)
               (*
                x
                (+
                 (+ (* y (- (* a b) (* c i))) (* y2 t_4))
                 (* j (- (* i y1) (* b y0)))))
               (if (<= b 1.55e-284)
                 (* k (* y5 (- (* y i) (* y0 y2))))
                 (if (<= b 2.15e-278)
                   (* x (* c (* y (- i))))
                   (if (<= b 8.2e-100)
                     (*
                      y2
                      (+
                       (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_4))
                       (* t t_3)))
                     (if (<= b 4.9e-42)
                       (*
                        c
                        (+
                         (+
                          (* y0 (- (* x y2) (* z y3)))
                          (* i (- (* z t) (* x y))))
                         (* y4 t_5)))
                       (if (<= b 1e+172)
                         (*
                          t
                          (+
                           (+
                            (* j (- (* b y4) (* i y5)))
                            (* z (- (* c i) (* a b))))
                           (* y2 t_3)))
                         t_2)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	double t_3 = (a * y5) - (c * y4);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (y * y3) - (t * y2);
	double tmp;
	if (b <= -6.8e+187) {
		tmp = t_2;
	} else if (b <= -2.3e+106) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= -1.45e+22) {
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	} else if (b <= -1.12e-66) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (b <= -1.38e-211) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5));
	} else if (b <= -2.2e-246) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	} else if (b <= 1.55e-284) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (b <= 2.15e-278) {
		tmp = x * (c * (y * -i));
	} else if (b <= 8.2e-100) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * t_3));
	} else if (b <= 4.9e-42) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_5));
	} else if (b <= 1e+172) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_3));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
    t_3 = (a * y5) - (c * y4)
    t_4 = (c * y0) - (a * y1)
    t_5 = (y * y3) - (t * y2)
    if (b <= (-6.8d+187)) then
        tmp = t_2
    else if (b <= (-2.3d+106)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (b <= (-1.45d+22)) then
        tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))))
    else if (b <= (-1.12d-66)) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (b <= (-1.38d-211)) then
        tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5))
    else if (b <= (-2.2d-246)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))))
    else if (b <= 1.55d-284) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (b <= 2.15d-278) then
        tmp = x * (c * (y * -i))
    else if (b <= 8.2d-100) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * t_3))
    else if (b <= 4.9d-42) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_5))
    else if (b <= 1d+172) then
        tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_3))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	double t_3 = (a * y5) - (c * y4);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (y * y3) - (t * y2);
	double tmp;
	if (b <= -6.8e+187) {
		tmp = t_2;
	} else if (b <= -2.3e+106) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= -1.45e+22) {
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	} else if (b <= -1.12e-66) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (b <= -1.38e-211) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5));
	} else if (b <= -2.2e-246) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	} else if (b <= 1.55e-284) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (b <= 2.15e-278) {
		tmp = x * (c * (y * -i));
	} else if (b <= 8.2e-100) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * t_3));
	} else if (b <= 4.9e-42) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_5));
	} else if (b <= 1e+172) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_3));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
	t_3 = (a * y5) - (c * y4)
	t_4 = (c * y0) - (a * y1)
	t_5 = (y * y3) - (t * y2)
	tmp = 0
	if b <= -6.8e+187:
		tmp = t_2
	elif b <= -2.3e+106:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif b <= -1.45e+22:
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))))
	elif b <= -1.12e-66:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif b <= -1.38e-211:
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5))
	elif b <= -2.2e-246:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))))
	elif b <= 1.55e-284:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif b <= 2.15e-278:
		tmp = x * (c * (y * -i))
	elif b <= 8.2e-100:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * t_3))
	elif b <= 4.9e-42:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_5))
	elif b <= 1e+172:
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_3))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_3 = Float64(Float64(a * y5) - Float64(c * y4))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(Float64(y * y3) - Float64(t * y2))
	tmp = 0.0
	if (b <= -6.8e+187)
		tmp = t_2;
	elseif (b <= -2.3e+106)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (b <= -1.45e+22)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(Float64(i * y1) + Float64(Float64(y5 * Float64(Float64(y0 * y2) - Float64(y * i))) / z)))));
	elseif (b <= -1.12e-66)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (b <= -1.38e-211)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_5)));
	elseif (b <= -2.2e-246)
		tmp = 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)))));
	elseif (b <= 1.55e-284)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (b <= 2.15e-278)
		tmp = Float64(x * Float64(c * Float64(y * Float64(-i))));
	elseif (b <= 8.2e-100)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_4)) + Float64(t * t_3)));
	elseif (b <= 4.9e-42)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * t_5)));
	elseif (b <= 1e+172)
		tmp = Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * t_3)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	t_3 = (a * y5) - (c * y4);
	t_4 = (c * y0) - (a * y1);
	t_5 = (y * y3) - (t * y2);
	tmp = 0.0;
	if (b <= -6.8e+187)
		tmp = t_2;
	elseif (b <= -2.3e+106)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (b <= -1.45e+22)
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	elseif (b <= -1.12e-66)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (b <= -1.38e-211)
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5));
	elseif (b <= -2.2e-246)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	elseif (b <= 1.55e-284)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (b <= 2.15e-278)
		tmp = x * (c * (y * -i));
	elseif (b <= 8.2e-100)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_4)) + (t * t_3));
	elseif (b <= 4.9e-42)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_5));
	elseif (b <= 1e+172)
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_3));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e+187], t$95$2, If[LessEqual[b, -2.3e+106], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.45e+22], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(N[(i * y1), $MachinePrecision] + N[(N[(y5 * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.12e-66], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.38e-211], N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.2e-246], 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], If[LessEqual[b, 1.55e-284], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e-278], N[(x * N[(c * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e-100], 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$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.9e-42], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+172], N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if b < -6.7999999999999999e187 or 1.0000000000000001e172 < b

   1. Initial program 26.3%

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

   3. Taylor expanded in b around inf 69.1%

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

   if -6.7999999999999999e187 < b < -2.3000000000000002e106

   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 a around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

      5. *-commutative 62.5%

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

      6. *-commutative 62.5%

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

      7. mul-1-neg 62.5%

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

      8. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in z around -inf 81.7%

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

      1. mul-1-neg 81.7%

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

   8. Simplified 81.7%

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

   if -2.3000000000000002e106 < b < -1.45e22

   1. Initial program 7.7%

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

   3. Taylor expanded in k around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. *-commutative 54.4%

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

      5. associate-*r* 54.4%

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

      6. neg-mul-1 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in z around -inf 69.2%

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

      1. associate-*r* 69.2%

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

      2. neg-mul-1 69.2%

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

      3. +-commutative 69.2%

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

      4. mul-1-neg 69.2%

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

      5. unsub-neg 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in y5 around -inf 77.4%

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

   if -1.45e22 < b < -1.12000000000000004e-66

   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 a around inf 78.8%

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

      1. +-commutative 78.8%

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

      2. mul-1-neg 78.8%

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

      3. unsub-neg 78.8%

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

      4. *-commutative 78.8%

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

      5. *-commutative 78.8%

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

      6. *-commutative 78.8%

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

      7. mul-1-neg 78.8%

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

      8. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in y1 around inf 65.4%

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

   if -1.12000000000000004e-66 < b < -1.38000000000000006e-211

   1. Initial program 22.7%

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

   3. Taylor expanded in y4 around inf 67.2%

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

   if -1.38000000000000006e-211 < b < -2.19999999999999998e-246

   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 84.0%

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

   if -2.19999999999999998e-246 < b < 1.5499999999999999e-284

   1. Initial program 21.3%

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

   3. Taylor expanded in k around inf 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

      4. *-commutative 50.5%

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

      5. associate-*r* 50.5%

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

      6. neg-mul-1 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in y5 around -inf 57.5%

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

      1. associate-*r* 57.5%

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

      2. neg-mul-1 57.5%

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

   8. Simplified 57.5%

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

   if 1.5499999999999999e-284 < b < 2.15e-278

   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 x around inf 50.6%

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

   4. Taylor expanded in y around inf 75.6%

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

   5. Taylor expanded in a around 0 75.6%

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

      1. mul-1-neg 75.6%

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

   7. Simplified 75.6%

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

   if 2.15e-278 < b < 8.1999999999999998e-100

   1. Initial program 26.0%

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

   3. Taylor expanded in y2 around inf 47.2%

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

   if 8.1999999999999998e-100 < b < 4.9e-42

   1. Initial program 36.0%

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

   3. Taylor expanded in c around inf 76.8%

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

      1. +-commutative 76.8%

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

      2. mul-1-neg 76.8%

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

      3. unsub-neg 76.8%

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

      4. *-commutative 76.8%

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

      5. *-commutative 76.8%

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

      6. *-commutative 76.8%

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

      7. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   if 4.9e-42 < b < 1.0000000000000001e172

   1. Initial program 32.7%

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

   3. Taylor expanded in t around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

   5. Simplified 47.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+187}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+22}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - \left(i \cdot y1 + \frac{y5 \cdot \left(y0 \cdot y2 - y \cdot i\right)}{z}\right)\right)\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-66}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq -1.38 \cdot 10^{-211}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-246}:\\ \;\;\;\;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}\;b \leq 1.55 \cdot 10^{-284}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-100}:\\ \;\;\;\;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}\;b \leq 4.9 \cdot 10^{-42}:\\ \;\;\;\;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}\;b \leq 10^{+172}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := x \cdot y - z \cdot t\\ t_4 := a \cdot \left(\left(b \cdot t\_3 + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_5 := y4 \cdot \left(\left(b \cdot t\_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t\_2\right)\\ \mathbf{if}\;y5 \leq -1.3 \cdot 10^{+246}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -6.8 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -2.9 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_3 + y4 \cdot t\_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1.7 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -4.4 \cdot 10^{-69}:\\ \;\;\;\;b \cdot \left(y \cdot \left(y4 \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -8.6 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot t\_2\right)\\ \mathbf{elif}\;y5 \leq -1 \cdot 10^{-177}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y5 \leq -2.5 \cdot 10^{-229}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y5 \leq 3.2 \cdot 10^{-212}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{+127}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (- (* x y) (* z t)))
        (t_4
         (*
          a
          (+
           (+ (* b t_3) (* y1 (- (* z y3) (* x y2))))
           (* y5 (- (* t y2) (* y y3))))))
        (t_5 (* y4 (+ (+ (* b t_1) (* y1 (- (* k y2) (* j y3)))) (* c t_2)))))
   (if (<= y5 -1.3e+246)
     (* a (* y (- (* x b) (* y3 y5))))
     (if (<= y5 -6.8e+135)
       (*
        t
        (+
         (+ (* j (- (* b y4) (* i y5))) (* z (- (* c i) (* a b))))
         (* y2 (- (* a y5) (* c y4)))))
       (if (<= y5 -2.9e+53)
         (* b (+ (+ (* a t_3) (* y4 t_1)) (* y0 (- (* z k) (* x j)))))
         (if (<= y5 -1.7e-55)
           (* j (* x (- (* i y1) (* b y0))))
           (if (<= y5 -4.4e-69)
             (* b (* y (* y4 (- k))))
             (if (<= y5 -8.6e-125)
               (*
                c
                (+
                 (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
                 (* y4 t_2)))
               (if (<= y5 -1e-177)
                 t_5
                 (if (<= y5 -2.5e-229)
                   t_4
                   (if (<= y5 3.2e-212)
                     t_5
                     (if (<= y5 2.7e+127)
                       t_4
                       (* k (* y5 (- (* y i) (* y0 y2))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (x * y) - (z * t);
	double t_4 = a * (((b * t_3) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	double t_5 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double tmp;
	if (y5 <= -1.3e+246) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y5 <= -6.8e+135) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y5 <= -2.9e+53) {
		tmp = b * (((a * t_3) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -1.7e-55) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y5 <= -4.4e-69) {
		tmp = b * (y * (y4 * -k));
	} else if (y5 <= -8.6e-125) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2));
	} else if (y5 <= -1e-177) {
		tmp = t_5;
	} else if (y5 <= -2.5e-229) {
		tmp = t_4;
	} else if (y5 <= 3.2e-212) {
		tmp = t_5;
	} else if (y5 <= 2.7e+127) {
		tmp = t_4;
	} else {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = (y * y3) - (t * y2)
    t_3 = (x * y) - (z * t)
    t_4 = a * (((b * t_3) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))))
    t_5 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
    if (y5 <= (-1.3d+246)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y5 <= (-6.8d+135)) then
        tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
    else if (y5 <= (-2.9d+53)) then
        tmp = b * (((a * t_3) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= (-1.7d-55)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y5 <= (-4.4d-69)) then
        tmp = b * (y * (y4 * -k))
    else if (y5 <= (-8.6d-125)) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2))
    else if (y5 <= (-1d-177)) then
        tmp = t_5
    else if (y5 <= (-2.5d-229)) then
        tmp = t_4
    else if (y5 <= 3.2d-212) then
        tmp = t_5
    else if (y5 <= 2.7d+127) then
        tmp = t_4
    else
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (x * y) - (z * t);
	double t_4 = a * (((b * t_3) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	double t_5 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double tmp;
	if (y5 <= -1.3e+246) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y5 <= -6.8e+135) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y5 <= -2.9e+53) {
		tmp = b * (((a * t_3) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -1.7e-55) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y5 <= -4.4e-69) {
		tmp = b * (y * (y4 * -k));
	} else if (y5 <= -8.6e-125) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2));
	} else if (y5 <= -1e-177) {
		tmp = t_5;
	} else if (y5 <= -2.5e-229) {
		tmp = t_4;
	} else if (y5 <= 3.2e-212) {
		tmp = t_5;
	} else if (y5 <= 2.7e+127) {
		tmp = t_4;
	} else {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = (y * y3) - (t * y2)
	t_3 = (x * y) - (z * t)
	t_4 = a * (((b * t_3) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))))
	t_5 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
	tmp = 0
	if y5 <= -1.3e+246:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y5 <= -6.8e+135:
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
	elif y5 <= -2.9e+53:
		tmp = b * (((a * t_3) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
	elif y5 <= -1.7e-55:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y5 <= -4.4e-69:
		tmp = b * (y * (y4 * -k))
	elif y5 <= -8.6e-125:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2))
	elif y5 <= -1e-177:
		tmp = t_5
	elif y5 <= -2.5e-229:
		tmp = t_4
	elif y5 <= 3.2e-212:
		tmp = t_5
	elif y5 <= 2.7e+127:
		tmp = t_4
	else:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	t_4 = Float64(a * Float64(Float64(Float64(b * t_3) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_2)))
	tmp = 0.0
	if (y5 <= -1.3e+246)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y5 <= -6.8e+135)
		tmp = Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y5 <= -2.9e+53)
		tmp = Float64(b * Float64(Float64(Float64(a * t_3) + Float64(y4 * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= -1.7e-55)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y5 <= -4.4e-69)
		tmp = Float64(b * Float64(y * Float64(y4 * Float64(-k))));
	elseif (y5 <= -8.6e-125)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * t_2)));
	elseif (y5 <= -1e-177)
		tmp = t_5;
	elseif (y5 <= -2.5e-229)
		tmp = t_4;
	elseif (y5 <= 3.2e-212)
		tmp = t_5;
	elseif (y5 <= 2.7e+127)
		tmp = t_4;
	else
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = (y * y3) - (t * y2);
	t_3 = (x * y) - (z * t);
	t_4 = a * (((b * t_3) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	t_5 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	tmp = 0.0;
	if (y5 <= -1.3e+246)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y5 <= -6.8e+135)
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (y5 <= -2.9e+53)
		tmp = b * (((a * t_3) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= -1.7e-55)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y5 <= -4.4e-69)
		tmp = b * (y * (y4 * -k));
	elseif (y5 <= -8.6e-125)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2));
	elseif (y5 <= -1e-177)
		tmp = t_5;
	elseif (y5 <= -2.5e-229)
		tmp = t_4;
	elseif (y5 <= 3.2e-212)
		tmp = t_5;
	elseif (y5 <= 2.7e+127)
		tmp = t_4;
	else
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(N[(b * t$95$3), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.3e+246], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6.8e+135], N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.9e+53], N[(b * N[(N[(N[(a * t$95$3), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.7e-55], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.4e-69], N[(b * N[(y * N[(y4 * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8.6e-125], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1e-177], t$95$5, If[LessEqual[y5, -2.5e-229], t$95$4, If[LessEqual[y5, 3.2e-212], t$95$5, If[LessEqual[y5, 2.7e+127], t$95$4, N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y5 < -1.30000000000000007e246

   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 a around inf 41.7%

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

      1. +-commutative 41.7%

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

      2. mul-1-neg 41.7%

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

      3. unsub-neg 41.7%

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

      4. *-commutative 41.7%

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

      5. *-commutative 41.7%

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

      6. *-commutative 41.7%

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

      7. mul-1-neg 41.7%

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

      8. *-commutative 41.7%

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

   5. Simplified 41.7%

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

   6. Taylor expanded in y around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. mul-1-neg 66.7%

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

      3. unsub-neg 66.7%

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

   8. Simplified 66.7%

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

   if -1.30000000000000007e246 < y5 < -6.80000000000000019e135

   1. Initial program 35.3%

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

   3. Taylor expanded in t around inf 80.1%

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

      1. +-commutative 80.1%

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

      2. mul-1-neg 80.1%

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

      3. unsub-neg 80.1%

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

      4. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   if -6.80000000000000019e135 < y5 < -2.9000000000000002e53

   1. Initial program 28.6%

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

   3. Taylor expanded in b around inf 85.9%

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

   if -2.9000000000000002e53 < y5 < -1.69999999999999986e-55

   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 x around inf 54.3%

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

   4. Taylor expanded in j around inf 54.8%

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

   if -1.69999999999999986e-55 < y5 < -4.4e-69

   1. Initial program 0.0%

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

   3. Taylor expanded in b around inf 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in a around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-lft-neg-in 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -4.4e-69 < y5 < -8.6000000000000004e-125

   1. Initial program 26.6%

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

   3. Taylor expanded in c around inf 67.0%

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

      1. +-commutative 67.0%

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

      2. mul-1-neg 67.0%

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

      3. unsub-neg 67.0%

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

      4. *-commutative 67.0%

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

      5. *-commutative 67.0%

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

      6. *-commutative 67.0%

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

      7. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   if -8.6000000000000004e-125 < y5 < -9.99999999999999952e-178 or -2.50000000000000008e-229 < y5 < 3.1999999999999999e-212

   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 70.0%

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

   if -9.99999999999999952e-178 < y5 < -2.50000000000000008e-229 or 3.1999999999999999e-212 < y5 < 2.7000000000000002e127

