Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.2% → 41.4%

Time: 1.3min

Alternatives: 43

Speedup: 3.1×

• 89.2% 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: 30.2% 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: 41.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := b \cdot y0 - i \cdot y1\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := c \cdot \left(\left(y0 \cdot t\_3 + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_5 := y1 \cdot y4 - y0 \cdot y5\\ t_6 := b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_7 := c \cdot y0 - a \cdot y1\\ t_8 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot t\_5 + z \cdot t\_7\right)\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{+88}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+54}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t\_7 - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot t\_1\right)\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-78}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(y2 \cdot t\_7 + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{-200}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot t\_3\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-290}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t\_5 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot t\_2\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-246}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot t\_1\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{-100}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-21}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(k \cdot t\_2 + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+170}:\\ \;\;\;\;t\_8\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2 (- (* b y0) (* i y1)))
        (t_3 (- (* x y2) (* z y3)))
        (t_4
         (*
          c
          (+
           (+ (* y0 t_3) (* i (- (* z t) (* x y))))
           (* y4 (- (* y y3) (* t y2))))))
        (t_5 (- (* y1 y4) (* y0 y5)))
        (t_6
         (*
          b
          (+
           (+ (* (- (* t j) (* y k)) y4) (* a (- (* x y) (* z t))))
           (* y0 (- (* z k) (* x j))))))
        (t_7 (- (* c y0) (* a y1)))
        (t_8 (* y3 (- (* y (- (* c y4) (* a y5))) (+ (* j t_5) (* z t_7))))))
   (if (<= c -8.5e+88)
     t_4
     (if (<= c -2.4e+54)
       t_6
       (if (<= c -1.75e-67)
         (* y2 (+ (- (* x t_7) (* k (- (* y0 y5) (* y1 y4)))) (* t t_1)))
         (if (<= c -7.6e-78)
           t_8
           (if (<= c -1.35e-115)
             (* x (+ (* y2 t_7) (* j (- (* i y1) (* b y0)))))
             (if (<= c -5e-200)
               (*
                y1
                (+
                 (* i (- (* x j) (* z k)))
                 (- (* y4 (- (* k y2) (* j y3))) (* a t_3))))
               (if (<= c 2.9e-290)
                 (* k (+ (+ (* y2 t_5) (* y (- (* i y5) (* b y4)))) (* z t_2)))
                 (if (<= c 5.8e-246)
                   t_6
                   (if (<= c 7.2e-194)
                     (*
                      t
                      (+
                       (+
                        (* z (- (* c i) (* a b)))
                        (* j (- (* b y4) (* i y5))))
                       (* y2 t_1)))
                     (if (<= c 8.2e-100)
                       t_6
                       (if (<= c 2.1e-21)
                         (* y0 (* y5 (- (* j y3) (* k y2))))
                         (if (<= c 6.6e+37)
                           (*
                            z
                            (+ (* k t_2) (- (* a (* y1 y3)) (* a (* t b)))))
                           (if (<= c 3.7e+170) t_8 t_4)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = (b * y0) - (i * y1);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = c * (((y0 * t_3) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double t_7 = (c * y0) - (a * y1);
	double t_8 = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_5) + (z * t_7)));
	double tmp;
	if (c <= -8.5e+88) {
		tmp = t_4;
	} else if (c <= -2.4e+54) {
		tmp = t_6;
	} else if (c <= -1.75e-67) {
		tmp = y2 * (((x * t_7) - (k * ((y0 * y5) - (y1 * y4)))) + (t * t_1));
	} else if (c <= -7.6e-78) {
		tmp = t_8;
	} else if (c <= -1.35e-115) {
		tmp = x * ((y2 * t_7) + (j * ((i * y1) - (b * y0))));
	} else if (c <= -5e-200) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_3)));
	} else if (c <= 2.9e-290) {
		tmp = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * t_2));
	} else if (c <= 5.8e-246) {
		tmp = t_6;
	} else if (c <= 7.2e-194) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_1));
	} else if (c <= 8.2e-100) {
		tmp = t_6;
	} else if (c <= 2.1e-21) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (c <= 6.6e+37) {
		tmp = z * ((k * t_2) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 3.7e+170) {
		tmp = t_8;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = (a * y5) - (c * y4)
    t_2 = (b * y0) - (i * y1)
    t_3 = (x * y2) - (z * y3)
    t_4 = c * (((y0 * t_3) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    t_5 = (y1 * y4) - (y0 * y5)
    t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
    t_7 = (c * y0) - (a * y1)
    t_8 = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_5) + (z * t_7)))
    if (c <= (-8.5d+88)) then
        tmp = t_4
    else if (c <= (-2.4d+54)) then
        tmp = t_6
    else if (c <= (-1.75d-67)) then
        tmp = y2 * (((x * t_7) - (k * ((y0 * y5) - (y1 * y4)))) + (t * t_1))
    else if (c <= (-7.6d-78)) then
        tmp = t_8
    else if (c <= (-1.35d-115)) then
        tmp = x * ((y2 * t_7) + (j * ((i * y1) - (b * y0))))
    else if (c <= (-5d-200)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_3)))
    else if (c <= 2.9d-290) then
        tmp = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * t_2))
    else if (c <= 5.8d-246) then
        tmp = t_6
    else if (c <= 7.2d-194) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_1))
    else if (c <= 8.2d-100) then
        tmp = t_6
    else if (c <= 2.1d-21) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (c <= 6.6d+37) then
        tmp = z * ((k * t_2) + ((a * (y1 * y3)) - (a * (t * b))))
    else if (c <= 3.7d+170) then
        tmp = t_8
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = (b * y0) - (i * y1);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = c * (((y0 * t_3) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double t_7 = (c * y0) - (a * y1);
	double t_8 = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_5) + (z * t_7)));
	double tmp;
	if (c <= -8.5e+88) {
		tmp = t_4;
	} else if (c <= -2.4e+54) {
		tmp = t_6;
	} else if (c <= -1.75e-67) {
		tmp = y2 * (((x * t_7) - (k * ((y0 * y5) - (y1 * y4)))) + (t * t_1));
	} else if (c <= -7.6e-78) {
		tmp = t_8;
	} else if (c <= -1.35e-115) {
		tmp = x * ((y2 * t_7) + (j * ((i * y1) - (b * y0))));
	} else if (c <= -5e-200) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_3)));
	} else if (c <= 2.9e-290) {
		tmp = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * t_2));
	} else if (c <= 5.8e-246) {
		tmp = t_6;
	} else if (c <= 7.2e-194) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_1));
	} else if (c <= 8.2e-100) {
		tmp = t_6;
	} else if (c <= 2.1e-21) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (c <= 6.6e+37) {
		tmp = z * ((k * t_2) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 3.7e+170) {
		tmp = t_8;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y5) - (c * y4)
	t_2 = (b * y0) - (i * y1)
	t_3 = (x * y2) - (z * y3)
	t_4 = c * (((y0 * t_3) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	t_5 = (y1 * y4) - (y0 * y5)
	t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
	t_7 = (c * y0) - (a * y1)
	t_8 = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_5) + (z * t_7)))
	tmp = 0
	if c <= -8.5e+88:
		tmp = t_4
	elif c <= -2.4e+54:
		tmp = t_6
	elif c <= -1.75e-67:
		tmp = y2 * (((x * t_7) - (k * ((y0 * y5) - (y1 * y4)))) + (t * t_1))
	elif c <= -7.6e-78:
		tmp = t_8
	elif c <= -1.35e-115:
		tmp = x * ((y2 * t_7) + (j * ((i * y1) - (b * y0))))
	elif c <= -5e-200:
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_3)))
	elif c <= 2.9e-290:
		tmp = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * t_2))
	elif c <= 5.8e-246:
		tmp = t_6
	elif c <= 7.2e-194:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_1))
	elif c <= 8.2e-100:
		tmp = t_6
	elif c <= 2.1e-21:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif c <= 6.6e+37:
		tmp = z * ((k * t_2) + ((a * (y1 * y3)) - (a * (t * b))))
	elif c <= 3.7e+170:
		tmp = t_8
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y5) - Float64(c * y4))
	t_2 = Float64(Float64(b * y0) - Float64(i * y1))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(c * Float64(Float64(Float64(y0 * t_3) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_5 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_6 = Float64(b * Float64(Float64(Float64(Float64(Float64(t * j) - Float64(y * k)) * y4) + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_7 = Float64(Float64(c * y0) - Float64(a * y1))
	t_8 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) - Float64(Float64(j * t_5) + Float64(z * t_7))))
	tmp = 0.0
	if (c <= -8.5e+88)
		tmp = t_4;
	elseif (c <= -2.4e+54)
		tmp = t_6;
	elseif (c <= -1.75e-67)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_7) - Float64(k * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(t * t_1)));
	elseif (c <= -7.6e-78)
		tmp = t_8;
	elseif (c <= -1.35e-115)
		tmp = Float64(x * Float64(Float64(y2 * t_7) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (c <= -5e-200)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(a * t_3))));
	elseif (c <= 2.9e-290)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_5) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * t_2)));
	elseif (c <= 5.8e-246)
		tmp = t_6;
	elseif (c <= 7.2e-194)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(y2 * t_1)));
	elseif (c <= 8.2e-100)
		tmp = t_6;
	elseif (c <= 2.1e-21)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (c <= 6.6e+37)
		tmp = Float64(z * Float64(Float64(k * t_2) + Float64(Float64(a * Float64(y1 * y3)) - Float64(a * Float64(t * b)))));
	elseif (c <= 3.7e+170)
		tmp = t_8;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y5) - (c * y4);
	t_2 = (b * y0) - (i * y1);
	t_3 = (x * y2) - (z * y3);
	t_4 = c * (((y0 * t_3) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	t_5 = (y1 * y4) - (y0 * y5);
	t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	t_7 = (c * y0) - (a * y1);
	t_8 = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_5) + (z * t_7)));
	tmp = 0.0;
	if (c <= -8.5e+88)
		tmp = t_4;
	elseif (c <= -2.4e+54)
		tmp = t_6;
	elseif (c <= -1.75e-67)
		tmp = y2 * (((x * t_7) - (k * ((y0 * y5) - (y1 * y4)))) + (t * t_1));
	elseif (c <= -7.6e-78)
		tmp = t_8;
	elseif (c <= -1.35e-115)
		tmp = x * ((y2 * t_7) + (j * ((i * y1) - (b * y0))));
	elseif (c <= -5e-200)
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_3)));
	elseif (c <= 2.9e-290)
		tmp = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * t_2));
	elseif (c <= 5.8e-246)
		tmp = t_6;
	elseif (c <= 7.2e-194)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_1));
	elseif (c <= 8.2e-100)
		tmp = t_6;
	elseif (c <= 2.1e-21)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (c <= 6.6e+37)
		tmp = z * ((k * t_2) + ((a * (y1 * y3)) - (a * (t * b))));
	elseif (c <= 3.7e+170)
		tmp = t_8;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(N[(y0 * t$95$3), $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]}, Block[{t$95$5 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(b * N[(N[(N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * t$95$5), $MachinePrecision] + N[(z * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.5e+88], t$95$4, If[LessEqual[c, -2.4e+54], t$95$6, If[LessEqual[c, -1.75e-67], N[(y2 * N[(N[(N[(x * t$95$7), $MachinePrecision] - N[(k * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.6e-78], t$95$8, If[LessEqual[c, -1.35e-115], N[(x * N[(N[(y2 * t$95$7), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5e-200], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e-290], N[(k * N[(N[(N[(y2 * t$95$5), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e-246], t$95$6, If[LessEqual[c, 7.2e-194], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.2e-100], t$95$6, If[LessEqual[c, 2.1e-21], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.6e+37], N[(z * N[(N[(k * t$95$2), $MachinePrecision] + N[(N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.7e+170], t$95$8, t$95$4]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if c < -8.5000000000000005e88 or 3.69999999999999987e170 < c

   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 c around inf 72.6%

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

      1. +-commutative 72.6%

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

      2. mul-1-neg 72.6%

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

      3. unsub-neg 72.6%

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

      4. *-commutative 72.6%

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

      5. *-commutative 72.6%

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

      6. *-commutative 72.6%

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

      7. *-commutative 72.6%

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

   5. Simplified 72.6%

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

   if -8.5000000000000005e88 < c < -2.39999999999999998e54 or 2.89999999999999994e-290 < c < 5.7999999999999999e-246 or 7.2e-194 < c < 8.1999999999999998e-100

   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 68.4%

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

   if -2.39999999999999998e54 < c < -1.75e-67

   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 y2 around inf 63.3%

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

   if -1.75e-67 < c < -7.5999999999999998e-78 or 6.6000000000000002e37 < c < 3.69999999999999987e170

   1. Initial program 33.5%

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

   3. Taylor expanded in y3 around -inf 66.2%

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

   if -7.5999999999999998e-78 < c < -1.35e-115

   1. Initial program 25.0%

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

   3. Taylor expanded in x around inf 50.3%

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

   4. Taylor expanded in y around 0 75.3%

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

      1. *-commutative 75.3%

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

      2. *-commutative 75.3%

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

   6. Simplified 75.3%

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

   if -1.35e-115 < c < -4.99999999999999991e-200

   1. Initial program 37.5%

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

   3. Taylor expanded in y1 around -inf 68.8%

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

      1. associate-*r* 68.8%

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

      2. neg-mul-1 68.8%

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

      3. +-commutative 68.8%

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

      4. mul-1-neg 68.8%

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

      5. unsub-neg 68.8%

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

      6. *-commutative 68.8%

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

      7. *-commutative 68.8%

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

      8. *-commutative 68.8%

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

      9. *-commutative 68.8%

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

   5. Simplified 68.8%

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

   if -4.99999999999999991e-200 < c < 2.89999999999999994e-290

   1. Initial program 43.6%

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

   3. Taylor expanded in k around inf 63.0%

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

      1. +-commutative 63.0%

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

      2. mul-1-neg 63.0%

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

      3. unsub-neg 63.0%

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

      4. *-commutative 63.0%

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

      5. associate-*r* 63.0%

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

      6. neg-mul-1 63.0%

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

   5. Simplified 63.0%

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

   if 5.7999999999999999e-246 < c < 7.2e-194

   1. Initial program 27.3%

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

   3. Taylor expanded in t around inf 79.6%

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

   if 8.1999999999999998e-100 < c < 2.10000000000000013e-21

   1. Initial program 35.6%

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

   3. Taylor expanded in y0 around inf 45.8%

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

      1. +-commutative 45.8%

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

      2. mul-1-neg 45.8%

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

      3. unsub-neg 45.8%

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

      4. *-commutative 45.8%

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

      5. *-commutative 45.8%

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

      6. *-commutative 45.8%

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

      7. *-commutative 45.8%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in y5 around inf 60.5%

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

   if 2.10000000000000013e-21 < c < 6.6000000000000002e37

   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 z around -inf 44.1%

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

   4. Taylor expanded in c around 0 62.8%

      \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(-1 \cdot \left(a \cdot \left(y1 \cdot y3\right)\right) + a \cdot \left(b \cdot t\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{+88}:\\ \;\;\;\;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}\;c \leq -2.4 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-78}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{-200}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-290}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-246}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{-100}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-21}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+170}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.0% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 87.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around inf 37.7%