   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 a around inf 56.0%

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

      1. +-commutative 56.0%

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

      2. mul-1-neg 56.0%

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

      3. unsub-neg 56.0%

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

      4. *-commutative 56.0%

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

      5. *-commutative 56.0%

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

      6. *-commutative 56.0%

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

      7. mul-1-neg 56.0%

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

      8. *-commutative 56.0%

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

   5. Simplified 56.0%

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

   if 2.7000000000000002e127 < y5

   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 k around inf 38.9%

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

      1. +-commutative 38.9%

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

      2. mul-1-neg 38.9%

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

      3. unsub-neg 38.9%

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

      4. *-commutative 38.9%

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

      5. associate-*r* 38.9%

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

      6. neg-mul-1 38.9%

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

   5. Simplified 38.9%

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

   6. Taylor expanded in y5 around -inf 55.6%

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

      1. associate-*r* 55.6%

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

      2. neg-mul-1 55.6%

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

   8. Simplified 55.6%

      \[\leadsto k \cdot \color{blue}{\left(\left(-y5\right) \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.3 \cdot 10^{+246}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -6.8 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -2.9 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1.7 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -4.4 \cdot 10^{-69}:\\ \;\;\;\;b \cdot \left(y \cdot \left(y4 \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -8.6 \cdot 10^{-125}:\\ \;\;\;\;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}\;y5 \leq -1 \cdot 10^{-177}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -2.5 \cdot 10^{-229}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 3.2 \cdot 10^{-212}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := y4 \cdot \left(\left(b \cdot t\_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t\_2\right)\\ t_4 := x \cdot y - z \cdot t\\ t_5 := a \cdot \left(\left(b \cdot t\_4 + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -6.5 \cdot 10^{+245}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -4.5 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1.25 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_4 + y4 \cdot t\_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -8.6 \cdot 10^{-75}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot t\_4\right)\right)\\ \mathbf{elif}\;y5 \leq -2.5 \cdot 10^{-123}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot t\_2\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-177}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y5 \leq -4 \cdot 10^{-229}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y5 \leq 1.4 \cdot 10^{-212}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y5 \leq 8 \cdot 10^{+127}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (* y4 (+ (+ (* b t_1) (* y1 (- (* k y2) (* j y3)))) (* c t_2))))
        (t_4 (- (* x y) (* z t)))
        (t_5
         (*
          a
          (+
           (+ (* b t_4) (* y1 (- (* z y3) (* x y2))))
           (* y5 (- (* t y2) (* y y3)))))))
   (if (<= y5 -6.5e+245)
     (* a (* y (- (* x b) (* y3 y5))))
     (if (<= y5 -4.5e+137)
       (*
        t
        (+
         (+ (* j (- (* b y4) (* i y5))) (* z (- (* c i) (* a b))))
         (* y2 (- (* a y5) (* c y4)))))
       (if (<= y5 -1.25e+56)
         (* b (+ (+ (* a t_4) (* y4 t_1)) (* y0 (- (* z k) (* x j)))))
         (if (<= y5 -8.6e-75)
           (*
            i
            (+
             (* y1 (- (* x j) (* z k)))
             (- (* y5 (- (* y k) (* t j))) (* c t_4))))
           (if (<= y5 -2.5e-123)
             (*
              c
              (+
               (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
               (* y4 t_2)))
             (if (<= y5 -1.45e-177)
               t_3
               (if (<= y5 -4e-229)
                 t_5
                 (if (<= y5 1.4e-212)
                   t_3
                   (if (<= y5 8e+127)
                     t_5
                     (* k (* y5 (- (* y i) (* y0 y2)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double t_4 = (x * y) - (z * t);
	double t_5 = a * (((b * t_4) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	double tmp;
	if (y5 <= -6.5e+245) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y5 <= -4.5e+137) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y5 <= -1.25e+56) {
		tmp = b * (((a * t_4) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -8.6e-75) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_4)));
	} else if (y5 <= -2.5e-123) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2));
	} else if (y5 <= -1.45e-177) {
		tmp = t_3;
	} else if (y5 <= -4e-229) {
		tmp = t_5;
	} else if (y5 <= 1.4e-212) {
		tmp = t_3;
	} else if (y5 <= 8e+127) {
		tmp = t_5;
	} else {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = (y * y3) - (t * y2)
    t_3 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
    t_4 = (x * y) - (z * t)
    t_5 = a * (((b * t_4) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))))
    if (y5 <= (-6.5d+245)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y5 <= (-4.5d+137)) then
        tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
    else if (y5 <= (-1.25d+56)) then
        tmp = b * (((a * t_4) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= (-8.6d-75)) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_4)))
    else if (y5 <= (-2.5d-123)) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2))
    else if (y5 <= (-1.45d-177)) then
        tmp = t_3
    else if (y5 <= (-4d-229)) then
        tmp = t_5
    else if (y5 <= 1.4d-212) then
        tmp = t_3
    else if (y5 <= 8d+127) then
        tmp = t_5
    else
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double t_4 = (x * y) - (z * t);
	double t_5 = a * (((b * t_4) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	double tmp;
	if (y5 <= -6.5e+245) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y5 <= -4.5e+137) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y5 <= -1.25e+56) {
		tmp = b * (((a * t_4) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -8.6e-75) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_4)));
	} else if (y5 <= -2.5e-123) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2));
	} else if (y5 <= -1.45e-177) {
		tmp = t_3;
	} else if (y5 <= -4e-229) {
		tmp = t_5;
	} else if (y5 <= 1.4e-212) {
		tmp = t_3;
	} else if (y5 <= 8e+127) {
		tmp = t_5;
	} else {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = (y * y3) - (t * y2)
	t_3 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
	t_4 = (x * y) - (z * t)
	t_5 = a * (((b * t_4) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))))
	tmp = 0
	if y5 <= -6.5e+245:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y5 <= -4.5e+137:
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
	elif y5 <= -1.25e+56:
		tmp = b * (((a * t_4) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
	elif y5 <= -8.6e-75:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_4)))
	elif y5 <= -2.5e-123:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2))
	elif y5 <= -1.45e-177:
		tmp = t_3
	elif y5 <= -4e-229:
		tmp = t_5
	elif y5 <= 1.4e-212:
		tmp = t_3
	elif y5 <= 8e+127:
		tmp = t_5
	else:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_2)))
	t_4 = Float64(Float64(x * y) - Float64(z * t))
	t_5 = Float64(a * Float64(Float64(Float64(b * t_4) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))))
	tmp = 0.0
	if (y5 <= -6.5e+245)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y5 <= -4.5e+137)
		tmp = Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y5 <= -1.25e+56)
		tmp = Float64(b * Float64(Float64(Float64(a * t_4) + Float64(y4 * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= -8.6e-75)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * Float64(Float64(y * k) - Float64(t * j))) - Float64(c * t_4))));
	elseif (y5 <= -2.5e-123)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * t_2)));
	elseif (y5 <= -1.45e-177)
		tmp = t_3;
	elseif (y5 <= -4e-229)
		tmp = t_5;
	elseif (y5 <= 1.4e-212)
		tmp = t_3;
	elseif (y5 <= 8e+127)
		tmp = t_5;
	else
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = (y * y3) - (t * y2);
	t_3 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	t_4 = (x * y) - (z * t);
	t_5 = a * (((b * t_4) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	tmp = 0.0;
	if (y5 <= -6.5e+245)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y5 <= -4.5e+137)
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (y5 <= -1.25e+56)
		tmp = b * (((a * t_4) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= -8.6e-75)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * t_4)));
	elseif (y5 <= -2.5e-123)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2));
	elseif (y5 <= -1.45e-177)
		tmp = t_3;
	elseif (y5 <= -4e-229)
		tmp = t_5;
	elseif (y5 <= 1.4e-212)
		tmp = t_3;
	elseif (y5 <= 8e+127)
		tmp = t_5;
	else
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(a * N[(N[(N[(b * t$95$4), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -6.5e+245], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.5e+137], N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.25e+56], N[(b * N[(N[(N[(a * t$95$4), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8.6e-75], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.5e-123], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.45e-177], t$95$3, If[LessEqual[y5, -4e-229], t$95$5, If[LessEqual[y5, 1.4e-212], t$95$3, If[LessEqual[y5, 8e+127], t$95$5, N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y5 < -6.50000000000000035e245

   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 a around inf 41.7%

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

      1. +-commutative 41.7%

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

      2. mul-1-neg 41.7%

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

      3. unsub-neg 41.7%

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

      4. *-commutative 41.7%

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

      5. *-commutative 41.7%

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

      6. *-commutative 41.7%

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

      7. mul-1-neg 41.7%

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

      8. *-commutative 41.7%

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

   5. Simplified 41.7%

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

   6. Taylor expanded in y around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. mul-1-neg 66.7%

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

      3. unsub-neg 66.7%

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

   8. Simplified 66.7%

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

   if -6.50000000000000035e245 < y5 < -4.5000000000000001e137

   1. Initial program 35.3%

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

   3. Taylor expanded in t around inf 80.1%

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

      1. +-commutative 80.1%

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

      2. mul-1-neg 80.1%

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

      3. unsub-neg 80.1%

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

      4. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   if -4.5000000000000001e137 < y5 < -1.25000000000000006e56

   1. Initial program 28.6%

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

   3. Taylor expanded in b around inf 85.9%

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

   if -1.25000000000000006e56 < y5 < -8.5999999999999998e-75

   1. Initial program 22.2%

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

   3. Taylor expanded in i around -inf 72.4%

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

   if -8.5999999999999998e-75 < y5 < -2.50000000000000015e-123

   1. Initial program 30.6%

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

   3. Taylor expanded in c around inf 69.7%

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

      1. +-commutative 69.7%

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

      2. mul-1-neg 69.7%

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

      3. unsub-neg 69.7%

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

      4. *-commutative 69.7%

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

      5. *-commutative 69.7%

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

      6. *-commutative 69.7%

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

      7. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   if -2.50000000000000015e-123 < y5 < -1.44999999999999999e-177 or -4.00000000000000028e-229 < y5 < 1.40000000000000007e-212

   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 70.0%

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

   if -1.44999999999999999e-177 < y5 < -4.00000000000000028e-229 or 1.40000000000000007e-212 < y5 < 7.99999999999999964e127

   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 a around inf 56.0%

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

      1. +-commutative 56.0%

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

      2. mul-1-neg 56.0%

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

      3. unsub-neg 56.0%

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

      4. *-commutative 56.0%

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

      5. *-commutative 56.0%

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

      6. *-commutative 56.0%

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

      7. mul-1-neg 56.0%

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

      8. *-commutative 56.0%

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

   5. Simplified 56.0%

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

   if 7.99999999999999964e127 < y5

   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 k around inf 38.9%

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

      1. +-commutative 38.9%

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

      2. mul-1-neg 38.9%

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

      3. unsub-neg 38.9%

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

      4. *-commutative 38.9%

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

      5. associate-*r* 38.9%

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

      6. neg-mul-1 38.9%

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

   5. Simplified 38.9%

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

   6. Taylor expanded in y5 around -inf 55.6%

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

      1. associate-*r* 55.6%

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

      2. neg-mul-1 55.6%

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

   8. Simplified 55.6%

      \[\leadsto k \cdot \color{blue}{\left(\left(-y5\right) \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -6.5 \cdot 10^{+245}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -4.5 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1.25 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -8.6 \cdot 10^{-75}:\\ \;\;\;\;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(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.5 \cdot 10^{-123}:\\ \;\;\;\;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}\;y5 \leq -1.45 \cdot 10^{-177}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -4 \cdot 10^{-229}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4 \cdot 10^{-212}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 8 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 34.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(z \cdot \left(b \cdot y0 - \left(i \cdot y1 + \frac{y5 \cdot \left(y0 \cdot y2 - y \cdot i\right)}{z}\right)\right)\right)\\ t_2 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{if}\;a \leq -1.08 \cdot 10^{+282}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+204}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot \left(a - k \cdot \frac{y4}{x}\right)\right)\right)\\ \mathbf{elif}\;a \leq -1.72 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(y \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-190}:\\ \;\;\;\;k \cdot \left(\left(z \cdot y1\right) \cdot \left(y2 \cdot \frac{y4}{z} - i\right)\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-270}:\\ \;\;\;\;x \cdot \left(\left(a \cdot \left(y \cdot b\right) - a \cdot \left(y1 \cdot y2\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+76}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          k
          (* z (- (* b y0) (+ (* i y1) (/ (* y5 (- (* y0 y2) (* y i))) z))))))
        (t_2 (* a (* z (- (* y1 y3) (* t b))))))
   (if (<= a -1.08e+282)
     t_2
     (if (<= a -5.5e+204)
       (* a (* y2 (- (* t y5) (* x y1))))
       (if (<= a -9.2e+22)
         (* b (* y (* x (- a (* k (/ y4 x))))))
         (if (<= a -1.72e-46)
           (* k (* y5 (- (* y i) (* y0 y2))))
           (if (<= a -1.15e-86)
             (* b (* y4 (* y (- k))))
             (if (<= a -8.8e-190)
               (* k (* (* z y1) (- (* y2 (/ y4 z)) i)))
               (if (<= a -4.6e-270)
                 (*
                  x
                  (+
                   (- (* a (* y b)) (* a (* y1 y2)))
                   (* j (- (* i y1) (* b y0)))))
                 (if (<= a 3.3e-22)
                   t_1
                   (if (<= a 9.8e+76)
                     (* c (* y4 (- (* y y3) (* t y2))))
                     (if (<= a 1.32e+141) t_1 t_2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	double t_2 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -1.08e+282) {
		tmp = t_2;
	} else if (a <= -5.5e+204) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (a <= -9.2e+22) {
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	} else if (a <= -1.72e-46) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (a <= -1.15e-86) {
		tmp = b * (y4 * (y * -k));
	} else if (a <= -8.8e-190) {
		tmp = k * ((z * y1) * ((y2 * (y4 / z)) - i));
	} else if (a <= -4.6e-270) {
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))));
	} else if (a <= 3.3e-22) {
		tmp = t_1;
	} else if (a <= 9.8e+76) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= 1.32e+141) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))))
    t_2 = a * (z * ((y1 * y3) - (t * b)))
    if (a <= (-1.08d+282)) then
        tmp = t_2
    else if (a <= (-5.5d+204)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (a <= (-9.2d+22)) then
        tmp = b * (y * (x * (a - (k * (y4 / x)))))
    else if (a <= (-1.72d-46)) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (a <= (-1.15d-86)) then
        tmp = b * (y4 * (y * -k))
    else if (a <= (-8.8d-190)) then
        tmp = k * ((z * y1) * ((y2 * (y4 / z)) - i))
    else if (a <= (-4.6d-270)) then
        tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))))
    else if (a <= 3.3d-22) then
        tmp = t_1
    else if (a <= 9.8d+76) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (a <= 1.32d+141) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	double t_2 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (a <= -1.08e+282) {
		tmp = t_2;
	} else if (a <= -5.5e+204) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (a <= -9.2e+22) {
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	} else if (a <= -1.72e-46) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (a <= -1.15e-86) {
		tmp = b * (y4 * (y * -k));
	} else if (a <= -8.8e-190) {
		tmp = k * ((z * y1) * ((y2 * (y4 / z)) - i));
	} else if (a <= -4.6e-270) {
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))));
	} else if (a <= 3.3e-22) {
		tmp = t_1;
	} else if (a <= 9.8e+76) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= 1.32e+141) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))))
	t_2 = a * (z * ((y1 * y3) - (t * b)))
	tmp = 0
	if a <= -1.08e+282:
		tmp = t_2
	elif a <= -5.5e+204:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif a <= -9.2e+22:
		tmp = b * (y * (x * (a - (k * (y4 / x)))))
	elif a <= -1.72e-46:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif a <= -1.15e-86:
		tmp = b * (y4 * (y * -k))
	elif a <= -8.8e-190:
		tmp = k * ((z * y1) * ((y2 * (y4 / z)) - i))
	elif a <= -4.6e-270:
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))))
	elif a <= 3.3e-22:
		tmp = t_1
	elif a <= 9.8e+76:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif a <= 1.32e+141:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(Float64(i * y1) + Float64(Float64(y5 * Float64(Float64(y0 * y2) - Float64(y * i))) / z)))))
	t_2 = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	tmp = 0.0
	if (a <= -1.08e+282)
		tmp = t_2;
	elseif (a <= -5.5e+204)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (a <= -9.2e+22)
		tmp = Float64(b * Float64(y * Float64(x * Float64(a - Float64(k * Float64(y4 / x))))));
	elseif (a <= -1.72e-46)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (a <= -1.15e-86)
		tmp = Float64(b * Float64(y4 * Float64(y * Float64(-k))));
	elseif (a <= -8.8e-190)
		tmp = Float64(k * Float64(Float64(z * y1) * Float64(Float64(y2 * Float64(y4 / z)) - i)));
	elseif (a <= -4.6e-270)
		tmp = Float64(x * Float64(Float64(Float64(a * Float64(y * b)) - Float64(a * Float64(y1 * y2))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (a <= 3.3e-22)
		tmp = t_1;
	elseif (a <= 9.8e+76)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (a <= 1.32e+141)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	t_2 = a * (z * ((y1 * y3) - (t * b)));
	tmp = 0.0;
	if (a <= -1.08e+282)
		tmp = t_2;
	elseif (a <= -5.5e+204)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (a <= -9.2e+22)
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	elseif (a <= -1.72e-46)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (a <= -1.15e-86)
		tmp = b * (y4 * (y * -k));
	elseif (a <= -8.8e-190)
		tmp = k * ((z * y1) * ((y2 * (y4 / z)) - i));
	elseif (a <= -4.6e-270)
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))));
	elseif (a <= 3.3e-22)
		tmp = t_1;
	elseif (a <= 9.8e+76)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (a <= 1.32e+141)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(N[(i * y1), $MachinePrecision] + N[(N[(y5 * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.08e+282], t$95$2, If[LessEqual[a, -5.5e+204], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.2e+22], N[(b * N[(y * N[(x * N[(a - N[(k * N[(y4 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.72e-46], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.15e-86], N[(b * N[(y4 * N[(y * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.8e-190], N[(k * N[(N[(z * y1), $MachinePrecision] * N[(N[(y2 * N[(y4 / z), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.6e-270], N[(x * N[(N[(N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-22], t$95$1, If[LessEqual[a, 9.8e+76], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.32e+141], t$95$1, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if a < -1.08000000000000004e282 or 1.3200000000000001e141 < a

   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 a around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

      4. *-commutative 69.3%

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

      5. *-commutative 69.3%

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

      6. *-commutative 69.3%

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

      7. mul-1-neg 69.3%

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

      8. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in z around -inf 67.5%

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

      1. mul-1-neg 67.5%

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

   8. Simplified 67.5%

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

   if -1.08000000000000004e282 < a < -5.4999999999999996e204

   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 a around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

      4. *-commutative 75.2%

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

      5. *-commutative 75.2%

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

      6. *-commutative 75.2%

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

      7. mul-1-neg 75.2%

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

      8. *-commutative 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in y2 around inf 70.8%

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

   if -5.4999999999999996e204 < a < -9.2000000000000008e22

   1. Initial program 29.0%

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

   3. Taylor expanded in b around inf 38.4%

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

   4. Taylor expanded in y around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

   6. Simplified 53.3%

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

   7. Taylor expanded in x around inf 55.6%

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

      1. mul-1-neg 55.6%

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

      2. unsub-neg 55.6%

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

      3. associate-/l* 57.9%

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

   9. Simplified 57.9%

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

   if -9.2000000000000008e22 < a < -1.7199999999999999e-46

   1. Initial program 7.7%

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

   3. Taylor expanded in k around inf 46.9%

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

      1. +-commutative 46.9%

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

      2. mul-1-neg 46.9%

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

      3. unsub-neg 46.9%

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

      4. *-commutative 46.9%

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

      5. associate-*r* 46.9%

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

      6. neg-mul-1 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in y5 around -inf 61.8%

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

      1. associate-*r* 61.8%

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

      2. neg-mul-1 61.8%

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

   8. Simplified 61.8%

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

   if -1.7199999999999999e-46 < a < -1.14999999999999998e-86

   1. Initial program 27.5%

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

   3. Taylor expanded in b around inf 46.9%

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

   4. Taylor expanded in y around inf 38.2%

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

      1. +-commutative 38.2%

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

      2. mul-1-neg 38.2%

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

      3. unsub-neg 38.2%

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

   6. Simplified 38.2%

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

   7. Taylor expanded in a around 0 38.3%

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

      1. associate-*r* 38.3%

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

      2. neg-mul-1 38.3%

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

      3. associate-*r* 47.1%

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

   9. Simplified 47.1%

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

   if -1.14999999999999998e-86 < a < -8.80000000000000017e-190

   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 k around inf 37.4%

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

      1. +-commutative 37.4%

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

      2. mul-1-neg 37.4%

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

      3. unsub-neg 37.4%

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

      4. *-commutative 37.4%

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

      5. associate-*r* 37.4%

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

      6. neg-mul-1 37.4%

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

   5. Simplified 37.4%

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

   6. Taylor expanded in z around -inf 42.0%

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

      1. associate-*r* 42.0%

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

      2. neg-mul-1 42.0%

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

      3. +-commutative 42.0%

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

      4. mul-1-neg 42.0%

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

      5. unsub-neg 42.0%

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

   8. Simplified 42.0%

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

   9. Taylor expanded in y1 around inf 51.2%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(z \cdot \left(i - \frac{y2 \cdot y4}{z}\right)\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 51.2%

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

       2. neg-mul-1 51.2%

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

       3. associate-*r* 51.2%

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

       4. *-commutative 51.2%

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

       5. associate-/l* 51.2%

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

   11. Simplified 51.2%

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

   if -8.80000000000000017e-190 < a < -4.6000000000000003e-270

   1. Initial program 22.1%

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

   3. Taylor expanded in x around inf 58.1%

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

   4. Taylor expanded in c around 0 65.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right) + a \cdot \left(b \cdot y\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

   6. Simplified 65.7%

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

   if -4.6000000000000003e-270 < a < 3.3000000000000001e-22 or 9.80000000000000053e76 < a < 1.3200000000000001e141

   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 k around inf 45.6%

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

      1. +-commutative 45.6%

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

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

      4. *-commutative 45.6%

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

      5. associate-*r* 45.6%

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

      6. neg-mul-1 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in z around -inf 49.2%

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

      1. associate-*r* 49.2%

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

      2. neg-mul-1 49.2%

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

      3. +-commutative 49.2%

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

      4. mul-1-neg 49.2%

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

      5. unsub-neg 49.2%

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

   8. Simplified 49.2%

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

   9. Taylor expanded in y5 around -inf 44.5%

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

   if 3.3000000000000001e-22 < a < 9.80000000000000053e76

   1. Initial program 30.0%

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

   3. Taylor expanded in y4 around inf 70.3%

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

   4. Taylor expanded in c around inf 80.5%

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

      1. *-commutative 80.5%

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

      2. *-commutative 80.5%

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

   6. Simplified 80.5%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{+282}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+204}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot \left(a - k \cdot \frac{y4}{x}\right)\right)\right)\\ \mathbf{elif}\;a \leq -1.72 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(y \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-190}:\\ \;\;\;\;k \cdot \left(\left(z \cdot y1\right) \cdot \left(y2 \cdot \frac{y4}{z} - i\right)\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-270}:\\ \;\;\;\;x \cdot \left(\left(a \cdot \left(y \cdot b\right) - a \cdot \left(y1 \cdot y2\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-22}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - \left(i \cdot y1 + \frac{y5 \cdot \left(y0 \cdot y2 - y \cdot i\right)}{z}\right)\right)\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+76}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+141}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - \left(i \cdot y1 + \frac{y5 \cdot \left(y0 \cdot y2 - y \cdot i\right)}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 32.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ t_2 := k \cdot \left(\left(z \cdot y1\right) \cdot \left(y2 \cdot \frac{y4}{z} - i\right)\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+204}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot \left(a - k \cdot \frac{y4}{x}\right)\right)\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(y \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-189}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-226}:\\ \;\;\;\;x \cdot \left(\left(a \cdot \left(y \cdot b\right) - a \cdot \left(y1 \cdot y2\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* z (- (* y1 y3) (* t b)))))
        (t_2 (* k (* (* z y1) (- (* y2 (/ y4 z)) i)))))
   (if (<= a -1.5e+282)
     t_1
     (if (<= a -5.5e+204)
       (* a (* y2 (- (* t y5) (* x y1))))
       (if (<= a -6.1e+22)
         (* b (* y (* x (- a (* k (/ y4 x))))))
         (if (<= a -4.6e-46)
           (* k (* y5 (- (* y i) (* y0 y2))))
           (if (<= a -1.1e-86)
             (* b (* y4 (* y (- k))))
             (if (<= a -3.1e-189)
               t_2
               (if (<= a -3.2e-226)
                 (*
                  x
                  (+
                   (- (* a (* y b)) (* a (* y1 y2)))
                   (* j (- (* i y1) (* b y0)))))
                 (if (<= a 4.6e-179)
                   (*
                    b
                    (+
                     (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
                     (* y0 (- (* z k) (* x j)))))
                   (if (<= a 2.9e-47) t_2 t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (z * ((y1 * y3) - (t * b)));
	double t_2 = k * ((z * y1) * ((y2 * (y4 / z)) - i));
	double tmp;
	if (a <= -1.5e+282) {
		tmp = t_1;
	} else if (a <= -5.5e+204) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (a <= -6.1e+22) {
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	} else if (a <= -4.6e-46) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (a <= -1.1e-86) {
		tmp = b * (y4 * (y * -k));
	} else if (a <= -3.1e-189) {
		tmp = t_2;
	} else if (a <= -3.2e-226) {
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))));
	} else if (a <= 4.6e-179) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (a <= 2.9e-47) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (z * ((y1 * y3) - (t * b)))
    t_2 = k * ((z * y1) * ((y2 * (y4 / z)) - i))
    if (a <= (-1.5d+282)) then
        tmp = t_1
    else if (a <= (-5.5d+204)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (a <= (-6.1d+22)) then
        tmp = b * (y * (x * (a - (k * (y4 / x)))))
    else if (a <= (-4.6d-46)) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (a <= (-1.1d-86)) then
        tmp = b * (y4 * (y * -k))
    else if (a <= (-3.1d-189)) then
        tmp = t_2
    else if (a <= (-3.2d-226)) then
        tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))))
    else if (a <= 4.6d-179) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (a <= 2.9d-47) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (z * ((y1 * y3) - (t * b)));
	double t_2 = k * ((z * y1) * ((y2 * (y4 / z)) - i));
	double tmp;
	if (a <= -1.5e+282) {
		tmp = t_1;
	} else if (a <= -5.5e+204) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (a <= -6.1e+22) {
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	} else if (a <= -4.6e-46) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (a <= -1.1e-86) {
		tmp = b * (y4 * (y * -k));
	} else if (a <= -3.1e-189) {
		tmp = t_2;
	} else if (a <= -3.2e-226) {
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))));
	} else if (a <= 4.6e-179) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (a <= 2.9e-47) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (z * ((y1 * y3) - (t * b)))
	t_2 = k * ((z * y1) * ((y2 * (y4 / z)) - i))
	tmp = 0
	if a <= -1.5e+282:
		tmp = t_1
	elif a <= -5.5e+204:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif a <= -6.1e+22:
		tmp = b * (y * (x * (a - (k * (y4 / x)))))
	elif a <= -4.6e-46:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif a <= -1.1e-86:
		tmp = b * (y4 * (y * -k))
	elif a <= -3.1e-189:
		tmp = t_2
	elif a <= -3.2e-226:
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))))
	elif a <= 4.6e-179:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif a <= 2.9e-47:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	t_2 = Float64(k * Float64(Float64(z * y1) * Float64(Float64(y2 * Float64(y4 / z)) - i)))
	tmp = 0.0
	if (a <= -1.5e+282)
		tmp = t_1;
	elseif (a <= -5.5e+204)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (a <= -6.1e+22)
		tmp = Float64(b * Float64(y * Float64(x * Float64(a - Float64(k * Float64(y4 / x))))));
	elseif (a <= -4.6e-46)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (a <= -1.1e-86)
		tmp = Float64(b * Float64(y4 * Float64(y * Float64(-k))));
	elseif (a <= -3.1e-189)
		tmp = t_2;
	elseif (a <= -3.2e-226)
		tmp = Float64(x * Float64(Float64(Float64(a * Float64(y * b)) - Float64(a * Float64(y1 * y2))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (a <= 4.6e-179)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (a <= 2.9e-47)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (z * ((y1 * y3) - (t * b)));
	t_2 = k * ((z * y1) * ((y2 * (y4 / z)) - i));
	tmp = 0.0;
	if (a <= -1.5e+282)
		tmp = t_1;
	elseif (a <= -5.5e+204)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (a <= -6.1e+22)
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	elseif (a <= -4.6e-46)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (a <= -1.1e-86)
		tmp = b * (y4 * (y * -k));
	elseif (a <= -3.1e-189)
		tmp = t_2;
	elseif (a <= -3.2e-226)
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))));
	elseif (a <= 4.6e-179)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (a <= 2.9e-47)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(N[(z * y1), $MachinePrecision] * N[(N[(y2 * N[(y4 / z), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+282], t$95$1, If[LessEqual[a, -5.5e+204], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.1e+22], N[(b * N[(y * N[(x * N[(a - N[(k * N[(y4 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.6e-46], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.1e-86], N[(b * N[(y4 * N[(y * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.1e-189], t$95$2, If[LessEqual[a, -3.2e-226], N[(x * N[(N[(N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e-179], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-47], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -1.49999999999999998e282 or 2.9e-47 < a

   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 a around inf 52.0%

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

      1. +-commutative 52.0%

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

      2. mul-1-neg 52.0%

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

      3. unsub-neg 52.0%

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

      4. *-commutative 52.0%

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

      5. *-commutative 52.0%

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

      6. *-commutative 52.0%

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

      7. mul-1-neg 52.0%

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

      8. *-commutative 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in z around -inf 55.2%

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

      1. mul-1-neg 55.2%

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

   8. Simplified 55.2%

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

   if -1.49999999999999998e282 < a < -5.4999999999999996e204

   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 a around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

      4. *-commutative 75.2%

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

      5. *-commutative 75.2%

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

      6. *-commutative 75.2%

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

      7. mul-1-neg 75.2%

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

      8. *-commutative 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in y2 around inf 70.8%

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

   if -5.4999999999999996e204 < a < -6.0999999999999998e22

   1. Initial program 29.0%

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

   3. Taylor expanded in b around inf 38.4%

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

   4. Taylor expanded in y around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

   6. Simplified 53.3%

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

   7. Taylor expanded in x around inf 55.6%

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

      1. mul-1-neg 55.6%

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

      2. unsub-neg 55.6%

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

      3. associate-/l* 57.9%

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

   9. Simplified 57.9%

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

   if -6.0999999999999998e22 < a < -4.5999999999999998e-46

   1. Initial program 7.7%

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

   3. Taylor expanded in k around inf 46.9%

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

      1. +-commutative 46.9%

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

      2. mul-1-neg 46.9%

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

      3. unsub-neg 46.9%

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

      4. *-commutative 46.9%

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

      5. associate-*r* 46.9%

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

      6. neg-mul-1 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in y5 around -inf 61.8%

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

      1. associate-*r* 61.8%

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

      2. neg-mul-1 61.8%

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

   8. Simplified 61.8%

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

   if -4.5999999999999998e-46 < a < -1.1000000000000001e-86

   1. Initial program 27.5%

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

   3. Taylor expanded in b around inf 46.9%

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

   4. Taylor expanded in y around inf 38.2%

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

      1. +-commutative 38.2%

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

      2. mul-1-neg 38.2%

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

      3. unsub-neg 38.2%

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

   6. Simplified 38.2%

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

   7. Taylor expanded in a around 0 38.3%

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

      1. associate-*r* 38.3%

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

      2. neg-mul-1 38.3%

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

      3. associate-*r* 47.1%

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

   9. Simplified 47.1%

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

   if -1.1000000000000001e-86 < a < -3.1e-189 or 4.59999999999999975e-179 < a < 2.9e-47

   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 k around inf 43.0%

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

      1. +-commutative 43.0%

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

      2. mul-1-neg 43.0%

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

      3. unsub-neg 43.0%

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

      4. *-commutative 43.0%

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

      5. associate-*r* 43.0%

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

      6. neg-mul-1 43.0%

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

   5. Simplified 43.0%

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

   6. Taylor expanded in z around -inf 48.6%

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

      1. associate-*r* 48.6%

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

      2. neg-mul-1 48.6%

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

      3. +-commutative 48.6%

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

      4. mul-1-neg 48.6%

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

      5. unsub-neg 48.6%

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

   8. Simplified 48.6%

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

   9. Taylor expanded in y1 around inf 49.2%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(z \cdot \left(i - \frac{y2 \cdot y4}{z}\right)\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 49.2%

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

       2. neg-mul-1 49.2%

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

       3. associate-*r* 49.0%

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

       4. *-commutative 49.0%

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

       5. associate-/l* 49.0%

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

   11. Simplified 49.0%

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

   if -3.1e-189 < a < -3.19999999999999982e-226

   1. Initial program 22.2%

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

   3. Taylor expanded in x around inf 67.1%

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

   4. Taylor expanded in c around 0 78.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right) + a \cdot \left(b \cdot y\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 78.2%

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

      2. mul-1-neg 78.2%

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

      3. unsub-neg 78.2%

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

   6. Simplified 78.2%

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

   if -3.19999999999999982e-226 < a < 4.59999999999999975e-179

   1. Initial program 38.2%

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

   3. Taylor expanded in b around inf 52.8%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+282}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+204}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot \left(a - k \cdot \frac{y4}{x}\right)\right)\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(y \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-189}:\\ \;\;\;\;k \cdot \left(\left(z \cdot y1\right) \cdot \left(y2 \cdot \frac{y4}{z} - i\right)\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-226}:\\ \;\;\;\;x \cdot \left(\left(a \cdot \left(y \cdot b\right) - a \cdot \left(y1 \cdot y2\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;k \cdot \left(\left(z \cdot y1\right) \cdot \left(y2 \cdot \frac{y4}{z} - i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := a \cdot y5 - c \cdot y4\\ \mathbf{if}\;b \leq -2.9 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - \left(i \cdot y1 + \frac{y5 \cdot \left(y0 \cdot y2 - y \cdot i\right)}{z}\right)\right)\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-98}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot t\_2\right)\\ \mathbf{elif}\;b \leq 10^{-41}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 10^{+172}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_2 (- (* a y5) (* c y4))))
   (if (<= b -2.9e+188)
     t_1
     (if (<= b -1.02e+105)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= b -3.6e+19)
         (*
          k
          (* z (- (* b y0) (+ (* i y1) (/ (* y5 (- (* y0 y2) (* y i))) z)))))
         (if (<= b -7e-83)
           (* a (* y1 (- (* z y3) (* x y2))))
           (if (<= b 8.8e-98)
             (*
              y2
              (+
               (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
               (* t t_2)))
             (if (<= b 1e-41)
               (*
                c
                (+
                 (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
                 (* y4 (- (* y y3) (* t y2)))))
               (if (<= b 1e+172)
                 (*
                  t
                  (+
                   (+ (* j (- (* b y4) (* i y5))) (* z (- (* c i) (* a b))))
                   (* y2 t_2)))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_2 = (a * y5) - (c * y4);
	double tmp;
	if (b <= -2.9e+188) {
		tmp = t_1;
	} else if (b <= -1.02e+105) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= -3.6e+19) {
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	} else if (b <= -7e-83) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (b <= 8.8e-98) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	} else if (b <= 1e-41) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (b <= 1e+172) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_2 = (a * y5) - (c * y4)
    if (b <= (-2.9d+188)) then
        tmp = t_1
    else if (b <= (-1.02d+105)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (b <= (-3.6d+19)) then
        tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))))
    else if (b <= (-7d-83)) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (b <= 8.8d-98) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2))
    else if (b <= 1d-41) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    else if (b <= 1d+172) then
        tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_2 = (a * y5) - (c * y4);
	double tmp;
	if (b <= -2.9e+188) {
		tmp = t_1;
	} else if (b <= -1.02e+105) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= -3.6e+19) {
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	} else if (b <= -7e-83) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (b <= 8.8e-98) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	} else if (b <= 1e-41) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (b <= 1e+172) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_2 = (a * y5) - (c * y4)
	tmp = 0
	if b <= -2.9e+188:
		tmp = t_1
	elif b <= -1.02e+105:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif b <= -3.6e+19:
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))))
	elif b <= -7e-83:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif b <= 8.8e-98:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2))
	elif b <= 1e-41:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	elif b <= 1e+172:
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	tmp = 0.0
	if (b <= -2.9e+188)
		tmp = t_1;
	elseif (b <= -1.02e+105)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (b <= -3.6e+19)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(Float64(i * y1) + Float64(Float64(y5 * Float64(Float64(y0 * y2) - Float64(y * i))) / z)))));
	elseif (b <= -7e-83)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (b <= 8.8e-98)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * t_2)));
	elseif (b <= 1e-41)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (b <= 1e+172)
		tmp = Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * t_2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_2 = (a * y5) - (c * y4);
	tmp = 0.0;
	if (b <= -2.9e+188)
		tmp = t_1;
	elseif (b <= -1.02e+105)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (b <= -3.6e+19)
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	elseif (b <= -7e-83)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (b <= 8.8e-98)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	elseif (b <= 1e-41)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (b <= 1e+172)
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.9e+188], t$95$1, If[LessEqual[b, -1.02e+105], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.6e+19], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(N[(i * y1), $MachinePrecision] + N[(N[(y5 * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7e-83], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.8e-98], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-41], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+172], N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -2.8999999999999999e188 or 1.0000000000000001e172 < b

   1. Initial program 26.3%

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

   3. Taylor expanded in b around inf 69.1%

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

   if -2.8999999999999999e188 < b < -1.02e105

   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 a around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

      5. *-commutative 62.5%

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

      6. *-commutative 62.5%

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

      7. mul-1-neg 62.5%

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

      8. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in z around -inf 81.7%

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

      1. mul-1-neg 81.7%

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

   8. Simplified 81.7%

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

   if -1.02e105 < b < -3.6e19

   1. Initial program 7.7%

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

   3. Taylor expanded in k around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. *-commutative 54.4%

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

      5. associate-*r* 54.4%

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

      6. neg-mul-1 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in z around -inf 69.2%

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

      1. associate-*r* 69.2%

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

      2. neg-mul-1 69.2%

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

      3. +-commutative 69.2%

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

      4. mul-1-neg 69.2%

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

      5. unsub-neg 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in y5 around -inf 77.4%

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

   if -3.6e19 < b < -7.00000000000000061e-83

   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 a around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

      4. *-commutative 75.2%

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

      5. *-commutative 75.2%

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

      6. *-commutative 75.2%

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

      7. mul-1-neg 75.2%

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

      8. *-commutative 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in y1 around inf 63.5%

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

   if -7.00000000000000061e-83 < b < 8.79999999999999985e-98

   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 y2 around inf 47.4%

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

   if 8.79999999999999985e-98 < b < 1.00000000000000001e-41

   1. Initial program 36.0%

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

   3. Taylor expanded in c around inf 76.8%

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

      1. +-commutative 76.8%

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

      2. mul-1-neg 76.8%

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

      3. unsub-neg 76.8%

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

      4. *-commutative 76.8%

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

      5. *-commutative 76.8%

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

      6. *-commutative 76.8%

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

      7. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   if 1.00000000000000001e-41 < b < 1.0000000000000001e172

   1. Initial program 32.7%

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

   3. Taylor expanded in t around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

   5. Simplified 47.6%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+188}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - \left(i \cdot y1 + \frac{y5 \cdot \left(y0 \cdot y2 - y \cdot i\right)}{z}\right)\right)\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-98}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 10^{-41}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 10^{+172}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ t_2 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;j \leq -8 \cdot 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{+148}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -25:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-251}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-127}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.28 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+57}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b - y1 \cdot y3\right) \cdot \left(j \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (- (* y2 y4) (* z i)))))
        (t_2 (* b (* a (- (* x y) (* z t))))))
   (if (<= j -8e+257)
     t_1
     (if (<= j -1.45e+175)
       (* x (* y2 (- (* c y0) (* a y1))))
       (if (<= j -1.95e+148)
         t_2
         (if (<= j -1.5e+99)
           t_1
           (if (<= j -25.0)
             (* b (* x (- (* y a) (* j y0))))
             (if (<= j 1.65e-251)
               (* y2 (* y4 (- (* k y1) (* t c))))
               (if (<= j 1.9e-127)
                 t_2
                 (if (<= j 1.28e+14)
                   (* a (* x (- (* y b) (* y1 y2))))
                   (if (<= j 5e+57)
                     (* i (* x (- (* j y1) (* y c))))
                     (if (<= j 3.9e+112)
                       (* a (* y1 (- (* z y3) (* x y2))))
                       (* (- (* t b) (* y1 y3)) (* j y4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * ((y2 * y4) - (z * i)));
	double t_2 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (j <= -8e+257) {
		tmp = t_1;
	} else if (j <= -1.45e+175) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= -1.95e+148) {
		tmp = t_2;
	} else if (j <= -1.5e+99) {
		tmp = t_1;
	} else if (j <= -25.0) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= 1.65e-251) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 1.9e-127) {
		tmp = t_2;
	} else if (j <= 1.28e+14) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (j <= 5e+57) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (j <= 3.9e+112) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (y1 * ((y2 * y4) - (z * i)))
    t_2 = b * (a * ((x * y) - (z * t)))
    if (j <= (-8d+257)) then
        tmp = t_1
    else if (j <= (-1.45d+175)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (j <= (-1.95d+148)) then
        tmp = t_2
    else if (j <= (-1.5d+99)) then
        tmp = t_1
    else if (j <= (-25.0d0)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (j <= 1.65d-251) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (j <= 1.9d-127) then
        tmp = t_2
    else if (j <= 1.28d+14) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else if (j <= 5d+57) then
        tmp = i * (x * ((j * y1) - (y * c)))
    else if (j <= 3.9d+112) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else
        tmp = ((t * b) - (y1 * y3)) * (j * y4)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * ((y2 * y4) - (z * i)));
	double t_2 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (j <= -8e+257) {
		tmp = t_1;
	} else if (j <= -1.45e+175) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= -1.95e+148) {
		tmp = t_2;
	} else if (j <= -1.5e+99) {
		tmp = t_1;
	} else if (j <= -25.0) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= 1.65e-251) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 1.9e-127) {
		tmp = t_2;
	} else if (j <= 1.28e+14) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (j <= 5e+57) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (j <= 3.9e+112) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * ((y2 * y4) - (z * i)))
	t_2 = b * (a * ((x * y) - (z * t)))
	tmp = 0
	if j <= -8e+257:
		tmp = t_1
	elif j <= -1.45e+175:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif j <= -1.95e+148:
		tmp = t_2
	elif j <= -1.5e+99:
		tmp = t_1
	elif j <= -25.0:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif j <= 1.65e-251:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif j <= 1.9e-127:
		tmp = t_2
	elif j <= 1.28e+14:
		tmp = a * (x * ((y * b) - (y1 * y2)))
	elif j <= 5e+57:
		tmp = i * (x * ((j * y1) - (y * c)))
	elif j <= 3.9e+112:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	else:
		tmp = ((t * b) - (y1 * y3)) * (j * y4)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))))
	t_2 = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (j <= -8e+257)
		tmp = t_1;
	elseif (j <= -1.45e+175)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (j <= -1.95e+148)
		tmp = t_2;
	elseif (j <= -1.5e+99)
		tmp = t_1;
	elseif (j <= -25.0)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (j <= 1.65e-251)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 1.9e-127)
		tmp = t_2;
	elseif (j <= 1.28e+14)
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (j <= 5e+57)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (j <= 3.9e+112)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(Float64(Float64(t * b) - Float64(y1 * y3)) * Float64(j * y4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y1 * ((y2 * y4) - (z * i)));
	t_2 = b * (a * ((x * y) - (z * t)));
	tmp = 0.0;
	if (j <= -8e+257)
		tmp = t_1;
	elseif (j <= -1.45e+175)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (j <= -1.95e+148)
		tmp = t_2;
	elseif (j <= -1.5e+99)
		tmp = t_1;
	elseif (j <= -25.0)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (j <= 1.65e-251)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (j <= 1.9e-127)
		tmp = t_2;
	elseif (j <= 1.28e+14)
		tmp = a * (x * ((y * b) - (y1 * y2)));
	elseif (j <= 5e+57)
		tmp = i * (x * ((j * y1) - (y * c)));
	elseif (j <= 3.9e+112)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	else
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8e+257], t$95$1, If[LessEqual[j, -1.45e+175], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.95e+148], t$95$2, If[LessEqual[j, -1.5e+99], t$95$1, If[LessEqual[j, -25.0], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.65e-251], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.9e-127], t$95$2, If[LessEqual[j, 1.28e+14], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e+57], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.9e+112], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision] * N[(j * y4), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -8.00000000000000024e257 or -1.95000000000000001e148 < j < -1.50000000000000007e99

   1. Initial program 9.5%

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

   3. Taylor expanded in k around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

      4. *-commutative 57.2%

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

      5. associate-*r* 57.2%

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

      6. neg-mul-1 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in y1 around inf 62.6%

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

   if -8.00000000000000024e257 < j < -1.45e175

   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 x around inf 53.9%

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

   4. Taylor expanded in y2 around inf 70.3%

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

   if -1.45e175 < j < -1.95000000000000001e148 or 1.65e-251 < j < 1.90000000000000001e-127