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

      1. fma-define 40.7%

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

      2. *-commutative 40.7%

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

      3. *-commutative 40.7%

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

      4. *-commutative 40.7%

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

   5. Simplified 40.7%

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

4. Final simplification 56.5%

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

Alternative 3: 53.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 87.7%

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

   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 x around inf 38.0%

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

   4. Taylor expanded in y around 0 39.9%

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

      1. *-commutative 39.9%

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

      2. *-commutative 39.9%

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

   6. Simplified 39.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.0%

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

Alternative 4: 41.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ t_2 := c \cdot \left(\left(y0 \cdot t\_1 + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_3 := b \cdot y0 - i \cdot y1\\ t_4 := b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_5 := c \cdot y0 - a \cdot y1\\ t_6 := x \cdot \left(y2 \cdot t\_5 + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_7 := z \cdot \left(k \cdot t\_3 + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{+54}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t\_5 - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-76}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-116}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-119}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-198}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot t\_1\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-290}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot t\_3\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-97}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-22}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+53}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+114}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3)))
        (t_2
         (*
          c
          (+
           (+ (* y0 t_1) (* i (- (* z t) (* x y))))
           (* y4 (- (* y y3) (* t y2))))))
        (t_3 (- (* b y0) (* i y1)))
        (t_4
         (*
          b
          (+
           (+ (* (- (* t j) (* y k)) y4) (* a (- (* x y) (* z t))))
           (* y0 (- (* z k) (* x j))))))
        (t_5 (- (* c y0) (* a y1)))
        (t_6 (* x (+ (* y2 t_5) (* j (- (* i y1) (* b y0))))))
        (t_7 (* z (+ (* k t_3) (- (* a (* y1 y3)) (* a (* t b)))))))
   (if (<= c -5.6e+92)
     t_2
     (if (<= c -1.16e+54)
       t_4
       (if (<= c -1.35e-67)
         (*
          y2
          (+
           (- (* x t_5) (* k (- (* y0 y5) (* y1 y4))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= c -4.5e-76)
           (* y3 (* y (- (* c y4) (* a y5))))
           (if (<= c -7.2e-116)
             t_6
             (if (<= c -1.5e-119)
               t_7
               (if (<= c -1.05e-198)
                 (*
                  y1
                  (+
                   (* i (- (* x j) (* z k)))
                   (- (* y4 (- (* k y2) (* j y3))) (* a t_1))))
                 (if (<= c 2.9e-290)
                   (*
                    k
                    (+
                     (+
                      (* y2 (- (* y1 y4) (* y0 y5)))
                      (* y (- (* i y5) (* b y4))))
                     (* z t_3)))
                   (if (<= c 3.2e-97)
                     t_4
                     (if (<= c 7.2e-22)
                       (* y0 (* y5 (- (* j y3) (* k y2))))
                       (if (<= c 7.2e+53)
                         t_7
                         (if (<= c 3.3e+114)
                           t_6
                           (if (<= c 1.7e+173)
                             (*
                              j
                              (+
                               (* t (- (* b y4) (* i y5)))
                               (- (* y0 (* y3 y5)) (* y0 (* x b)))))
                             t_2)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_3 = (b * y0) - (i * y1);
	double t_4 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double t_5 = (c * y0) - (a * y1);
	double t_6 = x * ((y2 * t_5) + (j * ((i * y1) - (b * y0))));
	double t_7 = z * ((k * t_3) + ((a * (y1 * y3)) - (a * (t * b))));
	double tmp;
	if (c <= -5.6e+92) {
		tmp = t_2;
	} else if (c <= -1.16e+54) {
		tmp = t_4;
	} else if (c <= -1.35e-67) {
		tmp = y2 * (((x * t_5) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -4.5e-76) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (c <= -7.2e-116) {
		tmp = t_6;
	} else if (c <= -1.5e-119) {
		tmp = t_7;
	} else if (c <= -1.05e-198) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_1)));
	} else if (c <= 2.9e-290) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_3));
	} else if (c <= 3.2e-97) {
		tmp = t_4;
	} else if (c <= 7.2e-22) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (c <= 7.2e+53) {
		tmp = t_7;
	} else if (c <= 3.3e+114) {
		tmp = t_6;
	} else if (c <= 1.7e+173) {
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (x * y2) - (z * y3)
    t_2 = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    t_3 = (b * y0) - (i * y1)
    t_4 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
    t_5 = (c * y0) - (a * y1)
    t_6 = x * ((y2 * t_5) + (j * ((i * y1) - (b * y0))))
    t_7 = z * ((k * t_3) + ((a * (y1 * y3)) - (a * (t * b))))
    if (c <= (-5.6d+92)) then
        tmp = t_2
    else if (c <= (-1.16d+54)) then
        tmp = t_4
    else if (c <= (-1.35d-67)) then
        tmp = y2 * (((x * t_5) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
    else if (c <= (-4.5d-76)) then
        tmp = y3 * (y * ((c * y4) - (a * y5)))
    else if (c <= (-7.2d-116)) then
        tmp = t_6
    else if (c <= (-1.5d-119)) then
        tmp = t_7
    else if (c <= (-1.05d-198)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_1)))
    else if (c <= 2.9d-290) then
        tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_3))
    else if (c <= 3.2d-97) then
        tmp = t_4
    else if (c <= 7.2d-22) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (c <= 7.2d+53) then
        tmp = t_7
    else if (c <= 3.3d+114) then
        tmp = t_6
    else if (c <= 1.7d+173) then
        tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_3 = (b * y0) - (i * y1);
	double t_4 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double t_5 = (c * y0) - (a * y1);
	double t_6 = x * ((y2 * t_5) + (j * ((i * y1) - (b * y0))));
	double t_7 = z * ((k * t_3) + ((a * (y1 * y3)) - (a * (t * b))));
	double tmp;
	if (c <= -5.6e+92) {
		tmp = t_2;
	} else if (c <= -1.16e+54) {
		tmp = t_4;
	} else if (c <= -1.35e-67) {
		tmp = y2 * (((x * t_5) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -4.5e-76) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (c <= -7.2e-116) {
		tmp = t_6;
	} else if (c <= -1.5e-119) {
		tmp = t_7;
	} else if (c <= -1.05e-198) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_1)));
	} else if (c <= 2.9e-290) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_3));
	} else if (c <= 3.2e-97) {
		tmp = t_4;
	} else if (c <= 7.2e-22) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (c <= 7.2e+53) {
		tmp = t_7;
	} else if (c <= 3.3e+114) {
		tmp = t_6;
	} else if (c <= 1.7e+173) {
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y2) - (z * y3)
	t_2 = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	t_3 = (b * y0) - (i * y1)
	t_4 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
	t_5 = (c * y0) - (a * y1)
	t_6 = x * ((y2 * t_5) + (j * ((i * y1) - (b * y0))))
	t_7 = z * ((k * t_3) + ((a * (y1 * y3)) - (a * (t * b))))
	tmp = 0
	if c <= -5.6e+92:
		tmp = t_2
	elif c <= -1.16e+54:
		tmp = t_4
	elif c <= -1.35e-67:
		tmp = y2 * (((x * t_5) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
	elif c <= -4.5e-76:
		tmp = y3 * (y * ((c * y4) - (a * y5)))
	elif c <= -7.2e-116:
		tmp = t_6
	elif c <= -1.5e-119:
		tmp = t_7
	elif c <= -1.05e-198:
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_1)))
	elif c <= 2.9e-290:
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_3))
	elif c <= 3.2e-97:
		tmp = t_4
	elif c <= 7.2e-22:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif c <= 7.2e+53:
		tmp = t_7
	elif c <= 3.3e+114:
		tmp = t_6
	elif c <= 1.7e+173:
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y2) - Float64(z * y3))
	t_2 = Float64(c * Float64(Float64(Float64(y0 * t_1) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_3 = Float64(Float64(b * y0) - Float64(i * y1))
	t_4 = Float64(b * Float64(Float64(Float64(Float64(Float64(t * j) - Float64(y * k)) * y4) + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_5 = Float64(Float64(c * y0) - Float64(a * y1))
	t_6 = Float64(x * Float64(Float64(y2 * t_5) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_7 = Float64(z * Float64(Float64(k * t_3) + Float64(Float64(a * Float64(y1 * y3)) - Float64(a * Float64(t * b)))))
	tmp = 0.0
	if (c <= -5.6e+92)
		tmp = t_2;
	elseif (c <= -1.16e+54)
		tmp = t_4;
	elseif (c <= -1.35e-67)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_5) - Float64(k * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= -4.5e-76)
		tmp = Float64(y3 * Float64(y * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (c <= -7.2e-116)
		tmp = t_6;
	elseif (c <= -1.5e-119)
		tmp = t_7;
	elseif (c <= -1.05e-198)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(a * t_1))));
	elseif (c <= 2.9e-290)
		tmp = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * t_3)));
	elseif (c <= 3.2e-97)
		tmp = t_4;
	elseif (c <= 7.2e-22)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (c <= 7.2e+53)
		tmp = t_7;
	elseif (c <= 3.3e+114)
		tmp = t_6;
	elseif (c <= 1.7e+173)
		tmp = Float64(j * Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(Float64(y0 * Float64(y3 * y5)) - Float64(y0 * Float64(x * b)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y2) - (z * y3);
	t_2 = c * (((y0 * t_1) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	t_3 = (b * y0) - (i * y1);
	t_4 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	t_5 = (c * y0) - (a * y1);
	t_6 = x * ((y2 * t_5) + (j * ((i * y1) - (b * y0))));
	t_7 = z * ((k * t_3) + ((a * (y1 * y3)) - (a * (t * b))));
	tmp = 0.0;
	if (c <= -5.6e+92)
		tmp = t_2;
	elseif (c <= -1.16e+54)
		tmp = t_4;
	elseif (c <= -1.35e-67)
		tmp = y2 * (((x * t_5) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	elseif (c <= -4.5e-76)
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	elseif (c <= -7.2e-116)
		tmp = t_6;
	elseif (c <= -1.5e-119)
		tmp = t_7;
	elseif (c <= -1.05e-198)
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_1)));
	elseif (c <= 2.9e-290)
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_3));
	elseif (c <= 3.2e-97)
		tmp = t_4;
	elseif (c <= 7.2e-22)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (c <= 7.2e+53)
		tmp = t_7;
	elseif (c <= 3.3e+114)
		tmp = t_6;
	elseif (c <= 1.7e+173)
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(N[(y0 * t$95$1), $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]}, Block[{t$95$3 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x * N[(N[(y2 * t$95$5), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(z * N[(N[(k * t$95$3), $MachinePrecision] + N[(N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.6e+92], t$95$2, If[LessEqual[c, -1.16e+54], t$95$4, If[LessEqual[c, -1.35e-67], N[(y2 * N[(N[(N[(x * t$95$5), $MachinePrecision] - N[(k * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.5e-76], N[(y3 * N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.2e-116], t$95$6, If[LessEqual[c, -1.5e-119], t$95$7, If[LessEqual[c, -1.05e-198], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e-290], N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e-97], t$95$4, If[LessEqual[c, 7.2e-22], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.2e+53], t$95$7, If[LessEqual[c, 3.3e+114], t$95$6, If[LessEqual[c, 1.7e+173], N[(j * N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if c < -5.60000000000000001e92 or 1.70000000000000011e173 < c

   1. Initial program 26.7%

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

   3. Taylor expanded in c around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. *-commutative 73.8%

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

      5. *-commutative 73.8%

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

      6. *-commutative 73.8%

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

      7. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   if -5.60000000000000001e92 < c < -1.1600000000000001e54 or 2.89999999999999994e-290 < c < 3.1999999999999998e-97

   1. Initial program 26.5%

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

   3. Taylor expanded in b around inf 62.4%

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

   if -1.1600000000000001e54 < c < -1.35000000000000008e-67

   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 y2 around inf 63.3%

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

   if -1.35000000000000008e-67 < c < -4.5000000000000001e-76

   1. Initial program 51.7%

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

   3. Taylor expanded in y3 around -inf 86.3%

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

   4. Taylor expanded in y around inf 61.5%

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

   if -4.5000000000000001e-76 < c < -7.19999999999999951e-116 or 7.2e53 < c < 3.3000000000000001e114

   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 x around inf 47.7%

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

   4. Taylor expanded in y around 0 63.7%

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

      1. *-commutative 63.7%

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

      2. *-commutative 63.7%

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

   6. Simplified 63.7%

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

   if -7.19999999999999951e-116 < c < -1.5000000000000001e-119 or 7.1999999999999996e-22 < c < 7.2e53

   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 z around -inf 50.3%

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

   4. Taylor expanded in c around 0 65.3%

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

   if -1.5000000000000001e-119 < c < -1.04999999999999996e-198

   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 y1 around -inf 71.5%

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

      1. associate-*r* 71.5%

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

      2. neg-mul-1 71.5%

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

      3. +-commutative 71.5%

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

      4. mul-1-neg 71.5%

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

      5. unsub-neg 71.5%

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

      6. *-commutative 71.5%

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

      7. *-commutative 71.5%

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

      8. *-commutative 71.5%

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

      9. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   if -1.04999999999999996e-198 < c < 2.89999999999999994e-290

   1. Initial program 43.6%

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

   3. Taylor expanded in k around inf 63.0%

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

      1. +-commutative 63.0%

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

      2. mul-1-neg 63.0%

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

      3. unsub-neg 63.0%

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

      4. *-commutative 63.0%

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

      5. associate-*r* 63.0%

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

      6. neg-mul-1 63.0%

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

   5. Simplified 63.0%

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

   if 3.1999999999999998e-97 < c < 7.1999999999999996e-22

   1. Initial program 35.6%

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

   3. Taylor expanded in y0 around inf 45.8%

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

      1. +-commutative 45.8%

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

      2. mul-1-neg 45.8%

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

      3. unsub-neg 45.8%

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

      4. *-commutative 45.8%

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

      5. *-commutative 45.8%

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

      6. *-commutative 45.8%

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

      7. *-commutative 45.8%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in y5 around inf 60.5%

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

   if 3.3000000000000001e114 < c < 1.70000000000000011e173

   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 j around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

      4. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in y1 around 0 69.3%

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

      1. *-commutative 69.3%

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

      2. *-commutative 69.3%

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

      3. +-commutative 69.3%

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

      4. mul-1-neg 69.3%

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

      5. unsub-neg 69.3%

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

      6. associate-*r* 69.3%

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

   8. Simplified 69.3%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \left(\left(b \cdot x\right) \cdot y0 - y0 \cdot \left(y3 \cdot y5\right)\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{+92}:\\ \;\;\;\;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}\;c \leq -1.16 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-76}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-119}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-198}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-290}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-97}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-22}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := c \cdot \left(\left(y0 \cdot t\_3 + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_5 := z \cdot k - x \cdot j\\ t_6 := b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot t\_5\right)\\ \mathbf{if}\;c \leq -5.4 \cdot 10^{+89}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-71}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-135}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-288}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-280}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot t\_3 + t\_1\right) + b \cdot t\_5\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-99}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-20}:\\ \;\;\;\;y0 \cdot t\_1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot t\_2\right)\\ \mathbf{elif}\;c \leq 7.7 \cdot 10^{+171}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t\_2\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+218}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(c \cdot y2 - b \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y5 (- (* j y3) (* k y2))))
        (t_2 (- (* i y1) (* b y0)))
        (t_3 (- (* x y2) (* z y3)))
        (t_4
         (*
          c
          (+
           (+ (* y0 t_3) (* i (- (* z t) (* x y))))
           (* y4 (- (* y y3) (* t y2))))))
        (t_5 (- (* z k) (* x j)))
        (t_6
         (*
          b
          (+
           (+ (* (- (* t j) (* y k)) y4) (* a (- (* x y) (* z t))))
           (* y0 t_5)))))
   (if (<= c -5.4e+89)
     t_4
     (if (<= c -2.4e+53)
       t_6
       (if (<= c -1.8e+20)
         (* a (* x (- (* y b) (* y1 y2))))
         (if (<= c -2.8e-71)
           (* k (* y1 (- (* y2 y4) (* z i))))
           (if (<= c -6.8e-135)
             (* y1 (* z (- (* a y3) (* i k))))
             (if (<= c -2.3e-288)
               t_6
               (if (<= c 4.6e-280)
                 (* y0 (+ (+ (* c t_3) t_1) (* b t_5)))
                 (if (<= c 2e-99)
                   t_6
                   (if (<= c 1.45e-20)
                     (* y0 t_1)
                     (if (<= c 1.1e+54)
                       (*
                        z
                        (+
                         (* k (- (* b y0) (* i y1)))
                         (- (* a (* y1 y3)) (* a (* t b)))))
                       (if (<= c 1.4e+146)
                         (* x (+ (* y2 (- (* c y0) (* a y1))) (* j t_2)))
                         (if (<= c 7.7e+171)
                           (*
                            j
                            (+
                             (+
                              (* t (- (* b y4) (* i y5)))
                              (* y3 (- (* y0 y5) (* y1 y4))))
                             (* x t_2)))
                           (if (<= c 2.8e+218)
                             (* (* x y0) (- (* c y2) (* b j)))
                             t_4)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y5 * ((j * y3) - (k * y2));
	double t_2 = (i * y1) - (b * y0);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = c * (((y0 * t_3) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_5 = (z * k) - (x * j);
	double t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * t_5));
	double tmp;
	if (c <= -5.4e+89) {
		tmp = t_4;
	} else if (c <= -2.4e+53) {
		tmp = t_6;
	} else if (c <= -1.8e+20) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (c <= -2.8e-71) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (c <= -6.8e-135) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -2.3e-288) {
		tmp = t_6;
	} else if (c <= 4.6e-280) {
		tmp = y0 * (((c * t_3) + t_1) + (b * t_5));
	} else if (c <= 2e-99) {
		tmp = t_6;
	} else if (c <= 1.45e-20) {
		tmp = y0 * t_1;
	} else if (c <= 1.1e+54) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 1.4e+146) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * t_2));
	} else if (c <= 7.7e+171) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	} else if (c <= 2.8e+218) {
		tmp = (x * y0) * ((c * y2) - (b * j));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = y5 * ((j * y3) - (k * y2))
    t_2 = (i * y1) - (b * y0)
    t_3 = (x * y2) - (z * y3)
    t_4 = c * (((y0 * t_3) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    t_5 = (z * k) - (x * j)
    t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * t_5))
    if (c <= (-5.4d+89)) then
        tmp = t_4
    else if (c <= (-2.4d+53)) then
        tmp = t_6
    else if (c <= (-1.8d+20)) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else if (c <= (-2.8d-71)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (c <= (-6.8d-135)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (c <= (-2.3d-288)) then
        tmp = t_6
    else if (c <= 4.6d-280) then
        tmp = y0 * (((c * t_3) + t_1) + (b * t_5))
    else if (c <= 2d-99) then
        tmp = t_6
    else if (c <= 1.45d-20) then
        tmp = y0 * t_1
    else if (c <= 1.1d+54) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))))
    else if (c <= 1.4d+146) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * t_2))
    else if (c <= 7.7d+171) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2))
    else if (c <= 2.8d+218) then
        tmp = (x * y0) * ((c * y2) - (b * j))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y5 * ((j * y3) - (k * y2));
	double t_2 = (i * y1) - (b * y0);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = c * (((y0 * t_3) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_5 = (z * k) - (x * j);
	double t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * t_5));
	double tmp;
	if (c <= -5.4e+89) {
		tmp = t_4;
	} else if (c <= -2.4e+53) {
		tmp = t_6;
	} else if (c <= -1.8e+20) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (c <= -2.8e-71) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (c <= -6.8e-135) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -2.3e-288) {
		tmp = t_6;
	} else if (c <= 4.6e-280) {
		tmp = y0 * (((c * t_3) + t_1) + (b * t_5));
	} else if (c <= 2e-99) {
		tmp = t_6;
	} else if (c <= 1.45e-20) {
		tmp = y0 * t_1;
	} else if (c <= 1.1e+54) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 1.4e+146) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * t_2));
	} else if (c <= 7.7e+171) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	} else if (c <= 2.8e+218) {
		tmp = (x * y0) * ((c * y2) - (b * j));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y5 * ((j * y3) - (k * y2))
	t_2 = (i * y1) - (b * y0)
	t_3 = (x * y2) - (z * y3)
	t_4 = c * (((y0 * t_3) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	t_5 = (z * k) - (x * j)
	t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * t_5))
	tmp = 0
	if c <= -5.4e+89:
		tmp = t_4
	elif c <= -2.4e+53:
		tmp = t_6
	elif c <= -1.8e+20:
		tmp = a * (x * ((y * b) - (y1 * y2)))
	elif c <= -2.8e-71:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif c <= -6.8e-135:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif c <= -2.3e-288:
		tmp = t_6
	elif c <= 4.6e-280:
		tmp = y0 * (((c * t_3) + t_1) + (b * t_5))
	elif c <= 2e-99:
		tmp = t_6
	elif c <= 1.45e-20:
		tmp = y0 * t_1
	elif c <= 1.1e+54:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))))
	elif c <= 1.4e+146:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * t_2))
	elif c <= 7.7e+171:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2))
	elif c <= 2.8e+218:
		tmp = (x * y0) * ((c * y2) - (b * j))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(c * Float64(Float64(Float64(y0 * t_3) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_5 = Float64(Float64(z * k) - Float64(x * j))
	t_6 = Float64(b * Float64(Float64(Float64(Float64(Float64(t * j) - Float64(y * k)) * y4) + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * t_5)))
	tmp = 0.0
	if (c <= -5.4e+89)
		tmp = t_4;
	elseif (c <= -2.4e+53)
		tmp = t_6;
	elseif (c <= -1.8e+20)
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (c <= -2.8e-71)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (c <= -6.8e-135)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (c <= -2.3e-288)
		tmp = t_6;
	elseif (c <= 4.6e-280)
		tmp = Float64(y0 * Float64(Float64(Float64(c * t_3) + t_1) + Float64(b * t_5)));
	elseif (c <= 2e-99)
		tmp = t_6;
	elseif (c <= 1.45e-20)
		tmp = Float64(y0 * t_1);
	elseif (c <= 1.1e+54)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(a * Float64(y1 * y3)) - Float64(a * Float64(t * b)))));
	elseif (c <= 1.4e+146)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * t_2)));
	elseif (c <= 7.7e+171)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_2)));
	elseif (c <= 2.8e+218)
		tmp = Float64(Float64(x * y0) * Float64(Float64(c * y2) - Float64(b * j)));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y5 * ((j * y3) - (k * y2));
	t_2 = (i * y1) - (b * y0);
	t_3 = (x * y2) - (z * y3);
	t_4 = c * (((y0 * t_3) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	t_5 = (z * k) - (x * j);
	t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * t_5));
	tmp = 0.0;
	if (c <= -5.4e+89)
		tmp = t_4;
	elseif (c <= -2.4e+53)
		tmp = t_6;
	elseif (c <= -1.8e+20)
		tmp = a * (x * ((y * b) - (y1 * y2)));
	elseif (c <= -2.8e-71)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (c <= -6.8e-135)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (c <= -2.3e-288)
		tmp = t_6;
	elseif (c <= 4.6e-280)
		tmp = y0 * (((c * t_3) + t_1) + (b * t_5));
	elseif (c <= 2e-99)
		tmp = t_6;
	elseif (c <= 1.45e-20)
		tmp = y0 * t_1;
	elseif (c <= 1.1e+54)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	elseif (c <= 1.4e+146)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * t_2));
	elseif (c <= 7.7e+171)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	elseif (c <= 2.8e+218)
		tmp = (x * y0) * ((c * y2) - (b * j));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(N[(y0 * t$95$3), $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]}, Block[{t$95$5 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(b * N[(N[(N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.4e+89], t$95$4, If[LessEqual[c, -2.4e+53], t$95$6, If[LessEqual[c, -1.8e+20], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.8e-71], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.8e-135], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.3e-288], t$95$6, If[LessEqual[c, 4.6e-280], N[(y0 * N[(N[(N[(c * t$95$3), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(b * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e-99], t$95$6, If[LessEqual[c, 1.45e-20], N[(y0 * t$95$1), $MachinePrecision], If[LessEqual[c, 1.1e+54], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.4e+146], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.7e+171], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.8e+218], N[(N[(x * y0), $MachinePrecision] * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if c < -5.4e89 or 2.7999999999999998e218 < c