   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 b around inf 57.4%

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

   4. Taylor expanded in a around inf 57.0%

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

   if -1.50000000000000007e99 < j < -25

   1. Initial program 24.8%

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

   3. Taylor expanded in b around inf 41.0%

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

   4. Taylor expanded in x around inf 56.3%

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

   if -25 < j < 1.65e-251

   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 y4 around inf 48.8%

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

   4. Taylor expanded in y2 around inf 52.8%

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

      1. *-commutative 52.8%

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

   6. Simplified 52.8%

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

   if 1.90000000000000001e-127 < j < 1.28e14

   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 a around inf 40.5%

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

      1. +-commutative 40.5%

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

      2. mul-1-neg 40.5%

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

      3. unsub-neg 40.5%

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

      4. *-commutative 40.5%

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

      5. *-commutative 40.5%

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

      6. *-commutative 40.5%

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

      7. mul-1-neg 40.5%

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

      8. *-commutative 40.5%

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

   5. Simplified 40.5%

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

   6. Taylor expanded in x around inf 50.8%

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

   if 1.28e14 < j < 4.99999999999999972e57

   1. Initial program 30.0%

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

   3. Taylor expanded in x around inf 60.1%

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

   4. Taylor expanded in i around -inf 60.5%

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

      1. mul-1-neg 60.5%

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

   6. Simplified 60.5%

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

   if 4.99999999999999972e57 < j < 3.89999999999999968e112

   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 a around inf 55.1%

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

      1. +-commutative 55.1%

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

      2. mul-1-neg 55.1%

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

      3. unsub-neg 55.1%

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

      4. *-commutative 55.1%

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

      5. *-commutative 55.1%

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

      6. *-commutative 55.1%

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

      7. mul-1-neg 55.1%

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

      8. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in y1 around inf 73.4%

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

   if 3.89999999999999968e112 < j

   1. Initial program 14.0%

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

   3. Taylor expanded in y4 around inf 49.4%

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

   4. Taylor expanded in j around inf 50.1%

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

      1. associate-*r* 54.5%

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

      2. *-commutative 54.5%

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

      3. +-commutative 54.5%

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

      4. mul-1-neg 54.5%

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

      5. unsub-neg 54.5%

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

      6. *-commutative 54.5%

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

   6. Simplified 54.5%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{+257}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -25:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-251}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.28 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+57}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b - y1 \cdot y3\right) \cdot \left(j \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 28.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ t_2 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;j \leq -5.5 \cdot 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{+148}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.8:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-251}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-127}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 185000000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+57}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b - y1 \cdot y3\right) \cdot \left(j \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (- (* y2 y4) (* z i)))))
        (t_2 (* b (* a (- (* x y) (* z t))))))
   (if (<= j -5.5e+257)
     t_1
     (if (<= j -8.5e+178)
       (* x (* y2 (- (* c y0) (* a y1))))
       (if (<= j -1.95e+148)
         t_2
         (if (<= j -1.05e+100)
           t_1
           (if (<= j -3.8)
             (* b (* x (- (* y a) (* j y0))))
             (if (<= j 1.6e-251)
               (* y2 (* y4 (- (* k y1) (* t c))))
               (if (<= j 3.4e-127)
                 t_2
                 (if (<= j 185000000000.0)
                   (* a (* x (- (* y b) (* y1 y2))))
                   (if (<= j 1.45e+57)
                     (* j (* x (- (* i y1) (* b y0))))
                     (if (<= j 3.2e+112)
                       (* a (* y1 (- (* z y3) (* x y2))))
                       (* (- (* t b) (* y1 y3)) (* j y4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * ((y2 * y4) - (z * i)));
	double t_2 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (j <= -5.5e+257) {
		tmp = t_1;
	} else if (j <= -8.5e+178) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= -1.95e+148) {
		tmp = t_2;
	} else if (j <= -1.05e+100) {
		tmp = t_1;
	} else if (j <= -3.8) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= 1.6e-251) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 3.4e-127) {
		tmp = t_2;
	} else if (j <= 185000000000.0) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (j <= 1.45e+57) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= 3.2e+112) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (y1 * ((y2 * y4) - (z * i)))
    t_2 = b * (a * ((x * y) - (z * t)))
    if (j <= (-5.5d+257)) then
        tmp = t_1
    else if (j <= (-8.5d+178)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (j <= (-1.95d+148)) then
        tmp = t_2
    else if (j <= (-1.05d+100)) then
        tmp = t_1
    else if (j <= (-3.8d0)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (j <= 1.6d-251) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (j <= 3.4d-127) then
        tmp = t_2
    else if (j <= 185000000000.0d0) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else if (j <= 1.45d+57) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (j <= 3.2d+112) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else
        tmp = ((t * b) - (y1 * y3)) * (j * y4)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * ((y2 * y4) - (z * i)));
	double t_2 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (j <= -5.5e+257) {
		tmp = t_1;
	} else if (j <= -8.5e+178) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= -1.95e+148) {
		tmp = t_2;
	} else if (j <= -1.05e+100) {
		tmp = t_1;
	} else if (j <= -3.8) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= 1.6e-251) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 3.4e-127) {
		tmp = t_2;
	} else if (j <= 185000000000.0) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (j <= 1.45e+57) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= 3.2e+112) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * ((y2 * y4) - (z * i)))
	t_2 = b * (a * ((x * y) - (z * t)))
	tmp = 0
	if j <= -5.5e+257:
		tmp = t_1
	elif j <= -8.5e+178:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif j <= -1.95e+148:
		tmp = t_2
	elif j <= -1.05e+100:
		tmp = t_1
	elif j <= -3.8:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif j <= 1.6e-251:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif j <= 3.4e-127:
		tmp = t_2
	elif j <= 185000000000.0:
		tmp = a * (x * ((y * b) - (y1 * y2)))
	elif j <= 1.45e+57:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif j <= 3.2e+112:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	else:
		tmp = ((t * b) - (y1 * y3)) * (j * y4)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))))
	t_2 = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (j <= -5.5e+257)
		tmp = t_1;
	elseif (j <= -8.5e+178)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (j <= -1.95e+148)
		tmp = t_2;
	elseif (j <= -1.05e+100)
		tmp = t_1;
	elseif (j <= -3.8)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (j <= 1.6e-251)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 3.4e-127)
		tmp = t_2;
	elseif (j <= 185000000000.0)
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (j <= 1.45e+57)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (j <= 3.2e+112)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(Float64(Float64(t * b) - Float64(y1 * y3)) * Float64(j * y4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y1 * ((y2 * y4) - (z * i)));
	t_2 = b * (a * ((x * y) - (z * t)));
	tmp = 0.0;
	if (j <= -5.5e+257)
		tmp = t_1;
	elseif (j <= -8.5e+178)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (j <= -1.95e+148)
		tmp = t_2;
	elseif (j <= -1.05e+100)
		tmp = t_1;
	elseif (j <= -3.8)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (j <= 1.6e-251)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (j <= 3.4e-127)
		tmp = t_2;
	elseif (j <= 185000000000.0)
		tmp = a * (x * ((y * b) - (y1 * y2)));
	elseif (j <= 1.45e+57)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (j <= 3.2e+112)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	else
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.5e+257], t$95$1, If[LessEqual[j, -8.5e+178], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.95e+148], t$95$2, If[LessEqual[j, -1.05e+100], t$95$1, If[LessEqual[j, -3.8], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.6e-251], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e-127], t$95$2, If[LessEqual[j, 185000000000.0], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e+57], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e+112], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision] * N[(j * y4), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -5.49999999999999957e257 or -1.95000000000000001e148 < j < -1.0499999999999999e100

   1. Initial program 9.5%

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

   3. Taylor expanded in k around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

      4. *-commutative 57.2%

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

      5. associate-*r* 57.2%

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

      6. neg-mul-1 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in y1 around inf 62.6%

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

   if -5.49999999999999957e257 < j < -8.49999999999999991e178

   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 x around inf 53.9%

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

   4. Taylor expanded in y2 around inf 70.3%

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

   if -8.49999999999999991e178 < j < -1.95000000000000001e148 or 1.59999999999999991e-251 < j < 3.3999999999999999e-127

   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 b around inf 57.4%

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

   4. Taylor expanded in a around inf 57.0%

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

   if -1.0499999999999999e100 < j < -3.7999999999999998

   1. Initial program 24.8%

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

   3. Taylor expanded in b around inf 41.0%

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

   4. Taylor expanded in x around inf 56.3%

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

   if -3.7999999999999998 < j < 1.59999999999999991e-251

   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 y4 around inf 48.8%

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

   4. Taylor expanded in y2 around inf 52.8%

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

      1. *-commutative 52.8%

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

   6. Simplified 52.8%

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

   if 3.3999999999999999e-127 < j < 1.85e11

   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 a around inf 40.5%

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

      1. +-commutative 40.5%

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

      2. mul-1-neg 40.5%

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

      3. unsub-neg 40.5%

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

      4. *-commutative 40.5%

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

      5. *-commutative 40.5%

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

      6. *-commutative 40.5%

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

      7. mul-1-neg 40.5%

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

      8. *-commutative 40.5%

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

   5. Simplified 40.5%

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

   6. Taylor expanded in x around inf 50.8%

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

   if 1.85e11 < j < 1.4500000000000001e57

   1. Initial program 30.0%

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

   3. Taylor expanded in x around inf 60.1%

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

   4. Taylor expanded in j around inf 51.2%

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

   if 1.4500000000000001e57 < j < 3.19999999999999986e112

   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 a around inf 55.1%

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

      1. +-commutative 55.1%

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

      2. mul-1-neg 55.1%

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

      3. unsub-neg 55.1%

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

      4. *-commutative 55.1%

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

      5. *-commutative 55.1%

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

      6. *-commutative 55.1%

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

      7. mul-1-neg 55.1%

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

      8. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in y1 around inf 73.4%

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

   if 3.19999999999999986e112 < j

   1. Initial program 14.0%

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

   3. Taylor expanded in y4 around inf 49.4%

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

   4. Taylor expanded in j around inf 50.1%

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

      1. associate-*r* 54.5%

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

      2. *-commutative 54.5%

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

      3. +-commutative 54.5%

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

      4. mul-1-neg 54.5%

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

      5. unsub-neg 54.5%

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

      6. *-commutative 54.5%

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

   6. Simplified 54.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.5 \cdot 10^{+257}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{+100}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -3.8:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-251}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 185000000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+57}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b - y1 \cdot y3\right) \cdot \left(j \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 33.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y5 \cdot \left(y2 - b \cdot \frac{z}{y5}\right)\right)\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot \left(a - k \cdot \frac{y4}{x}\right)\right)\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+87}:\\ \;\;\;\;\left(t \cdot b - y1 \cdot y3\right) \cdot \left(j \cdot y4\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+14}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-301}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(\left(a \cdot \left(y \cdot b\right) - a \cdot \left(y1 \cdot y2\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y5 (- y2 (* b (/ z y5))))))))
   (if (<= y -1.8e+140)
     (* b (* y (* x (- a (* k (/ y4 x))))))
     (if (<= y -5.4e+87)
       (* (- (* t b) (* y1 y3)) (* j y4))
       (if (<= y -8.5e+14)
         (* y2 (* y4 (- (* k y1) (* t c))))
         (if (<= y -9e-115)
           t_1
           (if (<= y -8.4e-301)
             (* x (* y2 (- (* c y0) (* a y1))))
             (if (<= y 6.4e-6)
               t_1
               (if (<= y 3.5e+159)
                 (*
                  x
                  (+
                   (- (* a (* y b)) (* a (* y1 y2)))
                   (* j (- (* i y1) (* b y0)))))
                 (* y (* y4 (- (* c y3) (* b 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 = a * (t * (y5 * (y2 - (b * (z / y5)))));
	double tmp;
	if (y <= -1.8e+140) {
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	} else if (y <= -5.4e+87) {
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	} else if (y <= -8.5e+14) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y <= -9e-115) {
		tmp = t_1;
	} else if (y <= -8.4e-301) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y <= 6.4e-6) {
		tmp = t_1;
	} else if (y <= 3.5e+159) {
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (y5 * (y2 - (b * (z / y5)))))
    if (y <= (-1.8d+140)) then
        tmp = b * (y * (x * (a - (k * (y4 / x)))))
    else if (y <= (-5.4d+87)) then
        tmp = ((t * b) - (y1 * y3)) * (j * y4)
    else if (y <= (-8.5d+14)) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y <= (-9d-115)) then
        tmp = t_1
    else if (y <= (-8.4d-301)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y <= 6.4d-6) then
        tmp = t_1
    else if (y <= 3.5d+159) then
        tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))))
    else
        tmp = y * (y4 * ((c * y3) - (b * 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 = a * (t * (y5 * (y2 - (b * (z / y5)))));
	double tmp;
	if (y <= -1.8e+140) {
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	} else if (y <= -5.4e+87) {
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	} else if (y <= -8.5e+14) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y <= -9e-115) {
		tmp = t_1;
	} else if (y <= -8.4e-301) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y <= 6.4e-6) {
		tmp = t_1;
	} else if (y <= 3.5e+159) {
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (t * (y5 * (y2 - (b * (z / y5)))))
	tmp = 0
	if y <= -1.8e+140:
		tmp = b * (y * (x * (a - (k * (y4 / x)))))
	elif y <= -5.4e+87:
		tmp = ((t * b) - (y1 * y3)) * (j * y4)
	elif y <= -8.5e+14:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y <= -9e-115:
		tmp = t_1
	elif y <= -8.4e-301:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y <= 6.4e-6:
		tmp = t_1
	elif y <= 3.5e+159:
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))))
	else:
		tmp = y * (y4 * ((c * y3) - (b * 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(a * Float64(t * Float64(y5 * Float64(y2 - Float64(b * Float64(z / y5))))))
	tmp = 0.0
	if (y <= -1.8e+140)
		tmp = Float64(b * Float64(y * Float64(x * Float64(a - Float64(k * Float64(y4 / x))))));
	elseif (y <= -5.4e+87)
		tmp = Float64(Float64(Float64(t * b) - Float64(y1 * y3)) * Float64(j * y4));
	elseif (y <= -8.5e+14)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y <= -9e-115)
		tmp = t_1;
	elseif (y <= -8.4e-301)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y <= 6.4e-6)
		tmp = t_1;
	elseif (y <= 3.5e+159)
		tmp = Float64(x * Float64(Float64(Float64(a * Float64(y * b)) - Float64(a * Float64(y1 * y2))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	else
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * 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 = a * (t * (y5 * (y2 - (b * (z / y5)))));
	tmp = 0.0;
	if (y <= -1.8e+140)
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	elseif (y <= -5.4e+87)
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	elseif (y <= -8.5e+14)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y <= -9e-115)
		tmp = t_1;
	elseif (y <= -8.4e-301)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y <= 6.4e-6)
		tmp = t_1;
	elseif (y <= 3.5e+159)
		tmp = x * (((a * (y * b)) - (a * (y1 * y2))) + (j * ((i * y1) - (b * y0))));
	else
		tmp = y * (y4 * ((c * y3) - (b * 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[(a * N[(t * N[(y5 * N[(y2 - N[(b * N[(z / y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+140], N[(b * N[(y * N[(x * N[(a - N[(k * N[(y4 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.4e+87], N[(N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision] * N[(j * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e+14], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-115], t$95$1, If[LessEqual[y, -8.4e-301], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-6], t$95$1, If[LessEqual[y, 3.5e+159], N[(x * N[(N[(N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.8e140

   1. Initial program 19.1%

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

   3. Taylor expanded in b around inf 30.1%

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

   4. Taylor expanded in y around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

   6. Simplified 62.6%

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

   7. Taylor expanded in x around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. unsub-neg 65.2%

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

      3. associate-/l* 65.1%

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

   9. Simplified 65.1%

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

   if -1.8e140 < y < -5.40000000000000013e87

   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 y4 around inf 40.5%

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

   4. Taylor expanded in j around inf 74.1%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

      3. +-commutative 67.8%

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

      4. mul-1-neg 67.8%

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

      5. unsub-neg 67.8%

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

      6. *-commutative 67.8%

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

   6. Simplified 67.8%

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

   if -5.40000000000000013e87 < y < -8.5e14

   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 y4 around inf 46.7%

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

   4. Taylor expanded in y2 around inf 54.5%

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

      1. *-commutative 54.5%

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

   6. Simplified 54.5%

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

   if -8.5e14 < y < -9.00000000000000046e-115 or -8.3999999999999995e-301 < y < 6.3999999999999997e-6

   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 a around inf 40.7%

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

      1. +-commutative 40.7%

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

      2. mul-1-neg 40.7%

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

      3. unsub-neg 40.7%

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

      4. *-commutative 40.7%

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

      5. *-commutative 40.7%

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

      6. *-commutative 40.7%

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

      7. mul-1-neg 40.7%

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

      8. *-commutative 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in t around inf 38.4%

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

      1. +-commutative 38.4%

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

      2. mul-1-neg 38.4%

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

      3. sub-neg 38.4%

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

   8. Simplified 38.4%

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

   9. Taylor expanded in y5 around inf 41.7%

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

       1. mul-1-neg 41.7%

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

       2. unsub-neg 41.7%

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

       3. associate-/l* 44.0%

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

   11. Simplified 44.0%

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

   if -9.00000000000000046e-115 < y < -8.3999999999999995e-301

   1. Initial program 27.4%

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

   3. Taylor expanded in x around inf 37.5%

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

   4. Taylor expanded in y2 around inf 43.5%

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

   if 6.3999999999999997e-6 < y < 3.4999999999999999e159

   1. Initial program 26.6%

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

   3. Taylor expanded in x around inf 45.7%

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

   4. Taylor expanded in c around 0 45.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right) + a \cdot \left(b \cdot y\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 45.8%

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

      2. mul-1-neg 45.8%

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

      3. unsub-neg 45.8%

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

   6. Simplified 45.8%

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

   if 3.4999999999999999e159 < y

   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 y4 around inf 57.1%

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

   4. Taylor expanded in y around inf 66.9%

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

      1. distribute-lft-out-- 66.9%

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

      2. *-commutative 66.9%

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

      3. *-commutative 66.9%

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

   6. Simplified 66.9%

      \[\leadsto \color{blue}{y \cdot \left(y4 \cdot \left(-1 \cdot \left(k \cdot b - y3 \cdot c\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot \left(a - k \cdot \frac{y4}{x}\right)\right)\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+87}:\\ \;\;\;\;\left(t \cdot b - y1 \cdot y3\right) \cdot \left(j \cdot y4\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+14}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-115}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y5 \cdot \left(y2 - b \cdot \frac{z}{y5}\right)\right)\right)\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-301}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y5 \cdot \left(y2 - b \cdot \frac{z}{y5}\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(\left(a \cdot \left(y \cdot b\right) - a \cdot \left(y1 \cdot y2\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -1.12 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{+39}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - \left(i \cdot y1 + \frac{y5 \cdot \left(y0 \cdot y2 - y \cdot i\right)}{z}\right)\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= b -1.12e+184)
     t_1
     (if (<= b -3.6e+113)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= b -2.65e+39)
         (*
          k
          (* z (- (* b y0) (+ (* i y1) (/ (* y5 (- (* y0 y2) (* y i))) z)))))
         (if (<= b 5.5e-42)
           (*
            c
            (+
             (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
             (* y4 (- (* y y3) (* t y2)))))
           (if (<= b 3.4e+171)
             (*
              t
              (+
               (+ (* j (- (* b y4) (* i y5))) (* z (- (* c i) (* a b))))
               (* y2 (- (* a y5) (* c y4)))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (b <= -1.12e+184) {
		tmp = t_1;
	} else if (b <= -3.6e+113) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= -2.65e+39) {
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	} else if (b <= 5.5e-42) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (b <= 3.4e+171) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    if (b <= (-1.12d+184)) then
        tmp = t_1
    else if (b <= (-3.6d+113)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (b <= (-2.65d+39)) then
        tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))))
    else if (b <= 5.5d-42) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    else if (b <= 3.4d+171) then
        tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (b <= -1.12e+184) {
		tmp = t_1;
	} else if (b <= -3.6e+113) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= -2.65e+39) {
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	} else if (b <= 5.5e-42) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (b <= 3.4e+171) {
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if b <= -1.12e+184:
		tmp = t_1
	elif b <= -3.6e+113:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif b <= -2.65e+39:
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))))
	elif b <= 5.5e-42:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	elif b <= 3.4e+171:
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (b <= -1.12e+184)
		tmp = t_1;
	elseif (b <= -3.6e+113)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (b <= -2.65e+39)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(Float64(i * y1) + Float64(Float64(y5 * Float64(Float64(y0 * y2) - Float64(y * i))) / z)))));
	elseif (b <= 5.5e-42)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (b <= 3.4e+171)
		tmp = Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	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 * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (b <= -1.12e+184)
		tmp = t_1;
	elseif (b <= -3.6e+113)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (b <= -2.65e+39)
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	elseif (b <= 5.5e-42)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (b <= 3.4e+171)
		tmp = t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.12e+184], t$95$1, If[LessEqual[b, -3.6e+113], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.65e+39], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(N[(i * y1), $MachinePrecision] + N[(N[(y5 * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-42], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+171], N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.12000000000000007e184 or 3.4000000000000001e171 < b

   1. Initial program 26.3%

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

   3. Taylor expanded in b around inf 69.1%

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

   if -1.12000000000000007e184 < b < -3.59999999999999992e113

   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 a around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

      5. *-commutative 62.5%

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

      6. *-commutative 62.5%

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

      7. mul-1-neg 62.5%

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

      8. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in z around -inf 81.7%

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

      1. mul-1-neg 81.7%

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

   8. Simplified 81.7%

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

   if -3.59999999999999992e113 < b < -2.64999999999999989e39

   1. Initial program 0.0%

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

   3. Taylor expanded in k around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. mul-1-neg 63.2%

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

      3. unsub-neg 63.2%

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

      4. *-commutative 63.2%

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

      5. associate-*r* 63.2%

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

      6. neg-mul-1 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in z around -inf 87.5%

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

      1. associate-*r* 87.5%

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

      2. neg-mul-1 87.5%

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

      3. +-commutative 87.5%

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

      4. mul-1-neg 87.5%

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

      5. unsub-neg 87.5%

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

   8. Simplified 87.5%

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

   9. Taylor expanded in y5 around -inf 87.5%

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

   if -2.64999999999999989e39 < b < 5.5e-42

   1. Initial program 24.9%

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

   3. Taylor expanded in c around inf 44.5%

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

      1. +-commutative 44.5%

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

      2. mul-1-neg 44.5%

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

      3. unsub-neg 44.5%

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

      4. *-commutative 44.5%

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

      5. *-commutative 44.5%

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

      6. *-commutative 44.5%

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

      7. *-commutative 44.5%

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

   5. Simplified 44.5%

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

   if 5.5e-42 < b < 3.4000000000000001e171

   1. Initial program 32.7%

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

   3. Taylor expanded in t around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

   5. Simplified 47.6%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{+184}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{+39}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - \left(i \cdot y1 + \frac{y5 \cdot \left(y0 \cdot y2 - y \cdot i\right)}{z}\right)\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+258}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -0.36:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{-252}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 17000000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+64}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b - y1 \cdot y3\right) \cdot \left(j \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.65e+258)
   (* k (* y1 (- (* y2 y4) (* z i))))
   (if (<= j -4.2e+179)
     (* x (* y2 (- (* c y0) (* a y1))))
     (if (<= j -0.36)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= j 2.05e-252)
         (* y2 (* y4 (- (* k y1) (* t c))))
         (if (<= j 8.5e-127)
           (* b (* a (- (* x y) (* z t))))
           (if (<= j 17000000000.0)
             (* a (* x (- (* y b) (* y1 y2))))
             (if (<= j 6e+64)
               (* k (* y5 (- (* y i) (* y0 y2))))
               (if (<= j 3.4e+112)
                 (* a (* y1 (- (* z y3) (* x y2))))
                 (* (- (* t b) (* y1 y3)) (* j y4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.65e+258) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -4.2e+179) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= -0.36) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= 2.05e-252) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 8.5e-127) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= 17000000000.0) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (j <= 6e+64) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (j <= 3.4e+112) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-1.65d+258)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (j <= (-4.2d+179)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (j <= (-0.36d0)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (j <= 2.05d-252) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (j <= 8.5d-127) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (j <= 17000000000.0d0) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else if (j <= 6d+64) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (j <= 3.4d+112) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else
        tmp = ((t * b) - (y1 * y3)) * (j * y4)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.65e+258) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -4.2e+179) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= -0.36) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= 2.05e-252) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 8.5e-127) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= 17000000000.0) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (j <= 6e+64) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (j <= 3.4e+112) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -1.65e+258:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif j <= -4.2e+179:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif j <= -0.36:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif j <= 2.05e-252:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif j <= 8.5e-127:
		tmp = b * (a * ((x * y) - (z * t)))
	elif j <= 17000000000.0:
		tmp = a * (x * ((y * b) - (y1 * y2)))
	elif j <= 6e+64:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif j <= 3.4e+112:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	else:
		tmp = ((t * b) - (y1 * y3)) * (j * y4)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.65e+258)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (j <= -4.2e+179)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (j <= -0.36)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (j <= 2.05e-252)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 8.5e-127)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (j <= 17000000000.0)
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (j <= 6e+64)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (j <= 3.4e+112)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(Float64(Float64(t * b) - Float64(y1 * y3)) * Float64(j * y4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -1.65e+258)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (j <= -4.2e+179)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (j <= -0.36)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (j <= 2.05e-252)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (j <= 8.5e-127)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (j <= 17000000000.0)
		tmp = a * (x * ((y * b) - (y1 * y2)));
	elseif (j <= 6e+64)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (j <= 3.4e+112)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	else
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.65e+258], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.2e+179], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -0.36], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.05e-252], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e-127], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 17000000000.0], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e+64], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e+112], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision] * N[(j * y4), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -1.64999999999999998e258

   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 k around inf 70.0%

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

      1. +-commutative 70.0%

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

      2. mul-1-neg 70.0%

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

      3. unsub-neg 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-*r* 70.0%

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

      6. neg-mul-1 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in y1 around inf 70.9%

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

   if -1.64999999999999998e258 < j < -4.1999999999999997e179

   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 x around inf 53.9%

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

   4. Taylor expanded in y2 around inf 70.3%

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

   if -4.1999999999999997e179 < j < -0.35999999999999999

   1. Initial program 20.6%

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

   3. Taylor expanded in b around inf 36.5%

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

   4. Taylor expanded in x around inf 47.4%

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

   if -0.35999999999999999 < j < 2.05000000000000007e-252

   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 y4 around inf 48.8%

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

   4. Taylor expanded in y2 around inf 52.8%

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

      1. *-commutative 52.8%

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

   6. Simplified 52.8%

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

   if 2.05000000000000007e-252 < j < 8.5e-127

   1. Initial program 35.2%

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

   3. Taylor expanded in b around inf 60.2%

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

   4. Taylor expanded in a around inf 51.1%

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

   if 8.5e-127 < j < 1.7e10

   1. Initial program 34.4%

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

   3. Taylor expanded in a around inf 41.7%

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

      1. +-commutative 41.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 41.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 41.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 52.4%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(b \cdot y - y1 \cdot y2\right)\right)} \]

   if 1.7e10 < j < 6.0000000000000004e64

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 40.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 40.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 40.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 40.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 40.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 40.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 40.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y5 around -inf 60.6%

      \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 60.6%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot y5\right) \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]

      2. neg-mul-1 60.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(-y5\right)} \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \]

   8. Simplified 60.6%

      \[\leadsto k \cdot \color{blue}{\left(\left(-y5\right) \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]

   if 6.0000000000000004e64 < j < 3.39999999999999993e112

   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 a around inf 55.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 55.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 55.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 55.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 55.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 55.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 55.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 55.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 55.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 73.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 3.39999999999999993e112 < j

   1. Initial program 14.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 49.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in j around inf 50.1%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 54.5%

         \[\leadsto \color{blue}{\left(j \cdot y4\right) \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)} \]

      2. *-commutative 54.5%

         \[\leadsto \color{blue}{\left(y4 \cdot j\right)} \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right) \]

      3. +-commutative 54.5%

         \[\leadsto \left(y4 \cdot j\right) \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)} \]

      4. mul-1-neg 54.5%

         \[\leadsto \left(y4 \cdot j\right) \cdot \left(b \cdot t + \color{blue}{\left(-y1 \cdot y3\right)}\right) \]

      5. unsub-neg 54.5%

         \[\leadsto \left(y4 \cdot j\right) \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)} \]

      6. *-commutative 54.5%

         \[\leadsto \left(y4 \cdot j\right) \cdot \left(\color{blue}{t \cdot b} - y1 \cdot y3\right) \]

   6. Simplified 54.5%

      \[\leadsto \color{blue}{\left(y4 \cdot j\right) \cdot \left(t \cdot b - y1 \cdot y3\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+258}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -0.36:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{-252}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 17000000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+64}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b - y1 \cdot y3\right) \cdot \left(j \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.18 \cdot 10^{+117}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y2 \leq -1.1 \cdot 10^{+79}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.45 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.7 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 9.6 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.18e+117)
   (* y2 (* y4 (- (* k y1) (* t c))))
   (if (<= y2 -1.1e+79)
     (* k (* y (- (* i y5) (* b y4))))
     (if (<= y2 -1.45e+32)
       (* b (* a (- (* x y) (* z t))))
       (if (<= y2 3.2e-200)
         (* a (* y (- (* x b) (* y3 y5))))
         (if (<= y2 3.7e-176)
           (* j (* x (- (* i y1) (* b y0))))
           (if (<= y2 4.2e-132)
             (* c (* i (* z t)))
             (if (<= y2 9.6e-40)
               (* b (* x (- (* y a) (* j y0))))
               (if (<= y2 1.45e+49)
                 (* b (* y (- (* x a) (* k y4))))
                 (* k (* y2 (- (* y1 y4) (* y0 y5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.18e+117) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y2 <= -1.1e+79) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y2 <= -1.45e+32) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y2 <= 3.2e-200) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y2 <= 3.7e-176) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y2 <= 4.2e-132) {
		tmp = c * (i * (z * t));
	} else if (y2 <= 9.6e-40) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 1.45e+49) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.18d+117)) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y2 <= (-1.1d+79)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (y2 <= (-1.45d+32)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y2 <= 3.2d-200) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y2 <= 3.7d-176) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y2 <= 4.2d-132) then
        tmp = c * (i * (z * t))
    else if (y2 <= 9.6d-40) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y2 <= 1.45d+49) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.18e+117) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y2 <= -1.1e+79) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y2 <= -1.45e+32) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y2 <= 3.2e-200) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y2 <= 3.7e-176) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y2 <= 4.2e-132) {
		tmp = c * (i * (z * t));
	} else if (y2 <= 9.6e-40) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 1.45e+49) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.18e+117:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y2 <= -1.1e+79:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif y2 <= -1.45e+32:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y2 <= 3.2e-200:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y2 <= 3.7e-176:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y2 <= 4.2e-132:
		tmp = c * (i * (z * t))
	elif y2 <= 9.6e-40:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y2 <= 1.45e+49:
		tmp = b * (y * ((x * a) - (k * y4)))
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.18e+117)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y2 <= -1.1e+79)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (y2 <= -1.45e+32)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y2 <= 3.2e-200)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y2 <= 3.7e-176)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y2 <= 4.2e-132)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (y2 <= 9.6e-40)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y2 <= 1.45e+49)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.18e+117)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y2 <= -1.1e+79)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (y2 <= -1.45e+32)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y2 <= 3.2e-200)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y2 <= 3.7e-176)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y2 <= 4.2e-132)
		tmp = c * (i * (z * t));
	elseif (y2 <= 9.6e-40)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y2 <= 1.45e+49)
		tmp = b * (y * ((x * a) - (k * y4)));
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.18e+117], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.1e+79], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.45e+32], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.2e-200], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.7e-176], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.2e-132], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.6e-40], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.45e+49], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y2 < -1.18e117

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 35.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in y2 around inf 65.0%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto y2 \cdot \left(y4 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   6. Simplified 65.0%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   if -1.18e117 < y2 < -1.0999999999999999e79

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 55.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 55.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 55.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 55.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 55.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 55.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 55.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 59.6%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]

   if -1.0999999999999999e79 < y2 < -1.45000000000000001e32

   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 b around inf 50.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 60.8%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.45000000000000001e32 < y2 < 3.19999999999999983e-200

   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 a around inf 40.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 40.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 40.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 40.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 40.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 40.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 40.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 40.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 40.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf 41.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 41.4%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 41.4%

         \[\leadsto a \cdot \left(y \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      3. unsub-neg 41.4%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   8. Simplified 41.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if 3.19999999999999983e-200 < y2 < 3.69999999999999984e-176

   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 60.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 83.5%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 3.69999999999999984e-176 < y2 < 4.2000000000000002e-132

   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 z around -inf 40.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in c around inf 32.4%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(z \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 32.4%

         \[\leadsto -1 \cdot \left(c \cdot \left(z \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)}\right)\right) \]

      2. mul-1-neg 32.4%

         \[\leadsto -1 \cdot \left(c \cdot \left(z \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right)\right) \]

      3. unsub-neg 32.4%

         \[\leadsto -1 \cdot \left(c \cdot \left(z \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right)\right) \]

   6. Simplified 32.4%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(z \cdot \left(y0 \cdot y3 - i \cdot t\right)\right)\right)} \]

   7. Taylor expanded in y0 around 0 51.7%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 51.7%

         \[\leadsto -1 \cdot \color{blue}{\left(-c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]

      2. *-commutative 51.7%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c}\right) \]

      3. distribute-lft-neg-in 51.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-i \cdot \left(t \cdot z\right)\right) \cdot c\right)} \]

      4. *-commutative 51.7%

         \[\leadsto -1 \cdot \left(\left(-\color{blue}{\left(t \cdot z\right) \cdot i}\right) \cdot c\right) \]

      5. distribute-lft-neg-in 51.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(\left(-t \cdot z\right) \cdot i\right)} \cdot c\right) \]

      6. *-commutative 51.7%

         \[\leadsto -1 \cdot \left(\left(\left(-\color{blue}{z \cdot t}\right) \cdot i\right) \cdot c\right) \]

      7. distribute-lft-neg-in 51.7%

         \[\leadsto -1 \cdot \left(\left(\color{blue}{\left(\left(-z\right) \cdot t\right)} \cdot i\right) \cdot c\right) \]

   9. Simplified 51.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(\left(\left(-z\right) \cdot t\right) \cdot i\right) \cdot c\right)} \]

   if 4.2000000000000002e-132 < y2 < 9.59999999999999965e-40

   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 b around inf 30.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 61.1%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 9.59999999999999965e-40 < y2 < 1.45e49

   1. Initial program 45.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 51.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 65.7%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 65.7%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 65.7%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 65.7%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 65.7%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if 1.45e49 < y2

   1. Initial program 14.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 45.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 45.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 45.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 45.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 45.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 45.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 45.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf 51.2%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.18 \cdot 10^{+117}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y2 \leq -1.1 \cdot 10^{+79}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.45 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.7 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 9.6 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-69}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* x (- (* i y1) (* b y0))))))
   (if (<= y -1.4e+144)
     (* b (* y (- (* x a) (* k y4))))
     (if (<= y -8.6e+103)
       (* b (* j (* t y4)))
       (if (<= y -6.4e+59)
         (* c (* y4 (- (* y y3) (* t y2))))
         (if (<= y -2.05e-174)
           t_1
           (if (<= y -7.3e-298)
             (* x (* y2 (- (* c y0) (* a y1))))
             (if (<= y 3.2e-253)
               t_1
               (if (<= y 9.5e-69)
                 (* a (* t (- (* y2 y5) (* z b))))
                 (if (<= y 9e+121)
                   (* a (* y1 (- (* z y3) (* x y2))))
                   (* k (* y (- (* i y5) (* b y4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (x * ((i * y1) - (b * y0)));
	double tmp;
	if (y <= -1.4e+144) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -8.6e+103) {
		tmp = b * (j * (t * y4));
	} else if (y <= -6.4e+59) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y <= -2.05e-174) {
		tmp = t_1;
	} else if (y <= -7.3e-298) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y <= 3.2e-253) {
		tmp = t_1;
	} else if (y <= 9.5e-69) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (y <= 9e+121) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = k * (y * ((i * y5) - (b * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (x * ((i * y1) - (b * y0)))
    if (y <= (-1.4d+144)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= (-8.6d+103)) then
        tmp = b * (j * (t * y4))
    else if (y <= (-6.4d+59)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y <= (-2.05d-174)) then
        tmp = t_1
    else if (y <= (-7.3d-298)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y <= 3.2d-253) then
        tmp = t_1
    else if (y <= 9.5d-69) then
        tmp = a * (t * ((y2 * y5) - (z * b)))
    else if (y <= 9d+121) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else
        tmp = k * (y * ((i * y5) - (b * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (x * ((i * y1) - (b * y0)));
	double tmp;
	if (y <= -1.4e+144) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -8.6e+103) {
		tmp = b * (j * (t * y4));
	} else if (y <= -6.4e+59) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y <= -2.05e-174) {
		tmp = t_1;
	} else if (y <= -7.3e-298) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y <= 3.2e-253) {
		tmp = t_1;
	} else if (y <= 9.5e-69) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (y <= 9e+121) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = k * (y * ((i * y5) - (b * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (x * ((i * y1) - (b * y0)))
	tmp = 0
	if y <= -1.4e+144:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= -8.6e+103:
		tmp = b * (j * (t * y4))
	elif y <= -6.4e+59:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y <= -2.05e-174:
		tmp = t_1
	elif y <= -7.3e-298:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y <= 3.2e-253:
		tmp = t_1
	elif y <= 9.5e-69:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	elif y <= 9e+121:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	else:
		tmp = k * (y * ((i * y5) - (b * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))))
	tmp = 0.0
	if (y <= -1.4e+144)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= -8.6e+103)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y <= -6.4e+59)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y <= -2.05e-174)
		tmp = t_1;
	elseif (y <= -7.3e-298)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y <= 3.2e-253)
		tmp = t_1;
	elseif (y <= 9.5e-69)
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (y <= 9e+121)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (x * ((i * y1) - (b * y0)));
	tmp = 0.0;
	if (y <= -1.4e+144)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= -8.6e+103)
		tmp = b * (j * (t * y4));
	elseif (y <= -6.4e+59)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y <= -2.05e-174)
		tmp = t_1;
	elseif (y <= -7.3e-298)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y <= 3.2e-253)
		tmp = t_1;
	elseif (y <= 9.5e-69)
		tmp = a * (t * ((y2 * y5) - (z * b)));
	elseif (y <= 9e+121)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	else
		tmp = k * (y * ((i * y5) - (b * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+144], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.6e+103], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.4e+59], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.05e-174], t$95$1, If[LessEqual[y, -7.3e-298], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-253], t$95$1, If[LessEqual[y, 9.5e-69], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+121], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -1.40000000000000003e144

   1. Initial program 16.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 30.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 61.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 61.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 61.5%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 61.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 61.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -1.40000000000000003e144 < y < -8.59999999999999938e103

   1. Initial program 41.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 42.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 42.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 67.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 67.2%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   7. Simplified 67.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -8.59999999999999938e103 < y < -6.39999999999999964e59

   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 y4 around inf 45.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 64.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 64.1%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 64.1%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   6. Simplified 64.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if -6.39999999999999964e59 < y < -2.05e-174 or -7.3000000000000003e-298 < y < 3.1999999999999997e-253

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 40.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 39.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -2.05e-174 < y < -7.3000000000000003e-298

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 39.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 47.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   if 3.1999999999999997e-253 < y < 9.50000000000000094e-69

   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 a around inf 42.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 42.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 42.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 48.0%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 48.0%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 48.0%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 48.0%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   if 9.50000000000000094e-69 < y < 9.0000000000000007e121

   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 a around inf 52.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 52.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 52.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 46.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 9.0000000000000007e121 < y

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 50.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 50.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 50.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 50.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 50.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 50.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 50.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 55.7%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-174}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-253}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-69}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+103}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-252}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-64}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y (- (* x a) (* k y4))))))
   (if (<= y -2.1e+142)
     t_1
     (if (<= y -5.3e+103)
       (* b (* j (* t y4)))
       (if (<= y -1.25e+103)
         (* a (* (* x y) b))
         (if (<= y -7.4e+59)
           (* c (* y4 (- (* y y3) (* t y2))))
           (if (<= y -1.1e+23)
             t_1
             (if (<= y 1.2e-252)
               (* j (* x (- (* i y1) (* b y0))))
               (if (<= y 1.35e-64)
                 (* a (* t (- (* y2 y5) (* z b))))
                 (if (<= y 2.1e+124)
                   (* a (* y1 (- (* z y3) (* x y2))))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y * ((x * a) - (k * y4)));
	double tmp;
	if (y <= -2.1e+142) {
		tmp = t_1;
	} else if (y <= -5.3e+103) {
		tmp = b * (j * (t * y4));
	} else if (y <= -1.25e+103) {
		tmp = a * ((x * y) * b);
	} else if (y <= -7.4e+59) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y <= -1.1e+23) {
		tmp = t_1;
	} else if (y <= 1.2e-252) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 1.35e-64) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (y <= 2.1e+124) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} 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 * (y * ((x * a) - (k * y4)))
    if (y <= (-2.1d+142)) then
        tmp = t_1
    else if (y <= (-5.3d+103)) then
        tmp = b * (j * (t * y4))
    else if (y <= (-1.25d+103)) then
        tmp = a * ((x * y) * b)
    else if (y <= (-7.4d+59)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y <= (-1.1d+23)) then
        tmp = t_1
    else if (y <= 1.2d-252) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y <= 1.35d-64) then
        tmp = a * (t * ((y2 * y5) - (z * b)))
    else if (y <= 2.1d+124) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    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 * (y * ((x * a) - (k * y4)));
	double tmp;
	if (y <= -2.1e+142) {
		tmp = t_1;
	} else if (y <= -5.3e+103) {
		tmp = b * (j * (t * y4));
	} else if (y <= -1.25e+103) {
		tmp = a * ((x * y) * b);
	} else if (y <= -7.4e+59) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y <= -1.1e+23) {
		tmp = t_1;
	} else if (y <= 1.2e-252) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 1.35e-64) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (y <= 2.1e+124) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} 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 * (y * ((x * a) - (k * y4)))
	tmp = 0
	if y <= -2.1e+142:
		tmp = t_1
	elif y <= -5.3e+103:
		tmp = b * (j * (t * y4))
	elif y <= -1.25e+103:
		tmp = a * ((x * y) * b)
	elif y <= -7.4e+59:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y <= -1.1e+23:
		tmp = t_1
	elif y <= 1.2e-252:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y <= 1.35e-64:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	elif y <= 2.1e+124:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	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(y * Float64(Float64(x * a) - Float64(k * y4))))
	tmp = 0.0
	if (y <= -2.1e+142)
		tmp = t_1;
	elseif (y <= -5.3e+103)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y <= -1.25e+103)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y <= -7.4e+59)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y <= -1.1e+23)
		tmp = t_1;
	elseif (y <= 1.2e-252)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y <= 1.35e-64)
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (y <= 2.1e+124)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	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 * (y * ((x * a) - (k * y4)));
	tmp = 0.0;
	if (y <= -2.1e+142)
		tmp = t_1;
	elseif (y <= -5.3e+103)
		tmp = b * (j * (t * y4));
	elseif (y <= -1.25e+103)
		tmp = a * ((x * y) * b);
	elseif (y <= -7.4e+59)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y <= -1.1e+23)
		tmp = t_1;
	elseif (y <= 1.2e-252)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y <= 1.35e-64)
		tmp = a * (t * ((y2 * y5) - (z * b)));
	elseif (y <= 2.1e+124)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	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[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+142], t$95$1, If[LessEqual[y, -5.3e+103], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e+103], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.4e+59], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e+23], t$95$1, If[LessEqual[y, 1.2e-252], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-64], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+124], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -2.1e142 or -7.39999999999999995e59 < y < -1.10000000000000004e23 or 2.10000000000000011e124 < y

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 39.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 60.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 60.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 60.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 60.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 60.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -2.1e142 < y < -5.29999999999999969e103

   1. Initial program 41.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 42.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 42.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 67.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 67.2%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   7. Simplified 67.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -5.29999999999999969e103 < y < -1.25e103

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 0.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 100.0%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 100.0%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if -1.25e103 < y < -7.39999999999999995e59

   1. Initial program 39.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 50.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 70.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 70.4%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 70.4%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   6. Simplified 70.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if -1.10000000000000004e23 < y < 1.2000000000000001e-252

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 40.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 34.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 1.2000000000000001e-252 < y < 1.34999999999999993e-64

   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 a around inf 42.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 42.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 42.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 48.0%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 48.0%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 48.0%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 48.0%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   if 1.34999999999999993e-64 < y < 2.10000000000000011e124