   1. Initial program 24.6%

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

   3. Taylor expanded in c around inf 77.8%

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

      1. +-commutative 77.8%

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

      2. mul-1-neg 77.8%

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

      3. unsub-neg 77.8%

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

      4. *-commutative 77.8%

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

      5. *-commutative 77.8%

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

      6. *-commutative 77.8%

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

      7. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   if -5.4e89 < c < -2.4e53 or -6.79999999999999978e-135 < c < -2.3e-288 or 4.5999999999999999e-280 < c < 2e-99

   1. Initial program 27.9%

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

   3. Taylor expanded in b around inf 60.6%

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

   if -2.4e53 < c < -1.8e20

   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 x around inf 28.7%

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

   4. Taylor expanded in a around -inf 85.9%

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

      1. associate-*r* 85.9%

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

      2. mul-1-neg 85.9%

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

      3. mul-1-neg 85.9%

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

      4. distribute-lft-neg-out 85.9%

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

      5. +-commutative 85.9%

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

      6. cancel-sign-sub-inv 85.9%

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

      7. *-commutative 85.9%

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

   6. Simplified 85.9%

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

   if -1.8e20 < c < -2.8e-71

   1. Initial program 16.3%

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

   3. Taylor expanded in k around inf 46.7%

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

      1. +-commutative 46.7%

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

      2. mul-1-neg 46.7%

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

      3. unsub-neg 46.7%

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

      4. *-commutative 46.7%

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

      5. associate-*r* 46.7%

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

      6. neg-mul-1 46.7%

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

   5. Simplified 46.7%

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

   6. Taylor expanded in y1 around inf 55.2%

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

      1. *-commutative 55.2%

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

      2. *-commutative 55.2%

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

   8. Simplified 55.2%

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

   if -2.8e-71 < c < -6.79999999999999978e-135

   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 z around -inf 33.6%

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

   4. Taylor expanded in y1 around -inf 50.6%

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

   if -2.3e-288 < c < 4.5999999999999999e-280

   1. Initial program 52.3%

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

   3. Taylor expanded in y0 around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. *-commutative 67.1%

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

      6. *-commutative 67.1%

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

      7. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   if 2e-99 < c < 1.45e-20

   1. Initial program 35.6%

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

   3. Taylor expanded in y0 around inf 45.8%

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

      1. +-commutative 45.8%

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

      2. mul-1-neg 45.8%

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

      3. unsub-neg 45.8%

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

      4. *-commutative 45.8%

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

      5. *-commutative 45.8%

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

      6. *-commutative 45.8%

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

      7. *-commutative 45.8%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in y5 around inf 60.5%

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

   if 1.45e-20 < c < 1.09999999999999995e54

   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 z around -inf 44.8%

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

   4. Taylor expanded in c around 0 61.4%

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

   if 1.09999999999999995e54 < c < 1.4e146

   1. Initial program 27.3%

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

   3. Taylor expanded in x around inf 50.3%

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

   4. Taylor expanded in y around 0 59.7%

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

      1. *-commutative 59.7%

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

      2. *-commutative 59.7%

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

   6. Simplified 59.7%

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

   if 1.4e146 < c < 7.70000000000000022e171

   1. Initial program 37.5%

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

   3. Taylor expanded in j around inf 87.5%

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

      1. +-commutative 87.5%

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

      2. mul-1-neg 87.5%

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

      3. unsub-neg 87.5%

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

      4. *-commutative 87.5%

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

   5. Simplified 87.5%

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

   if 7.70000000000000022e171 < c < 2.7999999999999998e218

   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 y0 around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

      5. *-commutative 59.2%

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

      6. *-commutative 59.2%

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

      7. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in x around inf 75.4%

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

      1. associate-*r* 67.5%

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

   8. Simplified 67.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.4 \cdot 10^{+89}:\\ \;\;\;\;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}\;c \leq -2.4 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-71}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-135}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-288}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-280}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-20}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 7.7 \cdot 10^{+171}:\\ \;\;\;\;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}\;c \leq 2.8 \cdot 10^{+218}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(c \cdot y2 - b \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := b \cdot y0 - i \cdot y1\\ t_3 := c \cdot y0 - a \cdot y1\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := i \cdot y5 - b \cdot y4\\ t_6 := t \cdot j - y \cdot k\\ t_7 := x \cdot y2 - z \cdot y3\\ t_8 := y2 \cdot t\_3\\ t_9 := a \cdot b - c \cdot i\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+122}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot t\_1\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(k \cdot t\_2 + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot t\_3\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(t\_6 \cdot y4\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+23}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot t\_5\right) + z \cdot t\_2\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-58}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot t\_6 + y0 \cdot t\_4\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(t\_8 + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-208}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(\left(t\_8 + y \cdot t\_9\right) + i \cdot \left(j \cdot y1 - b \cdot \frac{j \cdot y0}{i}\right)\right)\\ \mathbf{elif}\;t \leq 7400000000:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot t\_7 + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+100}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot t\_4 - a \cdot t\_7\right)\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+201}:\\ \;\;\;\;y \cdot \left(\left(k \cdot t\_5 + x \cdot t\_9\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot t\_1 + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2 (- (* b y0) (* i y1)))
        (t_3 (- (* c y0) (* a y1)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* i y5) (* b y4)))
        (t_6 (- (* t j) (* y k)))
        (t_7 (- (* x y2) (* z y3)))
        (t_8 (* y2 t_3))
        (t_9 (- (* a b) (* c i))))
   (if (<= t -2.6e+122)
     (*
      t
      (+ (+ (* z (- (* c i) (* a b))) (* j t_1)) (* y2 (- (* a y5) (* c y4)))))
     (if (<= t -6.5e+72)
       (* z (+ (* k t_2) (- (* a (* y1 y3)) (* a (* t b)))))
       (if (<= t -5e+70)
         (* (* x y2) t_3)
         (if (<= t -2.1e+50)
           (* b (* t_6 y4))
           (if (<= t -3.5e+23)
             (* k (+ (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y t_5)) (* z t_2)))
             (if (<= t -1.1e-58)
               (* y5 (- (* a (- (* t y2) (* y y3))) (+ (* i t_6) (* y0 t_4))))
               (if (<= t 8.5e-222)
                 (* x (+ t_8 (* j (- (* i y1) (* b y0)))))
                 (if (<= t 1.75e-208)
                   (* b (* k (* z y0)))
                   (if (<= t 1.05e-62)
                     (*
                      x
                      (+
                       (+ t_8 (* y t_9))
                       (* i (- (* j y1) (* b (/ (* j y0) i))))))
                     (if (<= t 7400000000.0)
                       (*
                        c
                        (+
                         (+ (* y0 t_7) (* i (- (* z t) (* x y))))
                         (* y4 (- (* y y3) (* t y2)))))
                       (if (<= t 7e+100)
                         (*
                          y1
                          (+
                           (* i (- (* x j) (* z k)))
                           (- (* y4 t_4) (* a t_7))))
                         (if (<= t 1.12e+201)
                           (*
                            y
                            (+
                             (+ (* k t_5) (* x t_9))
                             (* y3 (- (* c y4) (* a y5)))))
                           (*
                            j
                            (+
                             (* t t_1)
                             (-
                              (* y0 (* y3 y5))
                              (* y0 (* x b)))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (b * y0) - (i * y1);
	double t_3 = (c * y0) - (a * y1);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (i * y5) - (b * y4);
	double t_6 = (t * j) - (y * k);
	double t_7 = (x * y2) - (z * y3);
	double t_8 = y2 * t_3;
	double t_9 = (a * b) - (c * i);
	double tmp;
	if (t <= -2.6e+122) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * ((a * y5) - (c * y4))));
	} else if (t <= -6.5e+72) {
		tmp = z * ((k * t_2) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (t <= -5e+70) {
		tmp = (x * y2) * t_3;
	} else if (t <= -2.1e+50) {
		tmp = b * (t_6 * y4);
	} else if (t <= -3.5e+23) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * t_5)) + (z * t_2));
	} else if (t <= -1.1e-58) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((i * t_6) + (y0 * t_4)));
	} else if (t <= 8.5e-222) {
		tmp = x * (t_8 + (j * ((i * y1) - (b * y0))));
	} else if (t <= 1.75e-208) {
		tmp = b * (k * (z * y0));
	} else if (t <= 1.05e-62) {
		tmp = x * ((t_8 + (y * t_9)) + (i * ((j * y1) - (b * ((j * y0) / i)))));
	} else if (t <= 7400000000.0) {
		tmp = c * (((y0 * t_7) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (t <= 7e+100) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) - (a * t_7)));
	} else if (t <= 1.12e+201) {
		tmp = y * (((k * t_5) + (x * t_9)) + (y3 * ((c * y4) - (a * y5))));
	} else {
		tmp = j * ((t * t_1) + ((y0 * (y3 * y5)) - (y0 * (x * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (b * y4) - (i * y5)
    t_2 = (b * y0) - (i * y1)
    t_3 = (c * y0) - (a * y1)
    t_4 = (k * y2) - (j * y3)
    t_5 = (i * y5) - (b * y4)
    t_6 = (t * j) - (y * k)
    t_7 = (x * y2) - (z * y3)
    t_8 = y2 * t_3
    t_9 = (a * b) - (c * i)
    if (t <= (-2.6d+122)) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * ((a * y5) - (c * y4))))
    else if (t <= (-6.5d+72)) then
        tmp = z * ((k * t_2) + ((a * (y1 * y3)) - (a * (t * b))))
    else if (t <= (-5d+70)) then
        tmp = (x * y2) * t_3
    else if (t <= (-2.1d+50)) then
        tmp = b * (t_6 * y4)
    else if (t <= (-3.5d+23)) then
        tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * t_5)) + (z * t_2))
    else if (t <= (-1.1d-58)) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((i * t_6) + (y0 * t_4)))
    else if (t <= 8.5d-222) then
        tmp = x * (t_8 + (j * ((i * y1) - (b * y0))))
    else if (t <= 1.75d-208) then
        tmp = b * (k * (z * y0))
    else if (t <= 1.05d-62) then
        tmp = x * ((t_8 + (y * t_9)) + (i * ((j * y1) - (b * ((j * y0) / i)))))
    else if (t <= 7400000000.0d0) then
        tmp = c * (((y0 * t_7) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    else if (t <= 7d+100) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) - (a * t_7)))
    else if (t <= 1.12d+201) then
        tmp = y * (((k * t_5) + (x * t_9)) + (y3 * ((c * y4) - (a * y5))))
    else
        tmp = j * ((t * t_1) + ((y0 * (y3 * y5)) - (y0 * (x * 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 t_1 = (b * y4) - (i * y5);
	double t_2 = (b * y0) - (i * y1);
	double t_3 = (c * y0) - (a * y1);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (i * y5) - (b * y4);
	double t_6 = (t * j) - (y * k);
	double t_7 = (x * y2) - (z * y3);
	double t_8 = y2 * t_3;
	double t_9 = (a * b) - (c * i);
	double tmp;
	if (t <= -2.6e+122) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * ((a * y5) - (c * y4))));
	} else if (t <= -6.5e+72) {
		tmp = z * ((k * t_2) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (t <= -5e+70) {
		tmp = (x * y2) * t_3;
	} else if (t <= -2.1e+50) {
		tmp = b * (t_6 * y4);
	} else if (t <= -3.5e+23) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * t_5)) + (z * t_2));
	} else if (t <= -1.1e-58) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((i * t_6) + (y0 * t_4)));
	} else if (t <= 8.5e-222) {
		tmp = x * (t_8 + (j * ((i * y1) - (b * y0))));
	} else if (t <= 1.75e-208) {
		tmp = b * (k * (z * y0));
	} else if (t <= 1.05e-62) {
		tmp = x * ((t_8 + (y * t_9)) + (i * ((j * y1) - (b * ((j * y0) / i)))));
	} else if (t <= 7400000000.0) {
		tmp = c * (((y0 * t_7) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (t <= 7e+100) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) - (a * t_7)));
	} else if (t <= 1.12e+201) {
		tmp = y * (((k * t_5) + (x * t_9)) + (y3 * ((c * y4) - (a * y5))));
	} else {
		tmp = j * ((t * t_1) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y4) - (i * y5)
	t_2 = (b * y0) - (i * y1)
	t_3 = (c * y0) - (a * y1)
	t_4 = (k * y2) - (j * y3)
	t_5 = (i * y5) - (b * y4)
	t_6 = (t * j) - (y * k)
	t_7 = (x * y2) - (z * y3)
	t_8 = y2 * t_3
	t_9 = (a * b) - (c * i)
	tmp = 0
	if t <= -2.6e+122:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * ((a * y5) - (c * y4))))
	elif t <= -6.5e+72:
		tmp = z * ((k * t_2) + ((a * (y1 * y3)) - (a * (t * b))))
	elif t <= -5e+70:
		tmp = (x * y2) * t_3
	elif t <= -2.1e+50:
		tmp = b * (t_6 * y4)
	elif t <= -3.5e+23:
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * t_5)) + (z * t_2))
	elif t <= -1.1e-58:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((i * t_6) + (y0 * t_4)))
	elif t <= 8.5e-222:
		tmp = x * (t_8 + (j * ((i * y1) - (b * y0))))
	elif t <= 1.75e-208:
		tmp = b * (k * (z * y0))
	elif t <= 1.05e-62:
		tmp = x * ((t_8 + (y * t_9)) + (i * ((j * y1) - (b * ((j * y0) / i)))))
	elif t <= 7400000000.0:
		tmp = c * (((y0 * t_7) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	elif t <= 7e+100:
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) - (a * t_7)))
	elif t <= 1.12e+201:
		tmp = y * (((k * t_5) + (x * t_9)) + (y3 * ((c * y4) - (a * y5))))
	else:
		tmp = j * ((t * t_1) + ((y0 * (y3 * y5)) - (y0 * (x * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y4) - Float64(i * y5))
	t_2 = Float64(Float64(b * y0) - Float64(i * y1))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(i * y5) - Float64(b * y4))
	t_6 = Float64(Float64(t * j) - Float64(y * k))
	t_7 = Float64(Float64(x * y2) - Float64(z * y3))
	t_8 = Float64(y2 * t_3)
	t_9 = Float64(Float64(a * b) - Float64(c * i))
	tmp = 0.0
	if (t <= -2.6e+122)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * t_1)) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (t <= -6.5e+72)
		tmp = Float64(z * Float64(Float64(k * t_2) + Float64(Float64(a * Float64(y1 * y3)) - Float64(a * Float64(t * b)))));
	elseif (t <= -5e+70)
		tmp = Float64(Float64(x * y2) * t_3);
	elseif (t <= -2.1e+50)
		tmp = Float64(b * Float64(t_6 * y4));
	elseif (t <= -3.5e+23)
		tmp = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * t_5)) + Float64(z * t_2)));
	elseif (t <= -1.1e-58)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(Float64(i * t_6) + Float64(y0 * t_4))));
	elseif (t <= 8.5e-222)
		tmp = Float64(x * Float64(t_8 + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (t <= 1.75e-208)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (t <= 1.05e-62)
		tmp = Float64(x * Float64(Float64(t_8 + Float64(y * t_9)) + Float64(i * Float64(Float64(j * y1) - Float64(b * Float64(Float64(j * y0) / i))))));
	elseif (t <= 7400000000.0)
		tmp = Float64(c * Float64(Float64(Float64(y0 * t_7) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (t <= 7e+100)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y4 * t_4) - Float64(a * t_7))));
	elseif (t <= 1.12e+201)
		tmp = Float64(y * Float64(Float64(Float64(k * t_5) + Float64(x * t_9)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	else
		tmp = Float64(j * Float64(Float64(t * t_1) + Float64(Float64(y0 * Float64(y3 * y5)) - Float64(y0 * Float64(x * 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)
	t_1 = (b * y4) - (i * y5);
	t_2 = (b * y0) - (i * y1);
	t_3 = (c * y0) - (a * y1);
	t_4 = (k * y2) - (j * y3);
	t_5 = (i * y5) - (b * y4);
	t_6 = (t * j) - (y * k);
	t_7 = (x * y2) - (z * y3);
	t_8 = y2 * t_3;
	t_9 = (a * b) - (c * i);
	tmp = 0.0;
	if (t <= -2.6e+122)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * ((a * y5) - (c * y4))));
	elseif (t <= -6.5e+72)
		tmp = z * ((k * t_2) + ((a * (y1 * y3)) - (a * (t * b))));
	elseif (t <= -5e+70)
		tmp = (x * y2) * t_3;
	elseif (t <= -2.1e+50)
		tmp = b * (t_6 * y4);
	elseif (t <= -3.5e+23)
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * t_5)) + (z * t_2));
	elseif (t <= -1.1e-58)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - ((i * t_6) + (y0 * t_4)));
	elseif (t <= 8.5e-222)
		tmp = x * (t_8 + (j * ((i * y1) - (b * y0))));
	elseif (t <= 1.75e-208)
		tmp = b * (k * (z * y0));
	elseif (t <= 1.05e-62)
		tmp = x * ((t_8 + (y * t_9)) + (i * ((j * y1) - (b * ((j * y0) / i)))));
	elseif (t <= 7400000000.0)
		tmp = c * (((y0 * t_7) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (t <= 7e+100)
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) - (a * t_7)));
	elseif (t <= 1.12e+201)
		tmp = y * (((k * t_5) + (x * t_9)) + (y3 * ((c * y4) - (a * y5))));
	else
		tmp = j * ((t * t_1) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(y2 * t$95$3), $MachinePrecision]}, Block[{t$95$9 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+122], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e+72], N[(z * N[(N[(k * t$95$2), $MachinePrecision] + N[(N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e+70], N[(N[(x * y2), $MachinePrecision] * t$95$3), $MachinePrecision], If[LessEqual[t, -2.1e+50], N[(b * N[(t$95$6 * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e+23], N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.1e-58], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(i * t$95$6), $MachinePrecision] + N[(y0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-222], N[(x * N[(t$95$8 + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-208], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-62], N[(x * N[(N[(t$95$8 + N[(y * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(j * y1), $MachinePrecision] - N[(b * N[(N[(j * y0), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7400000000.0], N[(c * N[(N[(N[(y0 * t$95$7), $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[t, 7e+100], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * t$95$4), $MachinePrecision] - N[(a * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e+201], N[(y * N[(N[(N[(k * t$95$5), $MachinePrecision] + N[(x * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(t * t$95$1), $MachinePrecision] + N[(N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 13 regimes

2. if t < -2.60000000000000007e122

   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 t around inf 65.2%

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

   if -2.60000000000000007e122 < t < -6.5000000000000001e72

   1. Initial program 13.8%

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

   3. Taylor expanded in z around -inf 60.8%

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

   4. Taylor expanded in c around 0 74.1%

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

   if -6.5000000000000001e72 < t < -5.0000000000000002e70

   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 50.0%

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

   4. Taylor expanded in y2 around inf 100.0%

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

      1. associate-*r* 100.0%

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

   6. Simplified 100.0%

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

   if -5.0000000000000002e70 < t < -2.1e50

   1. Initial program 57.1%

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

   3. Taylor expanded in b around inf 71.4%

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

      1. fma-define 71.4%

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

      2. *-commutative 71.4%

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

      3. *-commutative 71.4%

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

      4. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in y4 around inf 86.1%

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

      1. *-commutative 86.1%

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

      2. *-commutative 86.1%

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

   8. Simplified 86.1%

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

   if -2.1e50 < t < -3.5000000000000002e23

   1. Initial program 75.0%

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

   3. Taylor expanded in k around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*r* 100.0%

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

      6. neg-mul-1 100.0%

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

   5. Simplified 100.0%

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

   if -3.5000000000000002e23 < t < -1.10000000000000003e-58

   1. Initial program 28.5%

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

   3. Taylor expanded in y5 around -inf 81.0%

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

   if -1.10000000000000003e-58 < t < 8.5000000000000003e-222

   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 x around inf 45.3%

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

   4. Taylor expanded in y around 0 55.8%

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

      1. *-commutative 55.8%

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

      2. *-commutative 55.8%

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

   6. Simplified 55.8%

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

   if 8.5000000000000003e-222 < t < 1.74999999999999996e-208

   1. Initial program 23.7%

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

   3. Taylor expanded in k around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. *-commutative 56.2%

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

      5. associate-*r* 56.2%

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

      6. neg-mul-1 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in z around inf 67.3%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in b around inf 77.7%

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

   if 1.74999999999999996e-208 < t < 1.05e-62

   1. Initial program 33.5%

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

   3. Taylor expanded in 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 i around inf 63.4%

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

      1. +-commutative 63.4%

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

      2. mul-1-neg 63.4%

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

      3. unsub-neg 63.4%

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

      4. associate-/l* 63.4%

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

      5. *-commutative 63.4%

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

      6. *-commutative 63.4%

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

   6. Simplified 63.4%

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

   if 1.05e-62 < t < 7.4e9

   1. Initial program 18.2%

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

   3. Taylor expanded in c around inf 90.9%

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

      1. +-commutative 90.9%

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

      2. mul-1-neg 90.9%

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

      3. unsub-neg 90.9%

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

      4. *-commutative 90.9%

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

      5. *-commutative 90.9%

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

      6. *-commutative 90.9%

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

      7. *-commutative 90.9%

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

   5. Simplified 90.9%

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

   if 7.4e9 < t < 6.99999999999999953e100

   1. Initial program 34.6%

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

   3. Taylor expanded in y1 around -inf 57.4%

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

      1. associate-*r* 57.4%

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

      2. neg-mul-1 57.4%

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

      3. +-commutative 57.4%

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

      4. mul-1-neg 57.4%

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

      5. unsub-neg 57.4%

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

      6. *-commutative 57.4%

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

      7. *-commutative 57.4%

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

      8. *-commutative 57.4%

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

      9. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   if 6.99999999999999953e100 < t < 1.11999999999999994e201

   1. Initial program 32.6%

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

   3. Taylor expanded in y around inf 63.7%

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

   if 1.11999999999999994e201 < t

   1. Initial program 14.9%

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

   3. Taylor expanded in j around inf 54.9%

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

      1. +-commutative 54.9%

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

      2. mul-1-neg 54.9%

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

      3. unsub-neg 54.9%

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

      4. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in y1 around 0 65.0%

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

      1. *-commutative 65.0%

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

      2. *-commutative 65.0%

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

      3. +-commutative 65.0%

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

      4. mul-1-neg 65.0%

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

      5. unsub-neg 65.0%

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

      6. associate-*r* 65.0%

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

   8. Simplified 65.0%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \left(\left(b \cdot x\right) \cdot y0 - y0 \cdot \left(y3 \cdot y5\right)\right)\right)} \]
3. Recombined 13 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+122}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+23}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-58}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-208}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + y \cdot \left(a \cdot b - c \cdot i\right)\right) + i \cdot \left(j \cdot y1 - b \cdot \frac{j \cdot y0}{i}\right)\right)\\ \mathbf{elif}\;t \leq 7400000000:\\ \;\;\;\;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}\;t \leq 7 \cdot 10^{+100}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+201}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := c \cdot \left(\left(y0 \cdot t\_2 + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_4 := y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\\ t_5 := z \cdot k - x \cdot j\\ t_6 := b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot t\_5\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+91}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{+53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq -5.1 \cdot 10^{-45}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t\_1 - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -2.15 \cdot 10^{-138}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-287}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-298}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot t\_2 + t\_4\right) + b \cdot t\_5\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-99}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-22}:\\ \;\;\;\;y0 \cdot t\_4\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(y2 \cdot t\_1 + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+176}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3
         (*
          c
          (+
           (+ (* y0 t_2) (* i (- (* z t) (* x y))))
           (* y4 (- (* y y3) (* t y2))))))
        (t_4 (* y5 (- (* j y3) (* k y2))))
        (t_5 (- (* z k) (* x j)))
        (t_6
         (*
          b
          (+
           (+ (* (- (* t j) (* y k)) y4) (* a (- (* x y) (* z t))))
           (* y0 t_5)))))
   (if (<= c -1e+91)
     t_3
     (if (<= c -2.7e+53)
       t_6
       (if (<= c -5.1e-45)
         (*
          y2
          (+
           (- (* x t_1) (* k (- (* y0 y5) (* y1 y4))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= c -2.15e-138)
           (* y1 (* z (- (* a y3) (* i k))))
           (if (<= c -1.7e-154)
             (* b (* t (* j y4)))
             (if (<= c -2.2e-287)
               t_6
               (if (<= c 3.5e-298)
                 (* y0 (+ (+ (* c t_2) t_4) (* b t_5)))
                 (if (<= c 7e-99)
                   t_6
                   (if (<= c 2.9e-22)
                     (* y0 t_4)
                     (if (<= c 1.5e+54)
                       (*
                        z
                        (+
                         (* k (- (* b y0) (* i y1)))
                         (- (* a (* y1 y3)) (* a (* t b)))))
                       (if (<= c 7.6e+116)
                         (* x (+ (* y2 t_1) (* j (- (* i y1) (* b y0)))))
                         (if (<= c 2.5e+176)
                           (*
                            j
                            (+
                             (* t (- (* b y4) (* i y5)))
                             (- (* y0 (* y3 y5)) (* y0 (* x b)))))
                           t_3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_4 = y5 * ((j * y3) - (k * y2));
	double t_5 = (z * k) - (x * j);
	double t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * t_5));
	double tmp;
	if (c <= -1e+91) {
		tmp = t_3;
	} else if (c <= -2.7e+53) {
		tmp = t_6;
	} else if (c <= -5.1e-45) {
		tmp = y2 * (((x * t_1) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -2.15e-138) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -1.7e-154) {
		tmp = b * (t * (j * y4));
	} else if (c <= -2.2e-287) {
		tmp = t_6;
	} else if (c <= 3.5e-298) {
		tmp = y0 * (((c * t_2) + t_4) + (b * t_5));
	} else if (c <= 7e-99) {
		tmp = t_6;
	} else if (c <= 2.9e-22) {
		tmp = y0 * t_4;
	} else if (c <= 1.5e+54) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 7.6e+116) {
		tmp = x * ((y2 * t_1) + (j * ((i * y1) - (b * y0))));
	} else if (c <= 2.5e+176) {
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (x * y2) - (z * y3)
    t_3 = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    t_4 = y5 * ((j * y3) - (k * y2))
    t_5 = (z * k) - (x * j)
    t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * t_5))
    if (c <= (-1d+91)) then
        tmp = t_3
    else if (c <= (-2.7d+53)) then
        tmp = t_6
    else if (c <= (-5.1d-45)) then
        tmp = y2 * (((x * t_1) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
    else if (c <= (-2.15d-138)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (c <= (-1.7d-154)) then
        tmp = b * (t * (j * y4))
    else if (c <= (-2.2d-287)) then
        tmp = t_6
    else if (c <= 3.5d-298) then
        tmp = y0 * (((c * t_2) + t_4) + (b * t_5))
    else if (c <= 7d-99) then
        tmp = t_6
    else if (c <= 2.9d-22) then
        tmp = y0 * t_4
    else if (c <= 1.5d+54) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))))
    else if (c <= 7.6d+116) then
        tmp = x * ((y2 * t_1) + (j * ((i * y1) - (b * y0))))
    else if (c <= 2.5d+176) then
        tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_4 = y5 * ((j * y3) - (k * y2));
	double t_5 = (z * k) - (x * j);
	double t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * t_5));
	double tmp;
	if (c <= -1e+91) {
		tmp = t_3;
	} else if (c <= -2.7e+53) {
		tmp = t_6;
	} else if (c <= -5.1e-45) {
		tmp = y2 * (((x * t_1) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -2.15e-138) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -1.7e-154) {
		tmp = b * (t * (j * y4));
	} else if (c <= -2.2e-287) {
		tmp = t_6;
	} else if (c <= 3.5e-298) {
		tmp = y0 * (((c * t_2) + t_4) + (b * t_5));
	} else if (c <= 7e-99) {
		tmp = t_6;
	} else if (c <= 2.9e-22) {
		tmp = y0 * t_4;
	} else if (c <= 1.5e+54) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 7.6e+116) {
		tmp = x * ((y2 * t_1) + (j * ((i * y1) - (b * y0))));
	} else if (c <= 2.5e+176) {
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (x * y2) - (z * y3)
	t_3 = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	t_4 = y5 * ((j * y3) - (k * y2))
	t_5 = (z * k) - (x * j)
	t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * t_5))
	tmp = 0
	if c <= -1e+91:
		tmp = t_3
	elif c <= -2.7e+53:
		tmp = t_6
	elif c <= -5.1e-45:
		tmp = y2 * (((x * t_1) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
	elif c <= -2.15e-138:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif c <= -1.7e-154:
		tmp = b * (t * (j * y4))
	elif c <= -2.2e-287:
		tmp = t_6
	elif c <= 3.5e-298:
		tmp = y0 * (((c * t_2) + t_4) + (b * t_5))
	elif c <= 7e-99:
		tmp = t_6
	elif c <= 2.9e-22:
		tmp = y0 * t_4
	elif c <= 1.5e+54:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))))
	elif c <= 7.6e+116:
		tmp = x * ((y2 * t_1) + (j * ((i * y1) - (b * y0))))
	elif c <= 2.5e+176:
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(c * Float64(Float64(Float64(y0 * t_2) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_4 = Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))
	t_5 = Float64(Float64(z * k) - Float64(x * j))
	t_6 = Float64(b * Float64(Float64(Float64(Float64(Float64(t * j) - Float64(y * k)) * y4) + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * t_5)))
	tmp = 0.0
	if (c <= -1e+91)
		tmp = t_3;
	elseif (c <= -2.7e+53)
		tmp = t_6;
	elseif (c <= -5.1e-45)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_1) - Float64(k * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= -2.15e-138)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (c <= -1.7e-154)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	elseif (c <= -2.2e-287)
		tmp = t_6;
	elseif (c <= 3.5e-298)
		tmp = Float64(y0 * Float64(Float64(Float64(c * t_2) + t_4) + Float64(b * t_5)));
	elseif (c <= 7e-99)
		tmp = t_6;
	elseif (c <= 2.9e-22)
		tmp = Float64(y0 * t_4);
	elseif (c <= 1.5e+54)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(a * Float64(y1 * y3)) - Float64(a * Float64(t * b)))));
	elseif (c <= 7.6e+116)
		tmp = Float64(x * Float64(Float64(y2 * t_1) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (c <= 2.5e+176)
		tmp = Float64(j * Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(Float64(y0 * Float64(y3 * y5)) - Float64(y0 * Float64(x * b)))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (x * y2) - (z * y3);
	t_3 = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	t_4 = y5 * ((j * y3) - (k * y2));
	t_5 = (z * k) - (x * j);
	t_6 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * t_5));
	tmp = 0.0;
	if (c <= -1e+91)
		tmp = t_3;
	elseif (c <= -2.7e+53)
		tmp = t_6;
	elseif (c <= -5.1e-45)
		tmp = y2 * (((x * t_1) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	elseif (c <= -2.15e-138)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (c <= -1.7e-154)
		tmp = b * (t * (j * y4));
	elseif (c <= -2.2e-287)
		tmp = t_6;
	elseif (c <= 3.5e-298)
		tmp = y0 * (((c * t_2) + t_4) + (b * t_5));
	elseif (c <= 7e-99)
		tmp = t_6;
	elseif (c <= 2.9e-22)
		tmp = y0 * t_4;
	elseif (c <= 1.5e+54)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	elseif (c <= 7.6e+116)
		tmp = x * ((y2 * t_1) + (j * ((i * y1) - (b * y0))));
	elseif (c <= 2.5e+176)
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(N[(y0 * t$95$2), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(b * N[(N[(N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e+91], t$95$3, If[LessEqual[c, -2.7e+53], t$95$6, If[LessEqual[c, -5.1e-45], N[(y2 * N[(N[(N[(x * t$95$1), $MachinePrecision] - N[(k * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.15e-138], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.7e-154], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.2e-287], t$95$6, If[LessEqual[c, 3.5e-298], N[(y0 * N[(N[(N[(c * t$95$2), $MachinePrecision] + t$95$4), $MachinePrecision] + N[(b * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7e-99], t$95$6, If[LessEqual[c, 2.9e-22], N[(y0 * t$95$4), $MachinePrecision], If[LessEqual[c, 1.5e+54], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.6e+116], N[(x * N[(N[(y2 * t$95$1), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+176], N[(j * N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if c < -1.00000000000000008e91 or 2.5e176 < c