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 51.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 51.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 51.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 51.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 51.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 51.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 51.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 51.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 51.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+142}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+103}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-252}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-64}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.05 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+39}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - \left(i \cdot y1 + \frac{y5 \cdot \left(y0 \cdot y2 - y \cdot i\right)}{z}\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-38}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= b -5e+182)
     t_1
     (if (<= b -4.05e+105)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= b -1.8e+39)
         (*
          k
          (* z (- (* b y0) (+ (* i y1) (/ (* y5 (- (* y0 y2) (* y i))) z)))))
         (if (<= b 2.1e-38)
           (*
            c
            (+
             (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
             (* y4 (- (* y y3) (* t y2)))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (b <= -5e+182) {
		tmp = t_1;
	} else if (b <= -4.05e+105) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= -1.8e+39) {
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	} else if (b <= 2.1e-38) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} 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 * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    if (b <= (-5d+182)) then
        tmp = t_1
    else if (b <= (-4.05d+105)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (b <= (-1.8d+39)) then
        tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))))
    else if (b <= 2.1d-38) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    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 * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (b <= -5e+182) {
		tmp = t_1;
	} else if (b <= -4.05e+105) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= -1.8e+39) {
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	} else if (b <= 2.1e-38) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} 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 * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if b <= -5e+182:
		tmp = t_1
	elif b <= -4.05e+105:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif b <= -1.8e+39:
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))))
	elif b <= 2.1e-38:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	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(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (b <= -5e+182)
		tmp = t_1;
	elseif (b <= -4.05e+105)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (b <= -1.8e+39)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(Float64(i * y1) + Float64(Float64(y5 * Float64(Float64(y0 * y2) - Float64(y * i))) / z)))));
	elseif (b <= 2.1e-38)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	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 * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (b <= -5e+182)
		tmp = t_1;
	elseif (b <= -4.05e+105)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (b <= -1.8e+39)
		tmp = k * (z * ((b * y0) - ((i * y1) + ((y5 * ((y0 * y2) - (y * i))) / z))));
	elseif (b <= 2.1e-38)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	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[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+182], t$95$1, If[LessEqual[b, -4.05e+105], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.8e+39], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(N[(i * y1), $MachinePrecision] + N[(N[(y5 * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-38], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.99999999999999973e182 or 2.10000000000000013e-38 < b

   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 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 -4.99999999999999973e182 < b < -4.04999999999999999e105

   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 a around inf 62.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 62.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 62.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 62.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 62.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 62.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 62.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 62.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 62.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 62.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around -inf 81.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(z \cdot \left(b \cdot t - y1 \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 81.7%

         \[\leadsto \color{blue}{-a \cdot \left(z \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   8. Simplified 81.7%

      \[\leadsto \color{blue}{-a \cdot \left(z \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   if -4.04999999999999999e105 < b < -1.79999999999999992e39

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 63.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 63.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 63.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 63.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 63.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 63.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 63.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around -inf 87.5%

      \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(\left(-1 \cdot \frac{y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)}{z} + i \cdot y1\right) - b \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 87.5%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot z\right) \cdot \left(\left(-1 \cdot \frac{y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)}{z} + i \cdot y1\right) - b \cdot y0\right)\right)} \]

      2. neg-mul-1 87.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(-z\right)} \cdot \left(\left(-1 \cdot \frac{y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)}{z} + i \cdot y1\right) - b \cdot y0\right)\right) \]

      3. +-commutative 87.5%

         \[\leadsto k \cdot \left(\left(-z\right) \cdot \left(\color{blue}{\left(i \cdot y1 + -1 \cdot \frac{y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)}{z}\right)} - b \cdot y0\right)\right) \]

      4. mul-1-neg 87.5%

         \[\leadsto k \cdot \left(\left(-z\right) \cdot \left(\left(i \cdot y1 + \color{blue}{\left(-\frac{y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)}{z}\right)}\right) - b \cdot y0\right)\right) \]

      5. unsub-neg 87.5%

         \[\leadsto k \cdot \left(\left(-z\right) \cdot \left(\color{blue}{\left(i \cdot y1 - \frac{y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)}{z}\right)} - b \cdot y0\right)\right) \]

   8. Simplified 87.5%

      \[\leadsto k \cdot \color{blue}{\left(\left(-z\right) \cdot \left(\left(i \cdot y1 - \frac{y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)}{z}\right) - b \cdot y0\right)\right)} \]

   9. Taylor expanded in y5 around -inf 87.5%

      \[\leadsto k \cdot \left(\left(-z\right) \cdot \left(\left(i \cdot y1 - \color{blue}{-1 \cdot \frac{y5 \cdot \left(y0 \cdot y2 - i \cdot y\right)}{z}}\right) - b \cdot y0\right)\right) \]

   if -1.79999999999999992e39 < b < 2.10000000000000013e-38

   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 c around inf 45.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. mul-1-neg 45.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. unsub-neg 45.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. *-commutative 45.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative 45.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-commutative 45.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-commutative 45.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 45.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+182}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -4.05 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+39}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - \left(i \cdot y1 + \frac{y5 \cdot \left(y0 \cdot y2 - y \cdot i\right)}{z}\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-38}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ t_2 := a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ t_3 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.56 \cdot 10^{+129}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+229}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (* t y4))))
        (t_2 (* a (* t (- (* y2 y5) (* z b)))))
        (t_3 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= t -2.1e+211)
     t_1
     (if (<= t -2.56e+129)
       t_3
       (if (<= t -3.2e+100)
         t_1
         (if (<= t -8.5e-53)
           t_2
           (if (<= t -2.7e-163)
             (* b (* x (- (* y a) (* j y0))))
             (if (<= t 6e+33)
               (* a (* y (- (* x b) (* y3 y5))))
               (if (<= t 7e+229) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * (t * y4));
	double t_2 = a * (t * ((y2 * y5) - (z * b)));
	double t_3 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (t <= -2.1e+211) {
		tmp = t_1;
	} else if (t <= -2.56e+129) {
		tmp = t_3;
	} else if (t <= -3.2e+100) {
		tmp = t_1;
	} else if (t <= -8.5e-53) {
		tmp = t_2;
	} else if (t <= -2.7e-163) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 6e+33) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 7e+229) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (j * (t * y4))
    t_2 = a * (t * ((y2 * y5) - (z * b)))
    t_3 = c * (y4 * ((y * y3) - (t * y2)))
    if (t <= (-2.1d+211)) then
        tmp = t_1
    else if (t <= (-2.56d+129)) then
        tmp = t_3
    else if (t <= (-3.2d+100)) then
        tmp = t_1
    else if (t <= (-8.5d-53)) then
        tmp = t_2
    else if (t <= (-2.7d-163)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (t <= 6d+33) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (t <= 7d+229) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * (t * y4));
	double t_2 = a * (t * ((y2 * y5) - (z * b)));
	double t_3 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (t <= -2.1e+211) {
		tmp = t_1;
	} else if (t <= -2.56e+129) {
		tmp = t_3;
	} else if (t <= -3.2e+100) {
		tmp = t_1;
	} else if (t <= -8.5e-53) {
		tmp = t_2;
	} else if (t <= -2.7e-163) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 6e+33) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 7e+229) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (j * (t * y4))
	t_2 = a * (t * ((y2 * y5) - (z * b)))
	t_3 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if t <= -2.1e+211:
		tmp = t_1
	elif t <= -2.56e+129:
		tmp = t_3
	elif t <= -3.2e+100:
		tmp = t_1
	elif t <= -8.5e-53:
		tmp = t_2
	elif t <= -2.7e-163:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif t <= 6e+33:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif t <= 7e+229:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(t * y4)))
	t_2 = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))))
	t_3 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (t <= -2.1e+211)
		tmp = t_1;
	elseif (t <= -2.56e+129)
		tmp = t_3;
	elseif (t <= -3.2e+100)
		tmp = t_1;
	elseif (t <= -8.5e-53)
		tmp = t_2;
	elseif (t <= -2.7e-163)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (t <= 6e+33)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (t <= 7e+229)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (j * (t * y4));
	t_2 = a * (t * ((y2 * y5) - (z * b)));
	t_3 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (t <= -2.1e+211)
		tmp = t_1;
	elseif (t <= -2.56e+129)
		tmp = t_3;
	elseif (t <= -3.2e+100)
		tmp = t_1;
	elseif (t <= -8.5e-53)
		tmp = t_2;
	elseif (t <= -2.7e-163)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (t <= 6e+33)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (t <= 7e+229)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+211], t$95$1, If[LessEqual[t, -2.56e+129], t$95$3, If[LessEqual[t, -3.2e+100], t$95$1, If[LessEqual[t, -8.5e-53], t$95$2, If[LessEqual[t, -2.7e-163], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+33], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+229], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.1e211 or -2.55999999999999988e129 < t < -3.1999999999999999e100

   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 40.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 45.2%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 64.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 64.6%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   7. Simplified 64.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -2.1e211 < t < -2.55999999999999988e129 or 5.99999999999999967e33 < t < 7.0000000000000005e229

   1. Initial program 20.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 41.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 48.0%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 48.0%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 48.0%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   6. Simplified 48.0%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if -3.1999999999999999e100 < t < -8.50000000000000044e-53 or 7.0000000000000005e229 < t

   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 a around inf 36.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 36.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 36.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 36.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 36.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 36.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 36.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 36.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 36.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 36.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 51.0%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 51.0%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 51.0%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 51.0%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 51.0%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   if -8.50000000000000044e-53 < t < -2.70000000000000015e-163

   1. Initial program 40.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 56.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 52.6%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -2.70000000000000015e-163 < t < 5.99999999999999967e33

   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 a around inf 41.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 41.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 41.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 41.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 41.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 41.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 41.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 41.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 41.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf 40.2%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 40.2%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 40.2%

         \[\leadsto a \cdot \left(y \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      3. unsub-neg 40.2%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+211}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -2.56 \cdot 10^{+129}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-53}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+229}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.2 \cdot 10^{+259}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -0.9:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 5.7 \cdot 10^{-249}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 24000000000:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot \left(a - k \cdot \frac{y4}{x}\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b - y1 \cdot y3\right) \cdot \left(j \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.2e+259)
   (* k (* y1 (- (* y2 y4) (* z i))))
   (if (<= j -1.3e+175)
     (* x (* y2 (- (* c y0) (* a y1))))
     (if (<= j -0.9)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= j 5.7e-249)
         (* y2 (* y4 (- (* k y1) (* t c))))
         (if (<= j 24000000000.0)
           (* b (* y (* x (- a (* k (/ y4 x))))))
           (if (<= j 3.4e+112)
             (* a (* y1 (- (* z y3) (* x y2))))
             (* (- (* t b) (* y1 y3)) (* j y4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.2e+259) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -1.3e+175) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= -0.9) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= 5.7e-249) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 24000000000.0) {
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	} else if (j <= 3.4e+112) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-1.2d+259)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (j <= (-1.3d+175)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (j <= (-0.9d0)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (j <= 5.7d-249) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (j <= 24000000000.0d0) then
        tmp = b * (y * (x * (a - (k * (y4 / x)))))
    else if (j <= 3.4d+112) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else
        tmp = ((t * b) - (y1 * y3)) * (j * y4)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.2e+259) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (j <= -1.3e+175) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= -0.9) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= 5.7e-249) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 24000000000.0) {
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	} else if (j <= 3.4e+112) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -1.2e+259:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif j <= -1.3e+175:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif j <= -0.9:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif j <= 5.7e-249:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif j <= 24000000000.0:
		tmp = b * (y * (x * (a - (k * (y4 / x)))))
	elif j <= 3.4e+112:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	else:
		tmp = ((t * b) - (y1 * y3)) * (j * y4)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.2e+259)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (j <= -1.3e+175)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (j <= -0.9)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (j <= 5.7e-249)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 24000000000.0)
		tmp = Float64(b * Float64(y * Float64(x * Float64(a - Float64(k * Float64(y4 / x))))));
	elseif (j <= 3.4e+112)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(Float64(Float64(t * b) - Float64(y1 * y3)) * Float64(j * y4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -1.2e+259)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (j <= -1.3e+175)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (j <= -0.9)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (j <= 5.7e-249)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (j <= 24000000000.0)
		tmp = b * (y * (x * (a - (k * (y4 / x)))));
	elseif (j <= 3.4e+112)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	else
		tmp = ((t * b) - (y1 * y3)) * (j * y4);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.2e+259], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.3e+175], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -0.9], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.7e-249], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 24000000000.0], N[(b * N[(y * N[(x * N[(a - N[(k * N[(y4 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e+112], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision] * N[(j * y4), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.2e259

   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 k around inf 70.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 70.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 70.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 70.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 70.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 70.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 70.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 70.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y1 around inf 70.9%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   if -1.2e259 < j < -1.3e175

   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 x around inf 53.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 70.3%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   if -1.3e175 < j < -0.900000000000000022

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 36.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 47.4%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -0.900000000000000022 < j < 5.69999999999999963e-249

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 50.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in y2 around inf 52.8%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 52.8%

         \[\leadsto y2 \cdot \left(y4 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   6. Simplified 52.8%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   if 5.69999999999999963e-249 < j < 2.4e10

   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 43.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in x around inf 45.8%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(x \cdot \left(a + -1 \cdot \frac{k \cdot y4}{x}\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 45.8%

         \[\leadsto b \cdot \left(y \cdot \left(x \cdot \left(a + \color{blue}{\left(-\frac{k \cdot y4}{x}\right)}\right)\right)\right) \]

      2. unsub-neg 45.8%

         \[\leadsto b \cdot \left(y \cdot \left(x \cdot \color{blue}{\left(a - \frac{k \cdot y4}{x}\right)}\right)\right) \]

      3. associate-/l* 47.4%

         \[\leadsto b \cdot \left(y \cdot \left(x \cdot \left(a - \color{blue}{k \cdot \frac{y4}{x}}\right)\right)\right) \]

   9. Simplified 47.4%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(x \cdot \left(a - k \cdot \frac{y4}{x}\right)\right)}\right) \]

   if 2.4e10 < j < 3.39999999999999993e112

   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 a around inf 43.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 43.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 43.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 43.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 43.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 43.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 43.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 43.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 43.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 53.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 3.39999999999999993e112 < j

   1. Initial program 14.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf 49.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in j around inf 50.1%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 54.5%

         \[\leadsto \color{blue}{\left(j \cdot y4\right) \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)} \]

      2. *-commutative 54.5%

         \[\leadsto \color{blue}{\left(y4 \cdot j\right)} \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right) \]

      3. +-commutative 54.5%

         \[\leadsto \left(y4 \cdot j\right) \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)} \]

      4. mul-1-neg 54.5%

         \[\leadsto \left(y4 \cdot j\right) \cdot \left(b \cdot t + \color{blue}{\left(-y1 \cdot y3\right)}\right) \]

      5. unsub-neg 54.5%

         \[\leadsto \left(y4 \cdot j\right) \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)} \]

      6. *-commutative 54.5%

         \[\leadsto \left(y4 \cdot j\right) \cdot \left(\color{blue}{t \cdot b} - y1 \cdot y3\right) \]

   6. Simplified 54.5%

      \[\leadsto \color{blue}{\left(y4 \cdot j\right) \cdot \left(t \cdot b - y1 \cdot y3\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.2 \cdot 10^{+259}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -0.9:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 5.7 \cdot 10^{-249}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 24000000000:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot \left(a - k \cdot \frac{y4}{x}\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b - y1 \cdot y3\right) \cdot \left(j \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 32.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+142}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-251}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-66}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -9.8e+142)
   (* b (* y (- (* x a) (* k y4))))
   (if (<= y -5.3e+103)
     (* b (* j (* t y4)))
     (if (<= y -7e+59)
       (* c (* y4 (- (* y y3) (* t y2))))
       (if (<= y 8e-251)
         (* j (* x (- (* i y1) (* b y0))))
         (if (<= y 9e-66)
           (* a (* t (- (* y2 y5) (* z b))))
           (if (<= y 3.6e+120)
             (* a (* y1 (- (* z y3) (* x y2))))
             (* k (* y (- (* i y5) (* b y4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -9.8e+142) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -5.3e+103) {
		tmp = b * (j * (t * y4));
	} else if (y <= -7e+59) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y <= 8e-251) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 9e-66) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (y <= 3.6e+120) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = k * (y * ((i * y5) - (b * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-9.8d+142)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y <= (-5.3d+103)) then
        tmp = b * (j * (t * y4))
    else if (y <= (-7d+59)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y <= 8d-251) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y <= 9d-66) then
        tmp = a * (t * ((y2 * y5) - (z * b)))
    else if (y <= 3.6d+120) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else
        tmp = k * (y * ((i * y5) - (b * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -9.8e+142) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y <= -5.3e+103) {
		tmp = b * (j * (t * y4));
	} else if (y <= -7e+59) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y <= 8e-251) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 9e-66) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (y <= 3.6e+120) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = k * (y * ((i * y5) - (b * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -9.8e+142:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y <= -5.3e+103:
		tmp = b * (j * (t * y4))
	elif y <= -7e+59:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y <= 8e-251:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y <= 9e-66:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	elif y <= 3.6e+120:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	else:
		tmp = k * (y * ((i * y5) - (b * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -9.8e+142)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= -5.3e+103)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y <= -7e+59)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y <= 8e-251)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y <= 9e-66)
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (y <= 3.6e+120)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -9.8e+142)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y <= -5.3e+103)
		tmp = b * (j * (t * y4));
	elseif (y <= -7e+59)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y <= 8e-251)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y <= 9e-66)
		tmp = a * (t * ((y2 * y5) - (z * b)));
	elseif (y <= 3.6e+120)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	else
		tmp = k * (y * ((i * y5) - (b * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -9.8e+142], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.3e+103], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e+59], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-251], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-66], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+120], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -9.80000000000000101e142

   1. Initial program 16.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 30.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 61.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 61.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 61.5%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 61.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 61.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -9.80000000000000101e142 < y < -5.29999999999999969e103

   1. Initial program 41.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 42.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 42.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 67.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 67.2%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   7. Simplified 67.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -5.29999999999999969e103 < y < -7e59

   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 y4 around inf 45.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in c around inf 64.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 64.1%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 64.1%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   6. Simplified 64.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if -7e59 < y < 8.00000000000000012e-251

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 40.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in j around inf 34.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 8.00000000000000012e-251 < y < 8.9999999999999995e-66

   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 a around inf 42.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 42.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 42.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 42.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 48.0%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 48.0%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 48.0%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 48.0%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   if 8.9999999999999995e-66 < y < 3.60000000000000016e120

   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 a around inf 52.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 52.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 52.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 52.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 46.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 3.60000000000000016e120 < y

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 50.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 50.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 50.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 50.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 50.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 50.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 50.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 55.7%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+142}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-251}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-66}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 22.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ t_2 := b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-299}:\\ \;\;\;\;b \cdot \left(y \cdot \left(y4 \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-240}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \left(b \cdot j\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y (* x a)))) (t_2 (* b (* y4 (* t j)))))
   (if (<= x -6.8e-35)
     t_1
     (if (<= x -1.46e-154)
       t_2
       (if (<= x -1.65e-299)
         (* b (* y (* y4 (- k))))
         (if (<= x 2.35e-240)
           (* (* t y4) (* b j))
           (if (<= x 3.2e-80)
             (* a (* t (* y2 y5)))
             (if (<= x 2.75e+42) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y * (x * a));
	double t_2 = b * (y4 * (t * j));
	double tmp;
	if (x <= -6.8e-35) {
		tmp = t_1;
	} else if (x <= -1.46e-154) {
		tmp = t_2;
	} else if (x <= -1.65e-299) {
		tmp = b * (y * (y4 * -k));
	} else if (x <= 2.35e-240) {
		tmp = (t * y4) * (b * j);
	} else if (x <= 3.2e-80) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 2.75e+42) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y * (x * a))
    t_2 = b * (y4 * (t * j))
    if (x <= (-6.8d-35)) then
        tmp = t_1
    else if (x <= (-1.46d-154)) then
        tmp = t_2
    else if (x <= (-1.65d-299)) then
        tmp = b * (y * (y4 * -k))
    else if (x <= 2.35d-240) then
        tmp = (t * y4) * (b * j)
    else if (x <= 3.2d-80) then
        tmp = a * (t * (y2 * y5))
    else if (x <= 2.75d+42) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y * (x * a));
	double t_2 = b * (y4 * (t * j));
	double tmp;
	if (x <= -6.8e-35) {
		tmp = t_1;
	} else if (x <= -1.46e-154) {
		tmp = t_2;
	} else if (x <= -1.65e-299) {
		tmp = b * (y * (y4 * -k));
	} else if (x <= 2.35e-240) {
		tmp = (t * y4) * (b * j);
	} else if (x <= 3.2e-80) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 2.75e+42) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y * (x * a))
	t_2 = b * (y4 * (t * j))
	tmp = 0
	if x <= -6.8e-35:
		tmp = t_1
	elif x <= -1.46e-154:
		tmp = t_2
	elif x <= -1.65e-299:
		tmp = b * (y * (y4 * -k))
	elif x <= 2.35e-240:
		tmp = (t * y4) * (b * j)
	elif x <= 3.2e-80:
		tmp = a * (t * (y2 * y5))
	elif x <= 2.75e+42:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y * Float64(x * a)))
	t_2 = Float64(b * Float64(y4 * Float64(t * j)))
	tmp = 0.0
	if (x <= -6.8e-35)
		tmp = t_1;
	elseif (x <= -1.46e-154)
		tmp = t_2;
	elseif (x <= -1.65e-299)
		tmp = Float64(b * Float64(y * Float64(y4 * Float64(-k))));
	elseif (x <= 2.35e-240)
		tmp = Float64(Float64(t * y4) * Float64(b * j));
	elseif (x <= 3.2e-80)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (x <= 2.75e+42)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y * (x * a));
	t_2 = b * (y4 * (t * j));
	tmp = 0.0;
	if (x <= -6.8e-35)
		tmp = t_1;
	elseif (x <= -1.46e-154)
		tmp = t_2;
	elseif (x <= -1.65e-299)
		tmp = b * (y * (y4 * -k));
	elseif (x <= 2.35e-240)
		tmp = (t * y4) * (b * j);
	elseif (x <= 3.2e-80)
		tmp = a * (t * (y2 * y5));
	elseif (x <= 2.75e+42)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y4 * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e-35], t$95$1, If[LessEqual[x, -1.46e-154], t$95$2, If[LessEqual[x, -1.65e-299], N[(b * N[(y * N[(y4 * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.35e-240], N[(N[(t * y4), $MachinePrecision] * N[(b * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-80], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.75e+42], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.8000000000000005e-35 or 2.75000000000000001e42 < x