   1. Initial program 26.7%

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

   3. Taylor expanded in c around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. *-commutative 73.8%

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

      5. *-commutative 73.8%

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

      6. *-commutative 73.8%

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

      7. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   if -1.00000000000000008e91 < c < -2.70000000000000019e53 or -1.6999999999999999e-154 < c < -2.2e-287 or 3.4999999999999998e-298 < c < 6.9999999999999997e-99

   1. Initial program 32.1%

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

   3. Taylor expanded in b around inf 60.3%

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

   if -2.70000000000000019e53 < c < -5.0999999999999997e-45

   1. Initial program 20.3%

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

   3. Taylor expanded in y2 around inf 60.2%

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

   if -5.0999999999999997e-45 < c < -2.15e-138

   1. Initial program 39.3%

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

   3. Taylor expanded in z around -inf 39.8%

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

   4. Taylor expanded in y1 around -inf 56.0%

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

   if -2.15e-138 < c < -1.6999999999999999e-154

   1. Initial program 33.3%

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

   3. Taylor expanded in b around inf 50.8%

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

      1. fma-define 67.4%

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

      2. *-commutative 67.4%

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

      3. *-commutative 67.4%

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

      4. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in t around inf 50.3%

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

   7. Taylor expanded in a around 0 66.9%

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

   if -2.2e-287 < c < 3.4999999999999998e-298

   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 y0 around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

      6. *-commutative 75.4%

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

      7. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if 6.9999999999999997e-99 < c < 2.9000000000000002e-22

   1. Initial program 35.6%

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

   3. Taylor expanded in y0 around inf 45.8%

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

      1. +-commutative 45.8%

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

      2. mul-1-neg 45.8%

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

      3. unsub-neg 45.8%

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

      4. *-commutative 45.8%

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

      5. *-commutative 45.8%

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

      6. *-commutative 45.8%

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

      7. *-commutative 45.8%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in y5 around inf 60.5%

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

   if 2.9000000000000002e-22 < c < 1.4999999999999999e54

   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 z around -inf 44.8%

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

   4. Taylor expanded in c around 0 61.4%

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

   if 1.4999999999999999e54 < c < 7.5999999999999998e116

   1. Initial program 26.7%

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

   3. Taylor expanded in x around inf 47.0%

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

   4. Taylor expanded in y around 0 60.7%

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

      1. *-commutative 60.7%

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

      2. *-commutative 60.7%

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

   6. Simplified 60.7%

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

   if 7.5999999999999998e116 < c < 2.5e176

   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 j around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

      4. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in y1 around 0 69.3%

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

      1. *-commutative 69.3%

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

      2. *-commutative 69.3%

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

      3. +-commutative 69.3%

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

      4. mul-1-neg 69.3%

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

      5. unsub-neg 69.3%

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

      6. associate-*r* 69.3%

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

   8. Simplified 69.3%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \left(\left(b \cdot x\right) \cdot y0 - y0 \cdot \left(y3 \cdot y5\right)\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+91}:\\ \;\;\;\;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}\;c \leq -2.7 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -5.1 \cdot 10^{-45}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -2.15 \cdot 10^{-138}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-298}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-22}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+176}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y0 - i \cdot y1\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := c \cdot \left(\left(y0 \cdot t\_2 + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_4 := y1 \cdot y4 - y0 \cdot y5\\ t_5 := b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_6 := c \cdot y0 - a \cdot y1\\ t_7 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot t\_4 + z \cdot t\_6\right)\right)\\ \mathbf{if}\;c \leq -5 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -2 \cdot 10^{+54}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t\_6 - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-77}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(y2 \cdot t\_6 + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-198}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot t\_2\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-290}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t\_4 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot t\_1\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-99}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-22}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(k \cdot t\_1 + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+170}:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y0) (* i y1)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3
         (*
          c
          (+
           (+ (* y0 t_2) (* i (- (* z t) (* x y))))
           (* y4 (- (* y y3) (* t y2))))))
        (t_4 (- (* y1 y4) (* y0 y5)))
        (t_5
         (*
          b
          (+
           (+ (* (- (* t j) (* y k)) y4) (* a (- (* x y) (* z t))))
           (* y0 (- (* z k) (* x j))))))
        (t_6 (- (* c y0) (* a y1)))
        (t_7 (* y3 (- (* y (- (* c y4) (* a y5))) (+ (* j t_4) (* z t_6))))))
   (if (<= c -5e+88)
     t_3
     (if (<= c -2e+54)
       t_5
       (if (<= c -1.6e-67)
         (*
          y2
          (+
           (- (* x t_6) (* k (- (* y0 y5) (* y1 y4))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= c -3e-77)
           t_7
           (if (<= c -1.45e-115)
             (* x (+ (* y2 t_6) (* j (- (* i y1) (* b y0)))))
             (if (<= c -2.7e-198)
               (*
                y1
                (+
                 (* i (- (* x j) (* z k)))
                 (- (* y4 (- (* k y2) (* j y3))) (* a t_2))))
               (if (<= c 2.9e-290)
                 (* k (+ (+ (* y2 t_4) (* y (- (* i y5) (* b y4)))) (* z t_1)))
                 (if (<= c 1.75e-99)
                   t_5
                   (if (<= c 2.9e-22)
                     (* y0 (* y5 (- (* j y3) (* k y2))))
                     (if (<= c 2e+37)
                       (* z (+ (* k t_1) (- (* a (* y1 y3)) (* a (* t b)))))
                       (if (<= c 4e+170) t_7 t_3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y0) - (i * y1);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double t_6 = (c * y0) - (a * y1);
	double t_7 = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_4) + (z * t_6)));
	double tmp;
	if (c <= -5e+88) {
		tmp = t_3;
	} else if (c <= -2e+54) {
		tmp = t_5;
	} else if (c <= -1.6e-67) {
		tmp = y2 * (((x * t_6) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -3e-77) {
		tmp = t_7;
	} else if (c <= -1.45e-115) {
		tmp = x * ((y2 * t_6) + (j * ((i * y1) - (b * y0))));
	} else if (c <= -2.7e-198) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_2)));
	} else if (c <= 2.9e-290) {
		tmp = k * (((y2 * t_4) + (y * ((i * y5) - (b * y4)))) + (z * t_1));
	} else if (c <= 1.75e-99) {
		tmp = t_5;
	} else if (c <= 2.9e-22) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (c <= 2e+37) {
		tmp = z * ((k * t_1) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 4e+170) {
		tmp = t_7;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (b * y0) - (i * y1)
    t_2 = (x * y2) - (z * y3)
    t_3 = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    t_4 = (y1 * y4) - (y0 * y5)
    t_5 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
    t_6 = (c * y0) - (a * y1)
    t_7 = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_4) + (z * t_6)))
    if (c <= (-5d+88)) then
        tmp = t_3
    else if (c <= (-2d+54)) then
        tmp = t_5
    else if (c <= (-1.6d-67)) then
        tmp = y2 * (((x * t_6) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
    else if (c <= (-3d-77)) then
        tmp = t_7
    else if (c <= (-1.45d-115)) then
        tmp = x * ((y2 * t_6) + (j * ((i * y1) - (b * y0))))
    else if (c <= (-2.7d-198)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_2)))
    else if (c <= 2.9d-290) then
        tmp = k * (((y2 * t_4) + (y * ((i * y5) - (b * y4)))) + (z * t_1))
    else if (c <= 1.75d-99) then
        tmp = t_5
    else if (c <= 2.9d-22) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (c <= 2d+37) then
        tmp = z * ((k * t_1) + ((a * (y1 * y3)) - (a * (t * b))))
    else if (c <= 4d+170) then
        tmp = t_7
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y0) - (i * y1);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double t_6 = (c * y0) - (a * y1);
	double t_7 = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_4) + (z * t_6)));
	double tmp;
	if (c <= -5e+88) {
		tmp = t_3;
	} else if (c <= -2e+54) {
		tmp = t_5;
	} else if (c <= -1.6e-67) {
		tmp = y2 * (((x * t_6) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -3e-77) {
		tmp = t_7;
	} else if (c <= -1.45e-115) {
		tmp = x * ((y2 * t_6) + (j * ((i * y1) - (b * y0))));
	} else if (c <= -2.7e-198) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_2)));
	} else if (c <= 2.9e-290) {
		tmp = k * (((y2 * t_4) + (y * ((i * y5) - (b * y4)))) + (z * t_1));
	} else if (c <= 1.75e-99) {
		tmp = t_5;
	} else if (c <= 2.9e-22) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (c <= 2e+37) {
		tmp = z * ((k * t_1) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 4e+170) {
		tmp = t_7;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y0) - (i * y1)
	t_2 = (x * y2) - (z * y3)
	t_3 = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	t_4 = (y1 * y4) - (y0 * y5)
	t_5 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
	t_6 = (c * y0) - (a * y1)
	t_7 = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_4) + (z * t_6)))
	tmp = 0
	if c <= -5e+88:
		tmp = t_3
	elif c <= -2e+54:
		tmp = t_5
	elif c <= -1.6e-67:
		tmp = y2 * (((x * t_6) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
	elif c <= -3e-77:
		tmp = t_7
	elif c <= -1.45e-115:
		tmp = x * ((y2 * t_6) + (j * ((i * y1) - (b * y0))))
	elif c <= -2.7e-198:
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_2)))
	elif c <= 2.9e-290:
		tmp = k * (((y2 * t_4) + (y * ((i * y5) - (b * y4)))) + (z * t_1))
	elif c <= 1.75e-99:
		tmp = t_5
	elif c <= 2.9e-22:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif c <= 2e+37:
		tmp = z * ((k * t_1) + ((a * (y1 * y3)) - (a * (t * b))))
	elif c <= 4e+170:
		tmp = t_7
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y0) - Float64(i * y1))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(c * Float64(Float64(Float64(y0 * t_2) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_4 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_5 = Float64(b * Float64(Float64(Float64(Float64(Float64(t * j) - Float64(y * k)) * y4) + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_6 = Float64(Float64(c * y0) - Float64(a * y1))
	t_7 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) - Float64(Float64(j * t_4) + Float64(z * t_6))))
	tmp = 0.0
	if (c <= -5e+88)
		tmp = t_3;
	elseif (c <= -2e+54)
		tmp = t_5;
	elseif (c <= -1.6e-67)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_6) - Float64(k * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= -3e-77)
		tmp = t_7;
	elseif (c <= -1.45e-115)
		tmp = Float64(x * Float64(Float64(y2 * t_6) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (c <= -2.7e-198)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(a * t_2))));
	elseif (c <= 2.9e-290)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_4) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * t_1)));
	elseif (c <= 1.75e-99)
		tmp = t_5;
	elseif (c <= 2.9e-22)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (c <= 2e+37)
		tmp = Float64(z * Float64(Float64(k * t_1) + Float64(Float64(a * Float64(y1 * y3)) - Float64(a * Float64(t * b)))));
	elseif (c <= 4e+170)
		tmp = t_7;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y0) - (i * y1);
	t_2 = (x * y2) - (z * y3);
	t_3 = c * (((y0 * t_2) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	t_4 = (y1 * y4) - (y0 * y5);
	t_5 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	t_6 = (c * y0) - (a * y1);
	t_7 = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_4) + (z * t_6)));
	tmp = 0.0;
	if (c <= -5e+88)
		tmp = t_3;
	elseif (c <= -2e+54)
		tmp = t_5;
	elseif (c <= -1.6e-67)
		tmp = y2 * (((x * t_6) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	elseif (c <= -3e-77)
		tmp = t_7;
	elseif (c <= -1.45e-115)
		tmp = x * ((y2 * t_6) + (j * ((i * y1) - (b * y0))));
	elseif (c <= -2.7e-198)
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * ((k * y2) - (j * y3))) - (a * t_2)));
	elseif (c <= 2.9e-290)
		tmp = k * (((y2 * t_4) + (y * ((i * y5) - (b * y4)))) + (z * t_1));
	elseif (c <= 1.75e-99)
		tmp = t_5;
	elseif (c <= 2.9e-22)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (c <= 2e+37)
		tmp = z * ((k * t_1) + ((a * (y1 * y3)) - (a * (t * b))));
	elseif (c <= 4e+170)
		tmp = t_7;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(N[(y0 * t$95$2), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(b * N[(N[(N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * t$95$4), $MachinePrecision] + N[(z * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5e+88], t$95$3, If[LessEqual[c, -2e+54], t$95$5, If[LessEqual[c, -1.6e-67], N[(y2 * N[(N[(N[(x * t$95$6), $MachinePrecision] - N[(k * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3e-77], t$95$7, If[LessEqual[c, -1.45e-115], N[(x * N[(N[(y2 * t$95$6), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.7e-198], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e-290], N[(k * N[(N[(N[(y2 * t$95$4), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.75e-99], t$95$5, If[LessEqual[c, 2.9e-22], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e+37], N[(z * N[(N[(k * t$95$1), $MachinePrecision] + N[(N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4e+170], t$95$7, t$95$3]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if c < -4.99999999999999997e88 or 4.00000000000000014e170 < c

   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 c around inf 72.6%

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

      1. +-commutative 72.6%

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

      2. mul-1-neg 72.6%

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

      3. unsub-neg 72.6%

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

      4. *-commutative 72.6%

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

      5. *-commutative 72.6%

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

      6. *-commutative 72.6%

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

      7. *-commutative 72.6%

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

   5. Simplified 72.6%

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

   if -4.99999999999999997e88 < c < -2.0000000000000002e54 or 2.89999999999999994e-290 < c < 1.7499999999999999e-99

   1. Initial program 26.5%

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

   3. Taylor expanded in b around inf 62.4%

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

   if -2.0000000000000002e54 < c < -1.60000000000000011e-67

   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 y2 around inf 63.3%

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

   if -1.60000000000000011e-67 < c < -3.00000000000000016e-77 or 1.99999999999999991e37 < c < 4.00000000000000014e170

   1. Initial program 33.5%

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

   3. Taylor expanded in y3 around -inf 66.2%

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

   if -3.00000000000000016e-77 < c < -1.4499999999999999e-115

   1. Initial program 25.0%

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

   3. Taylor expanded in x around inf 50.3%

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

   4. Taylor expanded in y around 0 75.3%

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

      1. *-commutative 75.3%

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

      2. *-commutative 75.3%

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

   6. Simplified 75.3%

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

   if -1.4499999999999999e-115 < c < -2.7000000000000002e-198

   1. Initial program 37.5%

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

   3. Taylor expanded in y1 around -inf 68.8%

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

      1. associate-*r* 68.8%

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

      2. neg-mul-1 68.8%

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

      3. +-commutative 68.8%

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

      4. mul-1-neg 68.8%

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

      5. unsub-neg 68.8%

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

      6. *-commutative 68.8%

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

      7. *-commutative 68.8%

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

      8. *-commutative 68.8%

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

      9. *-commutative 68.8%

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

   5. Simplified 68.8%

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

   if -2.7000000000000002e-198 < c < 2.89999999999999994e-290

   1. Initial program 43.6%

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

   3. Taylor expanded in k around inf 63.0%

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

      1. +-commutative 63.0%

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

      2. mul-1-neg 63.0%

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

      3. unsub-neg 63.0%

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

      4. *-commutative 63.0%

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

      5. associate-*r* 63.0%

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

      6. neg-mul-1 63.0%

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

   5. Simplified 63.0%

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

   if 1.7499999999999999e-99 < c < 2.9000000000000002e-22

   1. Initial program 35.6%

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

   3. Taylor expanded in y0 around inf 45.8%

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

      1. +-commutative 45.8%

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

      2. mul-1-neg 45.8%

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

      3. unsub-neg 45.8%

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

      4. *-commutative 45.8%

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

      5. *-commutative 45.8%

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

      6. *-commutative 45.8%

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

      7. *-commutative 45.8%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in y5 around inf 60.5%