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 41.8%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x\right)}\right) \]

   if -6.8000000000000005e-35 < x < -1.46000000000000007e-154 or 3.1999999999999999e-80 < x < 2.75000000000000001e42

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 35.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 35.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 35.5%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t\right)}\right) \]

   if -1.46000000000000007e-154 < x < -1.6500000000000001e-299

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 34.6%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 34.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 34.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 34.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 34.6%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 28.1%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y4\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 28.1%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(-k \cdot y4\right)}\right) \]

      2. distribute-lft-neg-in 28.1%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(\left(-k\right) \cdot y4\right)}\right) \]

      3. *-commutative 28.1%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(y4 \cdot \left(-k\right)\right)}\right) \]

   9. Simplified 28.1%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(y4 \cdot \left(-k\right)\right)}\right) \]

   if -1.6500000000000001e-299 < x < 2.35000000000000006e-240

   1. Initial program 61.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 32.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 35.8%

         \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

      2. *-commutative 35.8%

         \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

      3. *-commutative 35.8%

         \[\leadsto \left(j \cdot b\right) \cdot \color{blue}{\left(y4 \cdot t\right)} \]

   7. Simplified 35.8%

      \[\leadsto \color{blue}{\left(j \cdot b\right) \cdot \left(y4 \cdot t\right)} \]

   if 2.35000000000000006e-240 < x < 3.1999999999999999e-80

   1. Initial program 22.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 37.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 37.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 37.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 34.4%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 34.4%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 34.4%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 34.4%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around inf 29.4%

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 29.4%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 29.4%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-299}:\\ \;\;\;\;b \cdot \left(y \cdot \left(y4 \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-240}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \left(b \cdot j\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(z \cdot \left(b \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-231}:\\ \;\;\;\;\left(b \cdot k\right) \cdot \left(y \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y (* x a)))))
   (if (<= x -4.8e-46)
     t_1
     (if (<= x 1.2e-304)
       (* a (* z (* b (- t))))
       (if (<= x 7.2e-231)
         (* (* b k) (* y (- y4)))
         (if (<= x 6e-80)
           (* a (* t (* y2 y5)))
           (if (<= x 1.45e+42) (* b (* y4 (* t j))) 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 * (y * (x * a));
	double tmp;
	if (x <= -4.8e-46) {
		tmp = t_1;
	} else if (x <= 1.2e-304) {
		tmp = a * (z * (b * -t));
	} else if (x <= 7.2e-231) {
		tmp = (b * k) * (y * -y4);
	} else if (x <= 6e-80) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 1.45e+42) {
		tmp = b * (y4 * (t * j));
	} 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 * (y * (x * a))
    if (x <= (-4.8d-46)) then
        tmp = t_1
    else if (x <= 1.2d-304) then
        tmp = a * (z * (b * -t))
    else if (x <= 7.2d-231) then
        tmp = (b * k) * (y * -y4)
    else if (x <= 6d-80) then
        tmp = a * (t * (y2 * y5))
    else if (x <= 1.45d+42) then
        tmp = b * (y4 * (t * j))
    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 * (y * (x * a));
	double tmp;
	if (x <= -4.8e-46) {
		tmp = t_1;
	} else if (x <= 1.2e-304) {
		tmp = a * (z * (b * -t));
	} else if (x <= 7.2e-231) {
		tmp = (b * k) * (y * -y4);
	} else if (x <= 6e-80) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 1.45e+42) {
		tmp = b * (y4 * (t * j));
	} 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 * (y * (x * a))
	tmp = 0
	if x <= -4.8e-46:
		tmp = t_1
	elif x <= 1.2e-304:
		tmp = a * (z * (b * -t))
	elif x <= 7.2e-231:
		tmp = (b * k) * (y * -y4)
	elif x <= 6e-80:
		tmp = a * (t * (y2 * y5))
	elif x <= 1.45e+42:
		tmp = b * (y4 * (t * j))
	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(y * Float64(x * a)))
	tmp = 0.0
	if (x <= -4.8e-46)
		tmp = t_1;
	elseif (x <= 1.2e-304)
		tmp = Float64(a * Float64(z * Float64(b * Float64(-t))));
	elseif (x <= 7.2e-231)
		tmp = Float64(Float64(b * k) * Float64(y * Float64(-y4)));
	elseif (x <= 6e-80)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (x <= 1.45e+42)
		tmp = Float64(b * Float64(y4 * Float64(t * j)));
	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 * (y * (x * a));
	tmp = 0.0;
	if (x <= -4.8e-46)
		tmp = t_1;
	elseif (x <= 1.2e-304)
		tmp = a * (z * (b * -t));
	elseif (x <= 7.2e-231)
		tmp = (b * k) * (y * -y4);
	elseif (x <= 6e-80)
		tmp = a * (t * (y2 * y5));
	elseif (x <= 1.45e+42)
		tmp = b * (y4 * (t * j));
	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[(y * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e-46], t$95$1, If[LessEqual[x, 1.2e-304], N[(a * N[(z * N[(b * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-231], N[(N[(b * k), $MachinePrecision] * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-80], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e+42], N[(b * N[(y4 * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.80000000000000027e-46 or 1.4499999999999999e42 < x

   1. Initial program 22.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 y around inf 43.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 43.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 43.5%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 43.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 43.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 41.2%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x\right)}\right) \]

   if -4.80000000000000027e-46 < x < 1.2e-304

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 42.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 42.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 42.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 35.7%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 35.7%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 35.7%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 35.7%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 35.7%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around 0 32.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 32.1%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

       2. mul-1-neg 32.1%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

       3. associate-*r* 35.5%

          \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(b \cdot t\right) \cdot z\right)} \]

   11. Simplified 35.5%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(\left(b \cdot t\right) \cdot z\right)} \]

   if 1.2e-304 < x < 7.19999999999999946e-231

   1. Initial program 60.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 46.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 31.8%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 31.8%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 31.8%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 31.8%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 31.8%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 36.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.7%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]

      2. neg-mul-1 36.7%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(k \cdot \left(y \cdot y4\right)\right) \]

      3. associate-*r* 31.9%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot y4\right)} \]

   9. Simplified 31.9%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(\left(k \cdot y\right) \cdot y4\right)} \]

   10. Taylor expanded in b around 0 36.7%

       \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   11. Step-by-step derivation

       1. neg-mul-1 36.7%

          \[\leadsto \color{blue}{-b \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]

       2. associate-*r* 40.2%

          \[\leadsto -\color{blue}{\left(b \cdot k\right) \cdot \left(y \cdot y4\right)} \]

       3. distribute-lft-neg-in 40.2%

          \[\leadsto \color{blue}{\left(-b \cdot k\right) \cdot \left(y \cdot y4\right)} \]

       4. *-commutative 40.2%

          \[\leadsto \left(-\color{blue}{k \cdot b}\right) \cdot \left(y \cdot y4\right) \]

       5. distribute-rgt-neg-in 40.2%

          \[\leadsto \color{blue}{\left(k \cdot \left(-b\right)\right)} \cdot \left(y \cdot y4\right) \]

       6. *-commutative 40.2%

          \[\leadsto \left(k \cdot \left(-b\right)\right) \cdot \color{blue}{\left(y4 \cdot y\right)} \]

   12. Simplified 40.2%

       \[\leadsto \color{blue}{\left(k \cdot \left(-b\right)\right) \cdot \left(y4 \cdot y\right)} \]

   if 7.19999999999999946e-231 < x < 6.00000000000000014e-80

   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 a around inf 37.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 37.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 37.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 37.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 37.5%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 37.5%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 37.5%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 37.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around inf 31.8%

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 31.8%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 31.8%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   if 6.00000000000000014e-80 < x < 1.4499999999999999e42

   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 b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 35.8%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(z \cdot \left(b \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-231}:\\ \;\;\;\;\left(b \cdot k\right) \cdot \left(y \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(z \cdot \left(b \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-230}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y (* x a)))))
   (if (<= x -1.8e-47)
     t_1
     (if (<= x 2.9e-301)
       (* a (* z (* b (- t))))
       (if (<= x 1.35e-230)
         (* b (* k (* y (- y4))))
         (if (<= x 9e-80)
           (* a (* t (* y2 y5)))
           (if (<= x 1.6e+42) (* b (* y4 (* t j))) 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 * (y * (x * a));
	double tmp;
	if (x <= -1.8e-47) {
		tmp = t_1;
	} else if (x <= 2.9e-301) {
		tmp = a * (z * (b * -t));
	} else if (x <= 1.35e-230) {
		tmp = b * (k * (y * -y4));
	} else if (x <= 9e-80) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 1.6e+42) {
		tmp = b * (y4 * (t * j));
	} 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 * (y * (x * a))
    if (x <= (-1.8d-47)) then
        tmp = t_1
    else if (x <= 2.9d-301) then
        tmp = a * (z * (b * -t))
    else if (x <= 1.35d-230) then
        tmp = b * (k * (y * -y4))
    else if (x <= 9d-80) then
        tmp = a * (t * (y2 * y5))
    else if (x <= 1.6d+42) then
        tmp = b * (y4 * (t * j))
    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 * (y * (x * a));
	double tmp;
	if (x <= -1.8e-47) {
		tmp = t_1;
	} else if (x <= 2.9e-301) {
		tmp = a * (z * (b * -t));
	} else if (x <= 1.35e-230) {
		tmp = b * (k * (y * -y4));
	} else if (x <= 9e-80) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 1.6e+42) {
		tmp = b * (y4 * (t * j));
	} 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 * (y * (x * a))
	tmp = 0
	if x <= -1.8e-47:
		tmp = t_1
	elif x <= 2.9e-301:
		tmp = a * (z * (b * -t))
	elif x <= 1.35e-230:
		tmp = b * (k * (y * -y4))
	elif x <= 9e-80:
		tmp = a * (t * (y2 * y5))
	elif x <= 1.6e+42:
		tmp = b * (y4 * (t * j))
	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(y * Float64(x * a)))
	tmp = 0.0
	if (x <= -1.8e-47)
		tmp = t_1;
	elseif (x <= 2.9e-301)
		tmp = Float64(a * Float64(z * Float64(b * Float64(-t))));
	elseif (x <= 1.35e-230)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (x <= 9e-80)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (x <= 1.6e+42)
		tmp = Float64(b * Float64(y4 * Float64(t * j)));
	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 * (y * (x * a));
	tmp = 0.0;
	if (x <= -1.8e-47)
		tmp = t_1;
	elseif (x <= 2.9e-301)
		tmp = a * (z * (b * -t));
	elseif (x <= 1.35e-230)
		tmp = b * (k * (y * -y4));
	elseif (x <= 9e-80)
		tmp = a * (t * (y2 * y5));
	elseif (x <= 1.6e+42)
		tmp = b * (y4 * (t * j));
	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[(y * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e-47], t$95$1, If[LessEqual[x, 2.9e-301], N[(a * N[(z * N[(b * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e-230], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-80], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+42], N[(b * N[(y4 * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.79999999999999995e-47 or 1.60000000000000001e42 < x

   1. Initial program 22.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 y around inf 43.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 43.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 43.5%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 43.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 43.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 41.2%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x\right)}\right) \]

   if -1.79999999999999995e-47 < x < 2.89999999999999984e-301

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 42.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 42.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 42.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 35.7%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 35.7%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 35.7%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 35.7%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 35.7%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around 0 32.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 32.1%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

       2. mul-1-neg 32.1%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

       3. associate-*r* 35.5%

          \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(b \cdot t\right) \cdot z\right)} \]

   11. Simplified 35.5%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(\left(b \cdot t\right) \cdot z\right)} \]

   if 2.89999999999999984e-301 < x < 1.35000000000000006e-230

   1. Initial program 60.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 46.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 31.8%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 31.8%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 31.8%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 31.8%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 31.8%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 36.7%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 36.7%

         \[\leadsto b \cdot \color{blue}{\left(-k \cdot \left(y \cdot y4\right)\right)} \]

      2. *-commutative 36.7%

         \[\leadsto b \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot k}\right) \]

      3. distribute-lft-neg-in 36.7%

         \[\leadsto b \cdot \color{blue}{\left(\left(-y \cdot y4\right) \cdot k\right)} \]

      4. mul-1-neg 36.7%

         \[\leadsto b \cdot \left(\color{blue}{\left(-1 \cdot \left(y \cdot y4\right)\right)} \cdot k\right) \]

      5. associate-*r* 36.7%

         \[\leadsto b \cdot \left(\color{blue}{\left(\left(-1 \cdot y\right) \cdot y4\right)} \cdot k\right) \]

      6. neg-mul-1 36.7%

         \[\leadsto b \cdot \left(\left(\color{blue}{\left(-y\right)} \cdot y4\right) \cdot k\right) \]

   9. Simplified 36.7%

      \[\leadsto b \cdot \color{blue}{\left(\left(\left(-y\right) \cdot y4\right) \cdot k\right)} \]

   if 1.35000000000000006e-230 < x < 9.0000000000000006e-80

   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 a around inf 37.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 37.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 37.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 37.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 37.5%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 37.5%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 37.5%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 37.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around inf 31.8%

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 31.8%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 31.8%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   if 9.0000000000000006e-80 < x < 1.60000000000000001e42

   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 b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 35.8%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(z \cdot \left(b \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-230}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ t_2 := b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-231}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y (* x a)))) (t_2 (* b (* y4 (* t j)))))
   (if (<= x -2.7e-35)
     t_1
     (if (<= x -1.05e-154)
       t_2
       (if (<= x 9.2e-231)
         (* b (* k (* y (- y4))))
         (if (<= x 4.8e-80)
           (* a (* t (* y2 y5)))
           (if (<= x 8e+41) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y * (x * a));
	double t_2 = b * (y4 * (t * j));
	double tmp;
	if (x <= -2.7e-35) {
		tmp = t_1;
	} else if (x <= -1.05e-154) {
		tmp = t_2;
	} else if (x <= 9.2e-231) {
		tmp = b * (k * (y * -y4));
	} else if (x <= 4.8e-80) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 8e+41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y * (x * a))
    t_2 = b * (y4 * (t * j))
    if (x <= (-2.7d-35)) then
        tmp = t_1
    else if (x <= (-1.05d-154)) then
        tmp = t_2
    else if (x <= 9.2d-231) then
        tmp = b * (k * (y * -y4))
    else if (x <= 4.8d-80) then
        tmp = a * (t * (y2 * y5))
    else if (x <= 8d+41) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y * (x * a));
	double t_2 = b * (y4 * (t * j));
	double tmp;
	if (x <= -2.7e-35) {
		tmp = t_1;
	} else if (x <= -1.05e-154) {
		tmp = t_2;
	} else if (x <= 9.2e-231) {
		tmp = b * (k * (y * -y4));
	} else if (x <= 4.8e-80) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 8e+41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y * (x * a))
	t_2 = b * (y4 * (t * j))
	tmp = 0
	if x <= -2.7e-35:
		tmp = t_1
	elif x <= -1.05e-154:
		tmp = t_2
	elif x <= 9.2e-231:
		tmp = b * (k * (y * -y4))
	elif x <= 4.8e-80:
		tmp = a * (t * (y2 * y5))
	elif x <= 8e+41:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y * Float64(x * a)))
	t_2 = Float64(b * Float64(y4 * Float64(t * j)))
	tmp = 0.0
	if (x <= -2.7e-35)
		tmp = t_1;
	elseif (x <= -1.05e-154)
		tmp = t_2;
	elseif (x <= 9.2e-231)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (x <= 4.8e-80)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (x <= 8e+41)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y * (x * a));
	t_2 = b * (y4 * (t * j));
	tmp = 0.0;
	if (x <= -2.7e-35)
		tmp = t_1;
	elseif (x <= -1.05e-154)
		tmp = t_2;
	elseif (x <= 9.2e-231)
		tmp = b * (k * (y * -y4));
	elseif (x <= 4.8e-80)
		tmp = a * (t * (y2 * y5));
	elseif (x <= 8e+41)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y4 * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e-35], t$95$1, If[LessEqual[x, -1.05e-154], t$95$2, If[LessEqual[x, 9.2e-231], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e-80], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+41], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.6999999999999997e-35 or 8.00000000000000005e41 < x

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 41.8%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x\right)}\right) \]

   if -2.6999999999999997e-35 < x < -1.04999999999999992e-154 or 4.7999999999999998e-80 < x < 8.00000000000000005e41

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 35.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 35.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 35.5%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t\right)}\right) \]

   if -1.04999999999999992e-154 < x < 9.2e-231

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 30.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 30.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 30.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 30.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 30.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 30.2%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 30.2%

         \[\leadsto b \cdot \color{blue}{\left(-k \cdot \left(y \cdot y4\right)\right)} \]

      2. *-commutative 30.2%

         \[\leadsto b \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot k}\right) \]

      3. distribute-lft-neg-in 30.2%

         \[\leadsto b \cdot \color{blue}{\left(\left(-y \cdot y4\right) \cdot k\right)} \]

      4. mul-1-neg 30.2%

         \[\leadsto b \cdot \left(\color{blue}{\left(-1 \cdot \left(y \cdot y4\right)\right)} \cdot k\right) \]

      5. associate-*r* 30.2%

         \[\leadsto b \cdot \left(\color{blue}{\left(\left(-1 \cdot y\right) \cdot y4\right)} \cdot k\right) \]

      6. neg-mul-1 30.2%

         \[\leadsto b \cdot \left(\left(\color{blue}{\left(-y\right)} \cdot y4\right) \cdot k\right) \]

   9. Simplified 30.2%

      \[\leadsto b \cdot \color{blue}{\left(\left(\left(-y\right) \cdot y4\right) \cdot k\right)} \]

   if 9.2e-231 < x < 4.7999999999999998e-80

   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 a around inf 37.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 37.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 37.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 37.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 37.5%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 37.5%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 37.5%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 37.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around inf 31.8%

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 31.8%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 31.8%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-231}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 28.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-53}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-165}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -3.4e+100)
   (* b (* j (* t y4)))
   (if (<= t -9.6e-53)
     (* a (* t (- (* y2 y5) (* z b))))
     (if (<= t -7.6e-165)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= t 8.5e+94)
         (* a (* y (- (* x b) (* y3 y5))))
         (* a (* y2 (- (* t y5) (* 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 tmp;
	if (t <= -3.4e+100) {
		tmp = b * (j * (t * y4));
	} else if (t <= -9.6e-53) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (t <= -7.6e-165) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 8.5e+94) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = a * (y2 * ((t * y5) - (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) :: tmp
    if (t <= (-3.4d+100)) then
        tmp = b * (j * (t * y4))
    else if (t <= (-9.6d-53)) then
        tmp = a * (t * ((y2 * y5) - (z * b)))
    else if (t <= (-7.6d-165)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (t <= 8.5d+94) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else
        tmp = a * (y2 * ((t * y5) - (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 tmp;
	if (t <= -3.4e+100) {
		tmp = b * (j * (t * y4));
	} else if (t <= -9.6e-53) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (t <= -7.6e-165) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 8.5e+94) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -3.4e+100:
		tmp = b * (j * (t * y4))
	elif t <= -9.6e-53:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	elif t <= -7.6e-165:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif t <= 8.5e+94:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	else:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -3.4e+100)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (t <= -9.6e-53)
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (t <= -7.6e-165)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (t <= 8.5e+94)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	else
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - 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)
	tmp = 0.0;
	if (t <= -3.4e+100)
		tmp = b * (j * (t * y4));
	elseif (t <= -9.6e-53)
		tmp = a * (t * ((y2 * y5) - (z * b)));
	elseif (t <= -7.6e-165)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (t <= 8.5e+94)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	else
		tmp = a * (y2 * ((t * y5) - (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_] := If[LessEqual[t, -3.4e+100], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.6e-53], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.6e-165], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+94], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.39999999999999994e100

   1. Initial program 15.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 36.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.1%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.5%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   7. Simplified 45.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -3.39999999999999994e100 < t < -9.6000000000000003e-53

   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 a around inf 30.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 30.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 30.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 30.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 30.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 30.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 30.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 30.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 30.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 30.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 42.4%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 42.4%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 42.4%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 42.4%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 42.4%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   if -9.6000000000000003e-53 < t < -7.60000000000000037e-165

   1. Initial program 40.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 56.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 52.6%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -7.60000000000000037e-165 < t < 8.50000000000000054e94

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 45.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 45.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 45.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 45.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 45.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 45.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 45.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 45.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 45.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf 39.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 39.4%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 39.4%

         \[\leadsto a \cdot \left(y \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      3. unsub-neg 39.4%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if 8.50000000000000054e94 < t