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

   if 2.9000000000000002e-22 < c < 1.99999999999999991e37

   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 z around -inf 44.1%

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

   4. Taylor expanded in c around 0 62.8%

      \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(-1 \cdot \left(a \cdot \left(y1 \cdot y3\right)\right) + a \cdot \left(b \cdot t\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{+88}:\\ \;\;\;\;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}\;c \leq -2 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-77}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-198}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-290}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-22}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+170}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 40.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_4 := b \cdot y0 - i \cdot y1\\ \mathbf{if}\;c \leq -3 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{+53}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-39}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t\_2 - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-137}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -6.4 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-290}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot t\_4\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-97}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-22}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \left(k \cdot t\_4 + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(y2 \cdot t\_2 + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{+176}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          c
          (+
           (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
           (* y4 (- (* y y3) (* t y2))))))
        (t_2 (- (* c y0) (* a y1)))
        (t_3
         (*
          b
          (+
           (+ (* (- (* t j) (* y k)) y4) (* a (- (* x y) (* z t))))
           (* y0 (- (* z k) (* x j))))))
        (t_4 (- (* b y0) (* i y1))))
   (if (<= c -3e+88)
     t_1
     (if (<= c -9.5e+53)
       t_3
       (if (<= c -1.75e-39)
         (*
          y2
          (+
           (- (* x t_2) (* k (- (* y0 y5) (* y1 y4))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= c -5.8e-137)
           (* y1 (* z (- (* a y3) (* i k))))
           (if (<= c -6.4e-146)
             (* b (* t (* j y4)))
             (if (<= c 2.9e-290)
               (*
                k
                (+
                 (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* i y5) (* b y4))))
                 (* z t_4)))
               (if (<= c 2.3e-97)
                 t_3
                 (if (<= c 6.8e-22)
                   (* y0 (* y5 (- (* j y3) (* k y2))))
                   (if (<= c 7.6e+53)
                     (* z (+ (* k t_4) (- (* a (* y1 y3)) (* a (* t b)))))
                     (if (<= c 7.5e+114)
                       (* x (+ (* y2 t_2) (* j (- (* i y1) (* b y0)))))
                       (if (<= c 8.8e+176)
                         (*
                          j
                          (+
                           (* t (- (* b y4) (* i y5)))
                           (- (* y0 (* y3 y5)) (* y0 (* x b)))))
                         t_1)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double t_4 = (b * y0) - (i * y1);
	double tmp;
	if (c <= -3e+88) {
		tmp = t_1;
	} else if (c <= -9.5e+53) {
		tmp = t_3;
	} else if (c <= -1.75e-39) {
		tmp = y2 * (((x * t_2) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -5.8e-137) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -6.4e-146) {
		tmp = b * (t * (j * y4));
	} else if (c <= 2.9e-290) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_4));
	} else if (c <= 2.3e-97) {
		tmp = t_3;
	} else if (c <= 6.8e-22) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (c <= 7.6e+53) {
		tmp = z * ((k * t_4) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 7.5e+114) {
		tmp = x * ((y2 * t_2) + (j * ((i * y1) - (b * y0))));
	} else if (c <= 8.8e+176) {
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    t_2 = (c * y0) - (a * y1)
    t_3 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
    t_4 = (b * y0) - (i * y1)
    if (c <= (-3d+88)) then
        tmp = t_1
    else if (c <= (-9.5d+53)) then
        tmp = t_3
    else if (c <= (-1.75d-39)) then
        tmp = y2 * (((x * t_2) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
    else if (c <= (-5.8d-137)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (c <= (-6.4d-146)) then
        tmp = b * (t * (j * y4))
    else if (c <= 2.9d-290) then
        tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_4))
    else if (c <= 2.3d-97) then
        tmp = t_3
    else if (c <= 6.8d-22) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (c <= 7.6d+53) then
        tmp = z * ((k * t_4) + ((a * (y1 * y3)) - (a * (t * b))))
    else if (c <= 7.5d+114) then
        tmp = x * ((y2 * t_2) + (j * ((i * y1) - (b * y0))))
    else if (c <= 8.8d+176) then
        tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double t_4 = (b * y0) - (i * y1);
	double tmp;
	if (c <= -3e+88) {
		tmp = t_1;
	} else if (c <= -9.5e+53) {
		tmp = t_3;
	} else if (c <= -1.75e-39) {
		tmp = y2 * (((x * t_2) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -5.8e-137) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= -6.4e-146) {
		tmp = b * (t * (j * y4));
	} else if (c <= 2.9e-290) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_4));
	} else if (c <= 2.3e-97) {
		tmp = t_3;
	} else if (c <= 6.8e-22) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (c <= 7.6e+53) {
		tmp = z * ((k * t_4) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 7.5e+114) {
		tmp = x * ((y2 * t_2) + (j * ((i * y1) - (b * y0))));
	} else if (c <= 8.8e+176) {
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	t_2 = (c * y0) - (a * y1)
	t_3 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
	t_4 = (b * y0) - (i * y1)
	tmp = 0
	if c <= -3e+88:
		tmp = t_1
	elif c <= -9.5e+53:
		tmp = t_3
	elif c <= -1.75e-39:
		tmp = y2 * (((x * t_2) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
	elif c <= -5.8e-137:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif c <= -6.4e-146:
		tmp = b * (t * (j * y4))
	elif c <= 2.9e-290:
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_4))
	elif c <= 2.3e-97:
		tmp = t_3
	elif c <= 6.8e-22:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif c <= 7.6e+53:
		tmp = z * ((k * t_4) + ((a * (y1 * y3)) - (a * (t * b))))
	elif c <= 7.5e+114:
		tmp = x * ((y2 * t_2) + (j * ((i * y1) - (b * y0))))
	elif c <= 8.8e+176:
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(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)))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(b * Float64(Float64(Float64(Float64(Float64(t * j) - Float64(y * k)) * y4) + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_4 = Float64(Float64(b * y0) - Float64(i * y1))
	tmp = 0.0
	if (c <= -3e+88)
		tmp = t_1;
	elseif (c <= -9.5e+53)
		tmp = t_3;
	elseif (c <= -1.75e-39)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) - Float64(k * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= -5.8e-137)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (c <= -6.4e-146)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	elseif (c <= 2.9e-290)
		tmp = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * t_4)));
	elseif (c <= 2.3e-97)
		tmp = t_3;
	elseif (c <= 6.8e-22)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (c <= 7.6e+53)
		tmp = Float64(z * Float64(Float64(k * t_4) + Float64(Float64(a * Float64(y1 * y3)) - Float64(a * Float64(t * b)))));
	elseif (c <= 7.5e+114)
		tmp = Float64(x * Float64(Float64(y2 * t_2) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (c <= 8.8e+176)
		tmp = Float64(j * Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(Float64(y0 * Float64(y3 * y5)) - Float64(y0 * Float64(x * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	t_2 = (c * y0) - (a * y1);
	t_3 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	t_4 = (b * y0) - (i * y1);
	tmp = 0.0;
	if (c <= -3e+88)
		tmp = t_1;
	elseif (c <= -9.5e+53)
		tmp = t_3;
	elseif (c <= -1.75e-39)
		tmp = y2 * (((x * t_2) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	elseif (c <= -5.8e-137)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (c <= -6.4e-146)
		tmp = b * (t * (j * y4));
	elseif (c <= 2.9e-290)
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_4));
	elseif (c <= 2.3e-97)
		tmp = t_3;
	elseif (c <= 6.8e-22)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (c <= 7.6e+53)
		tmp = z * ((k * t_4) + ((a * (y1 * y3)) - (a * (t * b))));
	elseif (c <= 7.5e+114)
		tmp = x * ((y2 * t_2) + (j * ((i * y1) - (b * y0))));
	elseif (c <= 8.8e+176)
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(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]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+88], t$95$1, If[LessEqual[c, -9.5e+53], t$95$3, If[LessEqual[c, -1.75e-39], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] - N[(k * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.8e-137], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.4e-146], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e-290], N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e-97], t$95$3, If[LessEqual[c, 6.8e-22], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.6e+53], N[(z * N[(N[(k * t$95$4), $MachinePrecision] + N[(N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.5e+114], N[(x * N[(N[(y2 * t$95$2), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.8e+176], N[(j * N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if c < -3.00000000000000005e88 or 8.80000000000000029e176 < c

   1. Initial program 26.7%

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

   3. Taylor expanded in c around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. *-commutative 73.8%

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

      5. *-commutative 73.8%

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

      6. *-commutative 73.8%

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

      7. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   if -3.00000000000000005e88 < c < -9.5000000000000006e53 or 2.89999999999999994e-290 < c < 2.29999999999999994e-97

   1. Initial program 26.5%

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

   3. Taylor expanded in b around inf 62.4%

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

   if -9.5000000000000006e53 < c < -1.75e-39

   1. Initial program 20.3%

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

   3. Taylor expanded in y2 around inf 60.2%

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

   if -1.75e-39 < c < -5.7999999999999997e-137

   1. Initial program 39.3%

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

   3. Taylor expanded in z around -inf 39.8%

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

   4. Taylor expanded in y1 around -inf 56.0%

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

   if -5.7999999999999997e-137 < c < -6.3999999999999998e-146

   1. Initial program 20.0%

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

   3. Taylor expanded in b around inf 60.9%

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

      1. fma-define 80.9%

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

      2. *-commutative 80.9%

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

      3. *-commutative 80.9%

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

      4. *-commutative 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in t around inf 60.4%

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

   7. Taylor expanded in a around 0 80.3%

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

   if -6.3999999999999998e-146 < c < 2.89999999999999994e-290

   1. Initial program 43.1%

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

   3. Taylor expanded in k around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. associate-*r* 62.9%

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

      6. neg-mul-1 62.9%

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

   5. Simplified 62.9%

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

   if 2.29999999999999994e-97 < c < 6.7999999999999997e-22

   1. Initial program 35.6%

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

   3. Taylor expanded in y0 around inf 45.8%

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

      1. +-commutative 45.8%

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

      2. mul-1-neg 45.8%

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

      3. unsub-neg 45.8%

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

      4. *-commutative 45.8%

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

      5. *-commutative 45.8%

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

      6. *-commutative 45.8%

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

      7. *-commutative 45.8%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in y5 around inf 60.5%

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

   if 6.7999999999999997e-22 < c < 7.59999999999999995e53

   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 z around -inf 44.8%

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

   4. Taylor expanded in c around 0 61.4%

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

   if 7.59999999999999995e53 < c < 7.5000000000000001e114

   1. Initial program 26.7%

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

   3. Taylor expanded in x around inf 47.0%

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

   4. Taylor expanded in y around 0 60.7%

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

      1. *-commutative 60.7%

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

      2. *-commutative 60.7%

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

   6. Simplified 60.7%

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

   if 7.5000000000000001e114 < c < 8.80000000000000029e176

   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 j around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

      4. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in y1 around 0 69.3%

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

      1. *-commutative 69.3%

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

      2. *-commutative 69.3%

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

      3. +-commutative 69.3%

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

      4. mul-1-neg 69.3%

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

      5. unsub-neg 69.3%

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

      6. associate-*r* 69.3%

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

   8. Simplified 69.3%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \left(\left(b \cdot x\right) \cdot y0 - y0 \cdot \left(y3 \cdot y5\right)\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+88}:\\ \;\;\;\;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}\;c \leq -9.5 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-39}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-137}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq -6.4 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-290}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-97}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-22}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{+176}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y1 - b \cdot y0\\ t_2 := \left(t \cdot j - y \cdot k\right) \cdot y4\\ t_3 := i \cdot y5 - b \cdot y4\\ t_4 := y1 \cdot y4 - y0 \cdot y5\\ t_5 := c \cdot y0 - a \cdot y1\\ t_6 := c \cdot y4 - a \cdot y5\\ t_7 := y \cdot t\_6\\ t_8 := y3 \cdot \left(t\_7 - \left(j \cdot t\_4 + z \cdot t\_5\right)\right)\\ \mathbf{if}\;j \leq -1.55 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y2 \cdot t\_5 + j \cdot t\_1\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{+55}:\\ \;\;\;\;b \cdot t\_2\\ \mathbf{elif}\;j \leq -750000:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \left(\left(k \cdot t\_3 + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot t\_6\right)\\ \mathbf{elif}\;j \leq -2.45 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(\left(t\_2 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-276}:\\ \;\;\;\;t\_4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + t\_6 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-305}:\\ \;\;\;\;y3 \cdot t\_7\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-200}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t\_4 + y \cdot t\_3\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 0.0039:\\ \;\;\;\;t\_8\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* i y1) (* b y0)))
        (t_2 (* (- (* t j) (* y k)) y4))
        (t_3 (- (* i y5) (* b y4)))
        (t_4 (- (* y1 y4) (* y0 y5)))
        (t_5 (- (* c y0) (* a y1)))
        (t_6 (- (* c y4) (* a y5)))
        (t_7 (* y t_6))
        (t_8 (* y3 (- t_7 (+ (* j t_4) (* z t_5))))))
   (if (<= j -1.55e+154)
     (* x (+ (* y2 t_5) (* j t_1)))
     (if (<= j -2.8e+55)
       (* b t_2)
       (if (<= j -750000.0)
         t_8
         (if (<= j -1e-161)
           (* y (+ (+ (* k t_3) (* x (- (* a b) (* c i)))) (* y3 t_6)))
           (if (<= j -2.45e-250)
             (*
              b
              (+ (+ t_2 (* a (- (* x y) (* z t)))) (* y0 (- (* z k) (* x j)))))
             (if (<= j -6.5e-276)
               (+
                (* t_4 (- (* k y2) (* j y3)))
                (+
                 (*
                  c
                  (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y)))))
                 (* t_6 (- (* y y3) (* t y2)))))
               (if (<= j 1.2e-305)
                 (* y3 t_7)
                 (if (<= j 3.3e-200)
                   (*
                    k
                    (+ (+ (* y2 t_4) (* y t_3)) (* z (- (* b y0) (* i y1)))))
                   (if (<= j 0.0039)
                     t_8
                     (*
                      j
                      (+
                       (+
                        (* t (- (* b y4) (* i y5)))
                        (* y3 (- (* y0 y5) (* y1 y4))))
                       (* x t_1))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = ((t * j) - (y * k)) * y4;
	double t_3 = (i * y5) - (b * y4);
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = (c * y0) - (a * y1);
	double t_6 = (c * y4) - (a * y5);
	double t_7 = y * t_6;
	double t_8 = y3 * (t_7 - ((j * t_4) + (z * t_5)));
	double tmp;
	if (j <= -1.55e+154) {
		tmp = x * ((y2 * t_5) + (j * t_1));
	} else if (j <= -2.8e+55) {
		tmp = b * t_2;
	} else if (j <= -750000.0) {
		tmp = t_8;
	} else if (j <= -1e-161) {
		tmp = y * (((k * t_3) + (x * ((a * b) - (c * i)))) + (y3 * t_6));
	} else if (j <= -2.45e-250) {
		tmp = b * ((t_2 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= -6.5e-276) {
		tmp = (t_4 * ((k * y2) - (j * y3))) + ((c * ((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y))))) + (t_6 * ((y * y3) - (t * y2))));
	} else if (j <= 1.2e-305) {
		tmp = y3 * t_7;
	} else if (j <= 3.3e-200) {
		tmp = k * (((y2 * t_4) + (y * t_3)) + (z * ((b * y0) - (i * y1))));
	} else if (j <= 0.0039) {
		tmp = t_8;
	} else {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = (i * y1) - (b * y0)
    t_2 = ((t * j) - (y * k)) * y4
    t_3 = (i * y5) - (b * y4)
    t_4 = (y1 * y4) - (y0 * y5)
    t_5 = (c * y0) - (a * y1)
    t_6 = (c * y4) - (a * y5)
    t_7 = y * t_6
    t_8 = y3 * (t_7 - ((j * t_4) + (z * t_5)))
    if (j <= (-1.55d+154)) then
        tmp = x * ((y2 * t_5) + (j * t_1))
    else if (j <= (-2.8d+55)) then
        tmp = b * t_2
    else if (j <= (-750000.0d0)) then
        tmp = t_8
    else if (j <= (-1d-161)) then
        tmp = y * (((k * t_3) + (x * ((a * b) - (c * i)))) + (y3 * t_6))
    else if (j <= (-2.45d-250)) then
        tmp = b * ((t_2 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
    else if (j <= (-6.5d-276)) then
        tmp = (t_4 * ((k * y2) - (j * y3))) + ((c * ((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y))))) + (t_6 * ((y * y3) - (t * y2))))
    else if (j <= 1.2d-305) then
        tmp = y3 * t_7
    else if (j <= 3.3d-200) then
        tmp = k * (((y2 * t_4) + (y * t_3)) + (z * ((b * y0) - (i * y1))))
    else if (j <= 0.0039d0) then
        tmp = t_8
    else
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = ((t * j) - (y * k)) * y4;
	double t_3 = (i * y5) - (b * y4);
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = (c * y0) - (a * y1);
	double t_6 = (c * y4) - (a * y5);
	double t_7 = y * t_6;
	double t_8 = y3 * (t_7 - ((j * t_4) + (z * t_5)));
	double tmp;
	if (j <= -1.55e+154) {
		tmp = x * ((y2 * t_5) + (j * t_1));
	} else if (j <= -2.8e+55) {
		tmp = b * t_2;
	} else if (j <= -750000.0) {
		tmp = t_8;
	} else if (j <= -1e-161) {
		tmp = y * (((k * t_3) + (x * ((a * b) - (c * i)))) + (y3 * t_6));
	} else if (j <= -2.45e-250) {
		tmp = b * ((t_2 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= -6.5e-276) {
		tmp = (t_4 * ((k * y2) - (j * y3))) + ((c * ((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y))))) + (t_6 * ((y * y3) - (t * y2))));
	} else if (j <= 1.2e-305) {
		tmp = y3 * t_7;
	} else if (j <= 3.3e-200) {
		tmp = k * (((y2 * t_4) + (y * t_3)) + (z * ((b * y0) - (i * y1))));
	} else if (j <= 0.0039) {
		tmp = t_8;
	} else {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y1) - (b * y0)
	t_2 = ((t * j) - (y * k)) * y4
	t_3 = (i * y5) - (b * y4)
	t_4 = (y1 * y4) - (y0 * y5)
	t_5 = (c * y0) - (a * y1)
	t_6 = (c * y4) - (a * y5)
	t_7 = y * t_6
	t_8 = y3 * (t_7 - ((j * t_4) + (z * t_5)))
	tmp = 0
	if j <= -1.55e+154:
		tmp = x * ((y2 * t_5) + (j * t_1))
	elif j <= -2.8e+55:
		tmp = b * t_2
	elif j <= -750000.0:
		tmp = t_8
	elif j <= -1e-161:
		tmp = y * (((k * t_3) + (x * ((a * b) - (c * i)))) + (y3 * t_6))
	elif j <= -2.45e-250:
		tmp = b * ((t_2 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
	elif j <= -6.5e-276:
		tmp = (t_4 * ((k * y2) - (j * y3))) + ((c * ((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y))))) + (t_6 * ((y * y3) - (t * y2))))
	elif j <= 1.2e-305:
		tmp = y3 * t_7
	elif j <= 3.3e-200:
		tmp = k * (((y2 * t_4) + (y * t_3)) + (z * ((b * y0) - (i * y1))))
	elif j <= 0.0039:
		tmp = t_8
	else:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * 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(i * y1) - Float64(b * y0))
	t_2 = Float64(Float64(Float64(t * j) - Float64(y * k)) * y4)
	t_3 = Float64(Float64(i * y5) - Float64(b * y4))
	t_4 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_5 = Float64(Float64(c * y0) - Float64(a * y1))
	t_6 = Float64(Float64(c * y4) - Float64(a * y5))
	t_7 = Float64(y * t_6)
	t_8 = Float64(y3 * Float64(t_7 - Float64(Float64(j * t_4) + Float64(z * t_5))))
	tmp = 0.0
	if (j <= -1.55e+154)
		tmp = Float64(x * Float64(Float64(y2 * t_5) + Float64(j * t_1)));
	elseif (j <= -2.8e+55)
		tmp = Float64(b * t_2);
	elseif (j <= -750000.0)
		tmp = t_8;
	elseif (j <= -1e-161)
		tmp = Float64(y * Float64(Float64(Float64(k * t_3) + Float64(x * Float64(Float64(a * b) - Float64(c * i)))) + Float64(y3 * t_6)));
	elseif (j <= -2.45e-250)
		tmp = Float64(b * Float64(Float64(t_2 + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (j <= -6.5e-276)
		tmp = Float64(Float64(t_4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y))))) + Float64(t_6 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (j <= 1.2e-305)
		tmp = Float64(y3 * t_7);
	elseif (j <= 3.3e-200)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_4) + Float64(y * t_3)) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (j <= 0.0039)
		tmp = t_8;
	else
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (i * y1) - (b * y0);
	t_2 = ((t * j) - (y * k)) * y4;
	t_3 = (i * y5) - (b * y4);
	t_4 = (y1 * y4) - (y0 * y5);
	t_5 = (c * y0) - (a * y1);
	t_6 = (c * y4) - (a * y5);
	t_7 = y * t_6;
	t_8 = y3 * (t_7 - ((j * t_4) + (z * t_5)));
	tmp = 0.0;
	if (j <= -1.55e+154)
		tmp = x * ((y2 * t_5) + (j * t_1));
	elseif (j <= -2.8e+55)
		tmp = b * t_2;
	elseif (j <= -750000.0)
		tmp = t_8;
	elseif (j <= -1e-161)
		tmp = y * (((k * t_3) + (x * ((a * b) - (c * i)))) + (y3 * t_6));
	elseif (j <= -2.45e-250)
		tmp = b * ((t_2 + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	elseif (j <= -6.5e-276)
		tmp = (t_4 * ((k * y2) - (j * y3))) + ((c * ((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y))))) + (t_6 * ((y * y3) - (t * y2))));
	elseif (j <= 1.2e-305)
		tmp = y3 * t_7;
	elseif (j <= 3.3e-200)
		tmp = k * (((y2 * t_4) + (y * t_3)) + (z * ((b * y0) - (i * y1))));
	elseif (j <= 0.0039)
		tmp = t_8;
	else
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * 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[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(y3 * N[(t$95$7 - N[(N[(j * t$95$4), $MachinePrecision] + N[(z * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.55e+154], N[(x * N[(N[(y2 * t$95$5), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.8e+55], N[(b * t$95$2), $MachinePrecision], If[LessEqual[j, -750000.0], t$95$8, If[LessEqual[j, -1e-161], N[(y * N[(N[(N[(k * t$95$3), $MachinePrecision] + N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.45e-250], N[(b * N[(N[(t$95$2 + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.5e-276], N[(N[(t$95$4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * 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]), $MachinePrecision] + N[(t$95$6 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.2e-305], N[(y3 * t$95$7), $MachinePrecision], If[LessEqual[j, 3.3e-200], N[(k * N[(N[(N[(y2 * t$95$4), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.0039], t$95$8, N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -1.5500000000000001e154

   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 x around inf 55.7%

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

   4. Taylor expanded in y around 0 61.6%

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

      1. *-commutative 61.6%

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

      2. *-commutative 61.6%

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

   6. Simplified 61.6%

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

   if -1.5500000000000001e154 < j < -2.8000000000000001e55

   1. Initial program 17.5%

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

   3. Taylor expanded in b around inf 41.8%

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

      1. fma-define 48.7%

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

      2. *-commutative 48.7%

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

      3. *-commutative 48.7%

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

      4. *-commutative 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in y4 around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. *-commutative 66.0%

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

   8. Simplified 66.0%

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

   if -2.8000000000000001e55 < j < -7.5e5 or 3.2999999999999998e-200 < j < 0.0038999999999999998

   1. Initial program 28.5%

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

   3. Taylor expanded in y3 around -inf 59.5%

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

   if -7.5e5 < j < -1.00000000000000003e-161

   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 y around inf 62.3%

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

   if -1.00000000000000003e-161 < j < -2.44999999999999985e-250

   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 b around inf 62.2%

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

   if -2.44999999999999985e-250 < j < -6.49999999999999981e-276

   1. Initial program 44.5%

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

   3. Taylor expanded in c around inf 67.5%

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

      1. +-commutative 67.5%

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

      2. mul-1-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

      5. *-commutative 67.5%

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

      6. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if -6.49999999999999981e-276 < j < 1.2000000000000001e-305

   1. Initial program 19.3%

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

   3. Taylor expanded in y3 around -inf 37.1%

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

   4. Taylor expanded in y around inf 55.3%

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

   if 1.2000000000000001e-305 < j < 3.2999999999999998e-200

   1. Initial program 47.5%

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

   3. Taylor expanded in k around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. *-commutative 71.5%

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

      5. associate-*r* 71.5%

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

      6. neg-mul-1 71.5%

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

   5. Simplified 71.5%

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

   if 0.0038999999999999998 < j

   1. Initial program 32.0%

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

   3. Taylor expanded in j around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

   5. Simplified 61.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.55 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \mathbf{elif}\;j \leq -750000:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -2.45 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-276}:\\ \;\;\;\;\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-305}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-200}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 0.0039:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 40.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;c \leq -8.8 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -6.1 \cdot 10^{+19}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-72}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-135}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-20}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          c
          (+
           (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
           (* y4 (- (* y y3) (* t y2))))))
        (t_2
         (*
          b
          (+
           (+ (* (- (* t j) (* y k)) y4) (* a (- (* x y) (* z t))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= c -8.8e+87)
     t_1
     (if (<= c -5.8e+53)
       t_2
       (if (<= c -6.1e+19)
         (* a (* x (- (* y b) (* y1 y2))))
         (if (<= c -4e-72)
           (* k (* y1 (- (* y2 y4) (* z i))))
           (if (<= c -8.2e-135)
             (* y1 (* z (- (* a y3) (* i k))))
             (if (<= c 3.1e-97)
               t_2
               (if (<= c 1.2e-20)
                 (* y0 (* y5 (- (* j y3) (* k y2))))
                 (if (<= c 1.65e+54)
                   (*
                    z
                    (+
                     (* k (- (* b y0) (* i y1)))
                     (- (* a (* y1 y3)) (* a (* t b)))))
                   (if (<= c 2.2e+146)
                     (*
                      x
                      (+
                       (* y2 (- (* c y0) (* a y1)))
                       (* j (- (* i y1) (* b y0)))))
                     t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_2 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (c <= -8.8e+87) {
		tmp = t_1;
	} else if (c <= -5.8e+53) {
		tmp = t_2;
	} else if (c <= -6.1e+19) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (c <= -4e-72) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (c <= -8.2e-135) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= 3.1e-97) {
		tmp = t_2;
	} else if (c <= 1.2e-20) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (c <= 1.65e+54) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 2.2e+146) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    t_2 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
    if (c <= (-8.8d+87)) then
        tmp = t_1
    else if (c <= (-5.8d+53)) then
        tmp = t_2
    else if (c <= (-6.1d+19)) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else if (c <= (-4d-72)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (c <= (-8.2d-135)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (c <= 3.1d-97) then
        tmp = t_2
    else if (c <= 1.2d-20) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (c <= 1.65d+54) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))))
    else if (c <= 2.2d+146) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	double t_2 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (c <= -8.8e+87) {
		tmp = t_1;
	} else if (c <= -5.8e+53) {
		tmp = t_2;
	} else if (c <= -6.1e+19) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (c <= -4e-72) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (c <= -8.2e-135) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (c <= 3.1e-97) {
		tmp = t_2;
	} else if (c <= 1.2e-20) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (c <= 1.65e+54) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (c <= 2.2e+146) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	t_2 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if c <= -8.8e+87:
		tmp = t_1
	elif c <= -5.8e+53:
		tmp = t_2
	elif c <= -6.1e+19:
		tmp = a * (x * ((y * b) - (y1 * y2)))
	elif c <= -4e-72:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif c <= -8.2e-135:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif c <= 3.1e-97:
		tmp = t_2
	elif c <= 1.2e-20:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif c <= 1.65e+54:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))))
	elif c <= 2.2e+146:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(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)))))
	t_2 = Float64(b * Float64(Float64(Float64(Float64(Float64(t * j) - Float64(y * k)) * y4) + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (c <= -8.8e+87)
		tmp = t_1;
	elseif (c <= -5.8e+53)
		tmp = t_2;
	elseif (c <= -6.1e+19)
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (c <= -4e-72)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (c <= -8.2e-135)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (c <= 3.1e-97)
		tmp = t_2;
	elseif (c <= 1.2e-20)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (c <= 1.65e+54)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(a * Float64(y1 * y3)) - Float64(a * Float64(t * b)))));
	elseif (c <= 2.2e+146)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	t_2 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (c <= -8.8e+87)
		tmp = t_1;
	elseif (c <= -5.8e+53)
		tmp = t_2;
	elseif (c <= -6.1e+19)
		tmp = a * (x * ((y * b) - (y1 * y2)));
	elseif (c <= -4e-72)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (c <= -8.2e-135)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (c <= 3.1e-97)
		tmp = t_2;
	elseif (c <= 1.2e-20)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (c <= 1.65e+54)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	elseif (c <= 2.2e+146)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(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]}, Block[{t$95$2 = N[(b * N[(N[(N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.8e+87], t$95$1, If[LessEqual[c, -5.8e+53], t$95$2, If[LessEqual[c, -6.1e+19], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4e-72], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.2e-135], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.1e-97], t$95$2, If[LessEqual[c, 1.2e-20], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.65e+54], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+146], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if c < -8.8000000000000003e87 or 2.1999999999999998e146 < c

   1. Initial program 27.6%

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

   3. Taylor expanded in c around inf 68.8%

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

      1. +-commutative 68.8%

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

      2. mul-1-neg 68.8%

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

      3. unsub-neg 68.8%

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

      4. *-commutative 68.8%

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

      5. *-commutative 68.8%

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

      6. *-commutative 68.8%

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

      7. *-commutative 68.8%

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

   5. Simplified 68.8%

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

   if -8.8000000000000003e87 < c < -5.8000000000000004e53 or -8.2000000000000002e-135 < c < 3.10000000000000002e-97

   1. Initial program 33.0%

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

   3. Taylor expanded in b around inf 56.7%

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

   if -5.8000000000000004e53 < c < -6.1e19

   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 x around inf 28.7%

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

   4. Taylor expanded in a around -inf 85.9%

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

      1. associate-*r* 85.9%

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

      2. mul-1-neg 85.9%

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

      3. mul-1-neg 85.9%

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

      4. distribute-lft-neg-out 85.9%

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

      5. +-commutative 85.9%

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

      6. cancel-sign-sub-inv 85.9%

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

      7. *-commutative 85.9%

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

   6. Simplified 85.9%

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

   if -6.1e19 < c < -3.9999999999999999e-72

   1. Initial program 16.3%

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

   3. Taylor expanded in k around inf 46.7%

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

      1. +-commutative 46.7%

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

      2. mul-1-neg 46.7%

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

      3. unsub-neg 46.7%

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

      4. *-commutative 46.7%

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

      5. associate-*r* 46.7%

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

      6. neg-mul-1 46.7%

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

   5. Simplified 46.7%

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

   6. Taylor expanded in y1 around inf 55.2%

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

      1. *-commutative 55.2%

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

      2. *-commutative 55.2%

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

   8. Simplified 55.2%

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

   if -3.9999999999999999e-72 < c < -8.2000000000000002e-135

   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 z around -inf 33.6%

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

   4. Taylor expanded in y1 around -inf 50.6%

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

   if 3.10000000000000002e-97 < c < 1.19999999999999996e-20

   1. Initial program 35.6%

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

   3. Taylor expanded in y0 around inf 45.8%

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

      1. +-commutative 45.8%

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

      2. mul-1-neg 45.8%

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

      3. unsub-neg 45.8%

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

      4. *-commutative 45.8%

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

      5. *-commutative 45.8%

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

      6. *-commutative 45.8%

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

      7. *-commutative 45.8%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in y5 around inf 60.5%