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 41.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 41.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 41.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 41.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 41.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 41.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 41.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 41.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf 46.6%

      \[\leadsto \color{blue}{a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-53}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-165}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 21.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-240}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \left(b \cdot j\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-79}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y (* x a)))))
   (if (<= x -3.4e-35)
     t_1
     (if (<= x 6.2e-240)
       (* (* t y4) (* b j))
       (if (<= x 2.2e-79)
         (* a (* t (* y2 y5)))
         (if (<= x 2e+42) (* b (* y4 (* t j))) 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 * (y * (x * a));
	double tmp;
	if (x <= -3.4e-35) {
		tmp = t_1;
	} else if (x <= 6.2e-240) {
		tmp = (t * y4) * (b * j);
	} else if (x <= 2.2e-79) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 2e+42) {
		tmp = b * (y4 * (t * j));
	} 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 * (y * (x * a))
    if (x <= (-3.4d-35)) then
        tmp = t_1
    else if (x <= 6.2d-240) then
        tmp = (t * y4) * (b * j)
    else if (x <= 2.2d-79) then
        tmp = a * (t * (y2 * y5))
    else if (x <= 2d+42) then
        tmp = b * (y4 * (t * j))
    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 * (y * (x * a));
	double tmp;
	if (x <= -3.4e-35) {
		tmp = t_1;
	} else if (x <= 6.2e-240) {
		tmp = (t * y4) * (b * j);
	} else if (x <= 2.2e-79) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 2e+42) {
		tmp = b * (y4 * (t * j));
	} 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 * (y * (x * a))
	tmp = 0
	if x <= -3.4e-35:
		tmp = t_1
	elif x <= 6.2e-240:
		tmp = (t * y4) * (b * j)
	elif x <= 2.2e-79:
		tmp = a * (t * (y2 * y5))
	elif x <= 2e+42:
		tmp = b * (y4 * (t * j))
	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(y * Float64(x * a)))
	tmp = 0.0
	if (x <= -3.4e-35)
		tmp = t_1;
	elseif (x <= 6.2e-240)
		tmp = Float64(Float64(t * y4) * Float64(b * j));
	elseif (x <= 2.2e-79)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (x <= 2e+42)
		tmp = Float64(b * Float64(y4 * Float64(t * j)));
	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 * (y * (x * a));
	tmp = 0.0;
	if (x <= -3.4e-35)
		tmp = t_1;
	elseif (x <= 6.2e-240)
		tmp = (t * y4) * (b * j);
	elseif (x <= 2.2e-79)
		tmp = a * (t * (y2 * y5));
	elseif (x <= 2e+42)
		tmp = b * (y4 * (t * j));
	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[(y * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e-35], t$95$1, If[LessEqual[x, 6.2e-240], N[(N[(t * y4), $MachinePrecision] * N[(b * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-79], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+42], N[(b * N[(y4 * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.4000000000000003e-35 or 2.00000000000000009e42 < x

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 41.8%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x\right)}\right) \]

   if -3.4000000000000003e-35 < x < 6.20000000000000034e-240

   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 37.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 29.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 23.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 25.6%

         \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

      2. *-commutative 25.6%

         \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

      3. *-commutative 25.6%

         \[\leadsto \left(j \cdot b\right) \cdot \color{blue}{\left(y4 \cdot t\right)} \]

   7. Simplified 25.6%

      \[\leadsto \color{blue}{\left(j \cdot b\right) \cdot \left(y4 \cdot t\right)} \]

   if 6.20000000000000034e-240 < x < 2.1999999999999999e-79

   1. Initial program 22.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 37.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 37.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 37.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 34.4%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 34.4%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 34.4%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 34.4%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around inf 29.4%

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 29.4%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 29.4%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   if 2.1999999999999999e-79 < x < 2.00000000000000009e42

   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 b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 35.8%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-240}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \left(b \cdot j\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-79}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 22.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y (* x a)))))
   (if (<= x -7e-35)
     t_1
     (if (<= x 9.6e-240)
       (* b (* j (* t y4)))
       (if (<= x 3.2e-80)
         (* a (* t (* y2 y5)))
         (if (<= x 6.3e+41) (* b (* y4 (* t j))) 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 * (y * (x * a));
	double tmp;
	if (x <= -7e-35) {
		tmp = t_1;
	} else if (x <= 9.6e-240) {
		tmp = b * (j * (t * y4));
	} else if (x <= 3.2e-80) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 6.3e+41) {
		tmp = b * (y4 * (t * j));
	} 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 * (y * (x * a))
    if (x <= (-7d-35)) then
        tmp = t_1
    else if (x <= 9.6d-240) then
        tmp = b * (j * (t * y4))
    else if (x <= 3.2d-80) then
        tmp = a * (t * (y2 * y5))
    else if (x <= 6.3d+41) then
        tmp = b * (y4 * (t * j))
    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 * (y * (x * a));
	double tmp;
	if (x <= -7e-35) {
		tmp = t_1;
	} else if (x <= 9.6e-240) {
		tmp = b * (j * (t * y4));
	} else if (x <= 3.2e-80) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 6.3e+41) {
		tmp = b * (y4 * (t * j));
	} 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 * (y * (x * a))
	tmp = 0
	if x <= -7e-35:
		tmp = t_1
	elif x <= 9.6e-240:
		tmp = b * (j * (t * y4))
	elif x <= 3.2e-80:
		tmp = a * (t * (y2 * y5))
	elif x <= 6.3e+41:
		tmp = b * (y4 * (t * j))
	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(y * Float64(x * a)))
	tmp = 0.0
	if (x <= -7e-35)
		tmp = t_1;
	elseif (x <= 9.6e-240)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (x <= 3.2e-80)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (x <= 6.3e+41)
		tmp = Float64(b * Float64(y4 * Float64(t * j)));
	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 * (y * (x * a));
	tmp = 0.0;
	if (x <= -7e-35)
		tmp = t_1;
	elseif (x <= 9.6e-240)
		tmp = b * (j * (t * y4));
	elseif (x <= 3.2e-80)
		tmp = a * (t * (y2 * y5));
	elseif (x <= 6.3e+41)
		tmp = b * (y4 * (t * j));
	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[(y * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e-35], t$95$1, If[LessEqual[x, 9.6e-240], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-80], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.3e+41], N[(b * N[(y4 * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.99999999999999992e-35 or 6.2999999999999999e41 < x

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 41.8%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x\right)}\right) \]

   if -6.99999999999999992e-35 < x < 9.5999999999999997e-240

   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 37.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 29.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 23.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 23.1%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   7. Simplified 23.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if 9.5999999999999997e-240 < x < 3.1999999999999999e-80

   1. Initial program 22.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 37.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 37.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 37.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 37.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 34.4%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 34.4%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 34.4%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 34.4%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around inf 29.4%

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 29.4%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 29.4%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   if 3.1999999999999999e-80 < x < 6.2999999999999999e41

   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 b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 35.8%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 22.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ t_2 := b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{if}\;x \leq -1.12 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-239}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y (* x a)))) (t_2 (* b (* j (* t y4)))))
   (if (<= x -1.12e-33)
     t_1
     (if (<= x 1.95e-239)
       t_2
       (if (<= x 2.4e-82)
         (* a (* t (* y2 y5)))
         (if (<= x 7.6e+41) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y * (x * a));
	double t_2 = b * (j * (t * y4));
	double tmp;
	if (x <= -1.12e-33) {
		tmp = t_1;
	} else if (x <= 1.95e-239) {
		tmp = t_2;
	} else if (x <= 2.4e-82) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 7.6e+41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y * (x * a))
    t_2 = b * (j * (t * y4))
    if (x <= (-1.12d-33)) then
        tmp = t_1
    else if (x <= 1.95d-239) then
        tmp = t_2
    else if (x <= 2.4d-82) then
        tmp = a * (t * (y2 * y5))
    else if (x <= 7.6d+41) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y * (x * a));
	double t_2 = b * (j * (t * y4));
	double tmp;
	if (x <= -1.12e-33) {
		tmp = t_1;
	} else if (x <= 1.95e-239) {
		tmp = t_2;
	} else if (x <= 2.4e-82) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 7.6e+41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y * (x * a))
	t_2 = b * (j * (t * y4))
	tmp = 0
	if x <= -1.12e-33:
		tmp = t_1
	elif x <= 1.95e-239:
		tmp = t_2
	elif x <= 2.4e-82:
		tmp = a * (t * (y2 * y5))
	elif x <= 7.6e+41:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y * Float64(x * a)))
	t_2 = Float64(b * Float64(j * Float64(t * y4)))
	tmp = 0.0
	if (x <= -1.12e-33)
		tmp = t_1;
	elseif (x <= 1.95e-239)
		tmp = t_2;
	elseif (x <= 2.4e-82)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (x <= 7.6e+41)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y * (x * a));
	t_2 = b * (j * (t * y4));
	tmp = 0.0;
	if (x <= -1.12e-33)
		tmp = t_1;
	elseif (x <= 1.95e-239)
		tmp = t_2;
	elseif (x <= 2.4e-82)
		tmp = a * (t * (y2 * y5));
	elseif (x <= 7.6e+41)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.12e-33], t$95$1, If[LessEqual[x, 1.95e-239], t$95$2, If[LessEqual[x, 2.4e-82], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.6e+41], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.11999999999999999e-33 or 7.6000000000000003e41 < x

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 41.8%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x\right)}\right) \]

   if -1.11999999999999999e-33 < x < 1.95e-239 or 2.40000000000000008e-82 < x < 7.6000000000000003e41

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 32.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 25.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 25.2%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   7. Simplified 25.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if 1.95e-239 < x < 2.40000000000000008e-82

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 38.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 38.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 32.6%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 32.6%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 32.6%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 32.6%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 32.6%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around inf 27.3%

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 27.3%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 27.3%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-239}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ t_2 := b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{-240}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* (* x y) b))) (t_2 (* b (* j (* t y4)))))
   (if (<= x -5.8e-36)
     t_1
     (if (<= x 4.05e-240)
       t_2
       (if (<= x 8.2e-83)
         (* a (* t (* y2 y5)))
         (if (<= x 6.5e+41) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((x * y) * b);
	double t_2 = b * (j * (t * y4));
	double tmp;
	if (x <= -5.8e-36) {
		tmp = t_1;
	} else if (x <= 4.05e-240) {
		tmp = t_2;
	} else if (x <= 8.2e-83) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 6.5e+41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((x * y) * b)
    t_2 = b * (j * (t * y4))
    if (x <= (-5.8d-36)) then
        tmp = t_1
    else if (x <= 4.05d-240) then
        tmp = t_2
    else if (x <= 8.2d-83) then
        tmp = a * (t * (y2 * y5))
    else if (x <= 6.5d+41) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((x * y) * b);
	double t_2 = b * (j * (t * y4));
	double tmp;
	if (x <= -5.8e-36) {
		tmp = t_1;
	} else if (x <= 4.05e-240) {
		tmp = t_2;
	} else if (x <= 8.2e-83) {
		tmp = a * (t * (y2 * y5));
	} else if (x <= 6.5e+41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * ((x * y) * b)
	t_2 = b * (j * (t * y4))
	tmp = 0
	if x <= -5.8e-36:
		tmp = t_1
	elif x <= 4.05e-240:
		tmp = t_2
	elif x <= 8.2e-83:
		tmp = a * (t * (y2 * y5))
	elif x <= 6.5e+41:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(Float64(x * y) * b))
	t_2 = Float64(b * Float64(j * Float64(t * y4)))
	tmp = 0.0
	if (x <= -5.8e-36)
		tmp = t_1;
	elseif (x <= 4.05e-240)
		tmp = t_2;
	elseif (x <= 8.2e-83)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (x <= 6.5e+41)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * ((x * y) * b);
	t_2 = b * (j * (t * y4));
	tmp = 0.0;
	if (x <= -5.8e-36)
		tmp = t_1;
	elseif (x <= 4.05e-240)
		tmp = t_2;
	elseif (x <= 8.2e-83)
		tmp = a * (t * (y2 * y5));
	elseif (x <= 6.5e+41)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e-36], t$95$1, If[LessEqual[x, 4.05e-240], t$95$2, If[LessEqual[x, 8.2e-83], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+41], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.80000000000000026e-36 or 6.49999999999999975e41 < x

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 37.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if -5.80000000000000026e-36 < x < 4.05000000000000001e-240 or 8.1999999999999999e-83 < x < 6.49999999999999975e41

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 32.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 25.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 25.2%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   7. Simplified 25.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if 4.05000000000000001e-240 < x < 8.1999999999999999e-83

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 38.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 38.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 38.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 32.6%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 32.6%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 32.6%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 32.6%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 32.6%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around inf 27.3%

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 27.3%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 27.3%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 29.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+226}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(b \cdot \left(-t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -2.8e+148)
   (* b (* a (- (* x y) (* z t))))
   (if (<= z 3.7e-123)
     (* a (* x (- (* y b) (* y1 y2))))
     (if (<= z 1.85e+226)
       (* a (* y1 (- (* z y3) (* x y2))))
       (* a (* z (* b (- t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -2.8e+148) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (z <= 3.7e-123) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (z <= 1.85e+226) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = a * (z * (b * -t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (z <= (-2.8d+148)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (z <= 3.7d-123) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else if (z <= 1.85d+226) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else
        tmp = a * (z * (b * -t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -2.8e+148) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (z <= 3.7e-123) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (z <= 1.85e+226) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = a * (z * (b * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -2.8e+148:
		tmp = b * (a * ((x * y) - (z * t)))
	elif z <= 3.7e-123:
		tmp = a * (x * ((y * b) - (y1 * y2)))
	elif z <= 1.85e+226:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	else:
		tmp = a * (z * (b * -t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -2.8e+148)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (z <= 3.7e-123)
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (z <= 1.85e+226)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(a * Float64(z * Float64(b * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (z <= -2.8e+148)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (z <= 3.7e-123)
		tmp = a * (x * ((y * b) - (y1 * y2)));
	elseif (z <= 1.85e+226)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	else
		tmp = a * (z * (b * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -2.8e+148], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-123], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+226], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(z * N[(b * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7999999999999998e148

   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 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 49.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -2.7999999999999998e148 < z < 3.70000000000000015e-123

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 46.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 46.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 46.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 46.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 46.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 46.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 46.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 46.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 46.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 40.3%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(b \cdot y - y1 \cdot y2\right)\right)} \]

   if 3.70000000000000015e-123 < z < 1.84999999999999991e226

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 37.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 37.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 37.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 36.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 1.84999999999999991e226 < z

   1. Initial program 36.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 37.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 37.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 37.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 52.9%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 52.9%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 52.9%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 52.9%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 52.9%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around 0 53.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 53.0%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

       2. mul-1-neg 53.0%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

       3. associate-*r* 53.0%

          \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(b \cdot t\right) \cdot z\right)} \]

   11. Simplified 53.0%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(\left(b \cdot t\right) \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+226}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(b \cdot \left(-t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 29.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{+227}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(b \cdot \left(-t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -3.4e+46)
   (* a (* t (- (* y2 y5) (* z b))))
   (if (<= z 2.3e-122)
     (* a (* x (- (* y b) (* y1 y2))))
     (if (<= z 3.75e+227)
       (* a (* y1 (- (* z y3) (* x y2))))
       (* a (* z (* b (- t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -3.4e+46) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (z <= 2.3e-122) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (z <= 3.75e+227) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = a * (z * (b * -t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (z <= (-3.4d+46)) then
        tmp = a * (t * ((y2 * y5) - (z * b)))
    else if (z <= 2.3d-122) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else if (z <= 3.75d+227) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else
        tmp = a * (z * (b * -t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -3.4e+46) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (z <= 2.3e-122) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (z <= 3.75e+227) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else {
		tmp = a * (z * (b * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -3.4e+46:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	elif z <= 2.3e-122:
		tmp = a * (x * ((y * b) - (y1 * y2)))
	elif z <= 3.75e+227:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	else:
		tmp = a * (z * (b * -t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -3.4e+46)
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (z <= 2.3e-122)
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (z <= 3.75e+227)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(a * Float64(z * Float64(b * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (z <= -3.4e+46)
		tmp = a * (t * ((y2 * y5) - (z * b)));
	elseif (z <= 2.3e-122)
		tmp = a * (x * ((y * b) - (y1 * y2)));
	elseif (z <= 3.75e+227)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	else
		tmp = a * (z * (b * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -3.4e+46], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-122], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.75e+227], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(z * N[(b * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3999999999999998e46

   1. Initial program 19.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 37.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 37.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 37.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 37.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 37.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 37.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 37.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 37.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 37.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 39.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 39.5%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 39.5%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 39.5%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 39.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   if -3.3999999999999998e46 < z < 2.30000000000000007e-122

   1. Initial program 25.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 49.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 49.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 49.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 49.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 49.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 49.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 49.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 49.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 49.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 43.6%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(b \cdot y - y1 \cdot y2\right)\right)} \]

   if 2.30000000000000007e-122 < z < 3.7500000000000001e227

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 37.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 37.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 37.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 37.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 36.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 3.7500000000000001e227 < z

   1. Initial program 36.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 37.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 37.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 37.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 37.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 52.9%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 52.9%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 52.9%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 52.9%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 52.9%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around 0 53.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 53.0%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

       2. mul-1-neg 53.0%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

       3. associate-*r* 53.0%

          \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(b \cdot t\right) \cdot z\right)} \]

   11. Simplified 53.0%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(\left(b \cdot t\right) \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{+227}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(b \cdot \left(-t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 31.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-89} \lor \neg \left(x \leq 7.6 \cdot 10^{-67}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -1.55e-89) (not (<= x 7.6e-67)))
   (* a (* x (- (* y b) (* y1 y2))))
   (* a (* t (- (* y2 y5) (* z 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 <= -1.55e-89) || !(x <= 7.6e-67)) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 <= (-1.55d-89)) .or. (.not. (x <= 7.6d-67))) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else
        tmp = a * (t * ((y2 * y5) - (z * 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 <= -1.55e-89) || !(x <= 7.6e-67)) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 <= -1.55e-89) or not (x <= 7.6e-67):
		tmp = a * (x * ((y * b) - (y1 * y2)))
	else:
		tmp = a * (t * ((y2 * y5) - (z * 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 <= -1.55e-89) || !(x <= 7.6e-67))
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	else
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * 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 <= -1.55e-89) || ~((x <= 7.6e-67)))
		tmp = a * (x * ((y * b) - (y1 * y2)));
	else
		tmp = a * (t * ((y2 * y5) - (z * 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[x, -1.55e-89], N[Not[LessEqual[x, 7.6e-67]], $MachinePrecision]], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.54999999999999998e-89 or 7.59999999999999976e-67 < x

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 41.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 41.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 41.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 41.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 42.3%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(b \cdot y - y1 \cdot y2\right)\right)} \]

   if -1.54999999999999998e-89 < x < 7.59999999999999976e-67

   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 a around inf 42.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 42.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 42.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 42.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 34.9%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 34.9%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 34.9%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 34.9%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 34.9%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-89} \lor \neg \left(x \leq 7.6 \cdot 10^{-67}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 25.5% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-88} \lor \neg \left(x \leq 1.02 \cdot 10^{-32}\right):\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -3.9e-88) (not (<= x 1.02e-32)))
   (* b (* y (* x a)))
   (* a (* t (- (* y2 y5) (* z 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 <= -3.9e-88) || !(x <= 1.02e-32)) {
		tmp = b * (y * (x * a));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 <= (-3.9d-88)) .or. (.not. (x <= 1.02d-32))) then
        tmp = b * (y * (x * a))
    else
        tmp = a * (t * ((y2 * y5) - (z * 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 <= -3.9e-88) || !(x <= 1.02e-32)) {
		tmp = b * (y * (x * a));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 <= -3.9e-88) or not (x <= 1.02e-32):
		tmp = b * (y * (x * a))
	else:
		tmp = a * (t * ((y2 * y5) - (z * 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 <= -3.9e-88) || !(x <= 1.02e-32))
		tmp = Float64(b * Float64(y * Float64(x * a)));
	else
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * 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 <= -3.9e-88) || ~((x <= 1.02e-32)))
		tmp = b * (y * (x * a));
	else
		tmp = a * (t * ((y2 * y5) - (z * 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[x, -3.9e-88], N[Not[LessEqual[x, 1.02e-32]], $MachinePrecision]], N[(b * N[(y * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.89999999999999992e-88 or 1.02000000000000002e-32 < x

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 41.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 41.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 41.5%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 41.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 41.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 38.7%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x\right)}\right) \]

   if -3.89999999999999992e-88 < x < 1.02000000000000002e-32

   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 a around inf 41.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 41.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 41.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 41.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 41.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 41.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 41.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 41.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 32.7%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 32.7%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 32.7%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 32.7%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 32.7%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-88} \lor \neg \left(x \leq 1.02 \cdot 10^{-32}\right):\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 21.3% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-86} \lor \neg \left(x \leq 9.2 \cdot 10^{-75}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -5.5e-86) (not (<= x 9.2e-75)))
   (* a (* (* x y) b))
   (* a (* t (* y2 y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -5.5e-86) || !(x <= 9.2e-75)) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((x <= (-5.5d-86)) .or. (.not. (x <= 9.2d-75))) then
        tmp = a * ((x * y) * b)
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -5.5e-86) || !(x <= 9.2e-75)) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (x <= -5.5e-86) or not (x <= 9.2e-75):
		tmp = a * ((x * y) * b)
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((x <= -5.5e-86) || !(x <= 9.2e-75))
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((x <= -5.5e-86) || ~((x <= 9.2e-75)))
		tmp = a * ((x * y) * b);
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[x, -5.5e-86], N[Not[LessEqual[x, 9.2e-75]], $MachinePrecision]], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e-86 or 9.2e-75 < x

   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 b around inf 39.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y around inf 41.0%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 41.0%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 41.0%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 41.0%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   6. Simplified 41.0%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 33.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if -5.5e-86 < x < 9.2e-75

   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 a around inf 41.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 41.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 41.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 41.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 41.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 41.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 41.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 41.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 41.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf 34.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 34.5%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      2. mul-1-neg 34.5%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      3. sub-neg 34.5%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   8. Simplified 34.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   9. Taylor expanded in y2 around inf 21.1%

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 21.1%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 21.1%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-86} \lor \neg \left(x \leq 9.2 \cdot 10^{-75}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 16.8% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 26.3%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 37.5%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

4. Taylor expanded in y around inf 32.5%

   \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
5. Step-by-step derivation

   1. +-commutative 32.5%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

   2. mul-1-neg 32.5%

      \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

   3. unsub-neg 32.5%

      \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

6. Simplified 32.5%

   \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

7. Taylor expanded in a around inf 21.1%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

8. Final simplification 21.1%

   \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
9. Add Preprocessing

Developer target: 28.1% 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 2024096 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))