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

   if 1.19999999999999996e-20 < c < 1.65e54

   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 z around -inf 44.8%

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

   4. Taylor expanded in c around 0 61.4%

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

   if 1.65e54 < c < 2.1999999999999998e146

   1. Initial program 27.3%

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

   3. Taylor expanded in x around inf 50.3%

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

   4. Taylor expanded in y around 0 59.7%

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

      1. *-commutative 59.7%

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

      2. *-commutative 59.7%

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

   6. Simplified 59.7%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.8 \cdot 10^{+87}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -6.1 \cdot 10^{+19}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-72}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-135}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-20}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-92}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-274}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-244}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-48}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(c \cdot y2 - b \cdot j\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+247}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y2 (- (* x c) (* k y5)))))
        (t_2 (* k (* z (- (* b y0) (* i y1))))))
   (if (<= x -6.4e+118)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= x -1.95e-57)
       t_1
       (if (<= x -1.15e-92)
         (* j (* y5 (- (* y0 y3) (* t i))))
         (if (<= x -2.5e-202)
           t_2
           (if (<= x -1.1e-274)
             (* (* t j) (- (* b y4) (* i y5)))
             (if (<= x 5.5e-244)
               (* k (* y4 (- (* y1 y2) (* y b))))
               (if (<= x 1.8e-202)
                 t_2
                 (if (<= x 4e-48)
                   (* y3 (* y (- (* c y4) (* a y5))))
                   (if (<= x 8.5e+27)
                     (* (* x y0) (- (* c y2) (* b j)))
                     (if (<= x 1.65e+149)
                       (* b (* y (- (* x a) (* k y4))))
                       (if (<= x 1.25e+247)
                         t_1
                         (* x (* y (- (* a b) (* c i)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y2 * ((x * c) - (k * y5)));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (x <= -6.4e+118) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (x <= -1.95e-57) {
		tmp = t_1;
	} else if (x <= -1.15e-92) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (x <= -2.5e-202) {
		tmp = t_2;
	} else if (x <= -1.1e-274) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 5.5e-244) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (x <= 1.8e-202) {
		tmp = t_2;
	} else if (x <= 4e-48) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (x <= 8.5e+27) {
		tmp = (x * y0) * ((c * y2) - (b * j));
	} else if (x <= 1.65e+149) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (x <= 1.25e+247) {
		tmp = t_1;
	} else {
		tmp = x * (y * ((a * b) - (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y0 * (y2 * ((x * c) - (k * y5)))
    t_2 = k * (z * ((b * y0) - (i * y1)))
    if (x <= (-6.4d+118)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (x <= (-1.95d-57)) then
        tmp = t_1
    else if (x <= (-1.15d-92)) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (x <= (-2.5d-202)) then
        tmp = t_2
    else if (x <= (-1.1d-274)) then
        tmp = (t * j) * ((b * y4) - (i * y5))
    else if (x <= 5.5d-244) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else if (x <= 1.8d-202) then
        tmp = t_2
    else if (x <= 4d-48) then
        tmp = y3 * (y * ((c * y4) - (a * y5)))
    else if (x <= 8.5d+27) then
        tmp = (x * y0) * ((c * y2) - (b * j))
    else if (x <= 1.65d+149) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (x <= 1.25d+247) then
        tmp = t_1
    else
        tmp = x * (y * ((a * b) - (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y2 * ((x * c) - (k * y5)));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (x <= -6.4e+118) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (x <= -1.95e-57) {
		tmp = t_1;
	} else if (x <= -1.15e-92) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (x <= -2.5e-202) {
		tmp = t_2;
	} else if (x <= -1.1e-274) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 5.5e-244) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (x <= 1.8e-202) {
		tmp = t_2;
	} else if (x <= 4e-48) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (x <= 8.5e+27) {
		tmp = (x * y0) * ((c * y2) - (b * j));
	} else if (x <= 1.65e+149) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (x <= 1.25e+247) {
		tmp = t_1;
	} else {
		tmp = x * (y * ((a * b) - (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y2 * ((x * c) - (k * y5)))
	t_2 = k * (z * ((b * y0) - (i * y1)))
	tmp = 0
	if x <= -6.4e+118:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif x <= -1.95e-57:
		tmp = t_1
	elif x <= -1.15e-92:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif x <= -2.5e-202:
		tmp = t_2
	elif x <= -1.1e-274:
		tmp = (t * j) * ((b * y4) - (i * y5))
	elif x <= 5.5e-244:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	elif x <= 1.8e-202:
		tmp = t_2
	elif x <= 4e-48:
		tmp = y3 * (y * ((c * y4) - (a * y5)))
	elif x <= 8.5e+27:
		tmp = (x * y0) * ((c * y2) - (b * j))
	elif x <= 1.65e+149:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif x <= 1.25e+247:
		tmp = t_1
	else:
		tmp = x * (y * ((a * b) - (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))))
	t_2 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	tmp = 0.0
	if (x <= -6.4e+118)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (x <= -1.95e-57)
		tmp = t_1;
	elseif (x <= -1.15e-92)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (x <= -2.5e-202)
		tmp = t_2;
	elseif (x <= -1.1e-274)
		tmp = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)));
	elseif (x <= 5.5e-244)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (x <= 1.8e-202)
		tmp = t_2;
	elseif (x <= 4e-48)
		tmp = Float64(y3 * Float64(y * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (x <= 8.5e+27)
		tmp = Float64(Float64(x * y0) * Float64(Float64(c * y2) - Float64(b * j)));
	elseif (x <= 1.65e+149)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (x <= 1.25e+247)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y2 * ((x * c) - (k * y5)));
	t_2 = k * (z * ((b * y0) - (i * y1)));
	tmp = 0.0;
	if (x <= -6.4e+118)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (x <= -1.95e-57)
		tmp = t_1;
	elseif (x <= -1.15e-92)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (x <= -2.5e-202)
		tmp = t_2;
	elseif (x <= -1.1e-274)
		tmp = (t * j) * ((b * y4) - (i * y5));
	elseif (x <= 5.5e-244)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	elseif (x <= 1.8e-202)
		tmp = t_2;
	elseif (x <= 4e-48)
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	elseif (x <= 8.5e+27)
		tmp = (x * y0) * ((c * y2) - (b * j));
	elseif (x <= 1.65e+149)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (x <= 1.25e+247)
		tmp = t_1;
	else
		tmp = x * (y * ((a * b) - (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+118], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.95e-57], t$95$1, If[LessEqual[x, -1.15e-92], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e-202], t$95$2, If[LessEqual[x, -1.1e-274], N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e-244], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e-202], t$95$2, If[LessEqual[x, 4e-48], N[(y3 * N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+27], N[(N[(x * y0), $MachinePrecision] * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e+149], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e+247], t$95$1, N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if x < -6.40000000000000032e118

   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 b around inf 40.6%

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

      1. fma-define 43.3%

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

      2. *-commutative 43.3%

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

      3. *-commutative 43.3%

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

      4. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in j around inf 53.0%

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

   if -6.40000000000000032e118 < x < -1.95000000000000003e-57 or 1.65e149 < x < 1.25000000000000006e247

   1. Initial program 21.7%

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

   3. Taylor expanded in y0 around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

      4. *-commutative 57.2%

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

      5. *-commutative 57.2%

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

      6. *-commutative 57.2%

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

      7. *-commutative 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in y2 around inf 57.8%

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

   if -1.95000000000000003e-57 < x < -1.15000000000000008e-92

   1. Initial program 42.6%

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

   3. Taylor expanded in j around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in y5 around -inf 86.0%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 86.0%

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

      2. *-commutative 86.0%

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

      3. *-commutative 86.0%

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

   8. Simplified 86.0%

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

   if -1.15000000000000008e-92 < x < -2.49999999999999986e-202 or 5.4999999999999998e-244 < x < 1.8000000000000001e-202

   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 k around inf 49.0%

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

      1. +-commutative 49.0%

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

      2. mul-1-neg 49.0%

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

      3. unsub-neg 49.0%

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

      4. *-commutative 49.0%

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

      5. associate-*r* 49.0%

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

      6. neg-mul-1 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in z around inf 39.9%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.9%

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

   8. Simplified 39.9%

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

   if -2.49999999999999986e-202 < x < -1.09999999999999998e-274

   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 j around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in t around inf 74.6%

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

      1. associate-*r* 74.1%

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

      2. *-commutative 74.1%

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

      3. *-commutative 74.1%

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

   8. Simplified 74.1%

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

   if -1.09999999999999998e-274 < x < 5.4999999999999998e-244

   1. Initial program 15.4%

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

   3. Taylor expanded in k around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

      5. associate-*r* 54.2%

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

      6. neg-mul-1 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in y4 around inf 70.5%

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

      1. *-commutative 70.5%

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

   8. Simplified 70.5%

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

   if 1.8000000000000001e-202 < x < 3.9999999999999999e-48

   1. Initial program 47.8%

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

   3. Taylor expanded in y3 around -inf 51.6%

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

   4. Taylor expanded in y around inf 48.9%

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

   if 3.9999999999999999e-48 < x < 8.5e27

   1. Initial program 15.4%

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

   3. Taylor expanded in y0 around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

      4. *-commutative 69.3%

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

      5. *-commutative 69.3%

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

      6. *-commutative 69.3%

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

      7. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in x around inf 63.5%

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

      1. associate-*r* 63.5%

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

   8. Simplified 63.5%

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

   if 8.5e27 < x < 1.65e149

   1. Initial program 29.6%

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

   3. Taylor expanded in b around inf 35.5%

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

      1. fma-define 40.9%

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

      2. *-commutative 40.9%

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

      3. *-commutative 40.9%

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

      4. *-commutative 40.9%

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

   5. Simplified 40.9%

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

   6. Taylor expanded in y around inf 52.1%

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

   if 1.25000000000000006e247 < x

   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 x around inf 64.4%

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

   4. Taylor expanded in y around inf 72.1%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-57}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-92}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-202}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-274}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-244}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-202}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-48}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(c \cdot y2 - b \cdot j\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+247}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ t_2 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-92}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-279}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-244}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-49}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(c \cdot y2 - b \cdot j\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+155}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+244}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y2 (- (* x c) (* k y5)))))
        (t_2 (* k (* z (- (* b y0) (* i y1))))))
   (if (<= x -4.5e+119)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= x -1.18e-57)
       t_1
       (if (<= x -8e-92)
         (* j (* y5 (- (* y0 y3) (* t i))))
         (if (<= x -2.3e-202)
           t_2
           (if (<= x -1.45e-279)
             (* (* t j) (- (* b y4) (* i y5)))
             (if (<= x 8.5e-244)
               (* k (* y4 (- (* y1 y2) (* y b))))
               (if (<= x 1.8e-202)
                 t_2
                 (if (<= x 4.3e-49)
                   (* y3 (* y (- (* c y4) (* a y5))))
                   (if (<= x 5e+27)
                     (* (* x y0) (- (* c y2) (* b j)))
                     (if (<= x 2.6e+155)
                       (* a (* x (- (* y b) (* y1 y2))))
                       (if (<= x 3.2e+244)
                         t_1
                         (* x (* y (- (* a b) (* c i)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y2 * ((x * c) - (k * y5)));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (x <= -4.5e+119) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (x <= -1.18e-57) {
		tmp = t_1;
	} else if (x <= -8e-92) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (x <= -2.3e-202) {
		tmp = t_2;
	} else if (x <= -1.45e-279) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 8.5e-244) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (x <= 1.8e-202) {
		tmp = t_2;
	} else if (x <= 4.3e-49) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (x <= 5e+27) {
		tmp = (x * y0) * ((c * y2) - (b * j));
	} else if (x <= 2.6e+155) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (x <= 3.2e+244) {
		tmp = t_1;
	} else {
		tmp = x * (y * ((a * b) - (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y0 * (y2 * ((x * c) - (k * y5)))
    t_2 = k * (z * ((b * y0) - (i * y1)))
    if (x <= (-4.5d+119)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (x <= (-1.18d-57)) then
        tmp = t_1
    else if (x <= (-8d-92)) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (x <= (-2.3d-202)) then
        tmp = t_2
    else if (x <= (-1.45d-279)) then
        tmp = (t * j) * ((b * y4) - (i * y5))
    else if (x <= 8.5d-244) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else if (x <= 1.8d-202) then
        tmp = t_2
    else if (x <= 4.3d-49) then
        tmp = y3 * (y * ((c * y4) - (a * y5)))
    else if (x <= 5d+27) then
        tmp = (x * y0) * ((c * y2) - (b * j))
    else if (x <= 2.6d+155) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else if (x <= 3.2d+244) then
        tmp = t_1
    else
        tmp = x * (y * ((a * b) - (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y2 * ((x * c) - (k * y5)));
	double t_2 = k * (z * ((b * y0) - (i * y1)));
	double tmp;
	if (x <= -4.5e+119) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (x <= -1.18e-57) {
		tmp = t_1;
	} else if (x <= -8e-92) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (x <= -2.3e-202) {
		tmp = t_2;
	} else if (x <= -1.45e-279) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 8.5e-244) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (x <= 1.8e-202) {
		tmp = t_2;
	} else if (x <= 4.3e-49) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (x <= 5e+27) {
		tmp = (x * y0) * ((c * y2) - (b * j));
	} else if (x <= 2.6e+155) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (x <= 3.2e+244) {
		tmp = t_1;
	} else {
		tmp = x * (y * ((a * b) - (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y2 * ((x * c) - (k * y5)))
	t_2 = k * (z * ((b * y0) - (i * y1)))
	tmp = 0
	if x <= -4.5e+119:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif x <= -1.18e-57:
		tmp = t_1
	elif x <= -8e-92:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif x <= -2.3e-202:
		tmp = t_2
	elif x <= -1.45e-279:
		tmp = (t * j) * ((b * y4) - (i * y5))
	elif x <= 8.5e-244:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	elif x <= 1.8e-202:
		tmp = t_2
	elif x <= 4.3e-49:
		tmp = y3 * (y * ((c * y4) - (a * y5)))
	elif x <= 5e+27:
		tmp = (x * y0) * ((c * y2) - (b * j))
	elif x <= 2.6e+155:
		tmp = a * (x * ((y * b) - (y1 * y2)))
	elif x <= 3.2e+244:
		tmp = t_1
	else:
		tmp = x * (y * ((a * b) - (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))))
	t_2 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	tmp = 0.0
	if (x <= -4.5e+119)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (x <= -1.18e-57)
		tmp = t_1;
	elseif (x <= -8e-92)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (x <= -2.3e-202)
		tmp = t_2;
	elseif (x <= -1.45e-279)
		tmp = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)));
	elseif (x <= 8.5e-244)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (x <= 1.8e-202)
		tmp = t_2;
	elseif (x <= 4.3e-49)
		tmp = Float64(y3 * Float64(y * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (x <= 5e+27)
		tmp = Float64(Float64(x * y0) * Float64(Float64(c * y2) - Float64(b * j)));
	elseif (x <= 2.6e+155)
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (x <= 3.2e+244)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y2 * ((x * c) - (k * y5)));
	t_2 = k * (z * ((b * y0) - (i * y1)));
	tmp = 0.0;
	if (x <= -4.5e+119)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (x <= -1.18e-57)
		tmp = t_1;
	elseif (x <= -8e-92)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (x <= -2.3e-202)
		tmp = t_2;
	elseif (x <= -1.45e-279)
		tmp = (t * j) * ((b * y4) - (i * y5));
	elseif (x <= 8.5e-244)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	elseif (x <= 1.8e-202)
		tmp = t_2;
	elseif (x <= 4.3e-49)
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	elseif (x <= 5e+27)
		tmp = (x * y0) * ((c * y2) - (b * j));
	elseif (x <= 2.6e+155)
		tmp = a * (x * ((y * b) - (y1 * y2)));
	elseif (x <= 3.2e+244)
		tmp = t_1;
	else
		tmp = x * (y * ((a * b) - (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+119], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.18e-57], t$95$1, If[LessEqual[x, -8e-92], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.3e-202], t$95$2, If[LessEqual[x, -1.45e-279], N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-244], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e-202], t$95$2, If[LessEqual[x, 4.3e-49], N[(y3 * N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+27], N[(N[(x * y0), $MachinePrecision] * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+155], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+244], t$95$1, N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if x < -4.5000000000000002e119

   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 b around inf 40.6%

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

      1. fma-define 43.3%

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

      2. *-commutative 43.3%

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

      3. *-commutative 43.3%

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

      4. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in j around inf 53.0%

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

   if -4.5000000000000002e119 < x < -1.18e-57 or 2.6000000000000002e155 < x < 3.2000000000000002e244

   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 y0 around inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

      4. *-commutative 58.3%

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

      5. *-commutative 58.3%

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

      6. *-commutative 58.3%

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

      7. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in y2 around inf 58.9%

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

   if -1.18e-57 < x < -7.9999999999999999e-92

   1. Initial program 42.6%

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

   3. Taylor expanded in j around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in y5 around -inf 86.0%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 86.0%

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

      2. *-commutative 86.0%

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

      3. *-commutative 86.0%

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

   8. Simplified 86.0%

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

   if -7.9999999999999999e-92 < x < -2.2999999999999999e-202 or 8.4999999999999999e-244 < x < 1.8000000000000001e-202

   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 k around inf 49.0%

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

      1. +-commutative 49.0%

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

      2. mul-1-neg 49.0%

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

      3. unsub-neg 49.0%

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

      4. *-commutative 49.0%

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

      5. associate-*r* 49.0%

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

      6. neg-mul-1 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in z around inf 39.9%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.9%

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

   8. Simplified 39.9%

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

   if -2.2999999999999999e-202 < x < -1.45e-279

   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 j around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in t around inf 74.6%

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

      1. associate-*r* 74.1%

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

      2. *-commutative 74.1%

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

      3. *-commutative 74.1%

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

   8. Simplified 74.1%

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

   if -1.45e-279 < x < 8.4999999999999999e-244

   1. Initial program 15.4%

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

   3. Taylor expanded in k around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

      5. associate-*r* 54.2%

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

      6. neg-mul-1 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in y4 around inf 70.5%

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

      1. *-commutative 70.5%

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

   8. Simplified 70.5%

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

   if 1.8000000000000001e-202 < x < 4.30000000000000016e-49

   1. Initial program 47.8%

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

   3. Taylor expanded in y3 around -inf 51.6%

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

   4. Taylor expanded in y around inf 48.9%

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

   if 4.30000000000000016e-49 < x < 4.99999999999999979e27

   1. Initial program 15.4%

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

   3. Taylor expanded in y0 around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

      4. *-commutative 69.3%

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

      5. *-commutative 69.3%

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

      6. *-commutative 69.3%

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

      7. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in x around inf 63.5%

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

      1. associate-*r* 63.5%

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

   8. Simplified 63.5%

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

   if 4.99999999999999979e27 < x < 2.6000000000000002e155

   1. Initial program 28.9%

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

   3. Taylor expanded in x around inf 45.3%

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

   4. Taylor expanded in a around -inf 50.8%

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

      1. associate-*r* 50.8%

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

      2. mul-1-neg 50.8%

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

      3. mul-1-neg 50.8%

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

      4. distribute-lft-neg-out 50.8%

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

      5. +-commutative 50.8%

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

      6. cancel-sign-sub-inv 50.8%

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

      7. *-commutative 50.8%

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

   6. Simplified 50.8%

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

   if 3.2000000000000002e244 < x

   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 x around inf 64.4%

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

   4. Taylor expanded in y around inf 72.1%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-57}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-92}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-202}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-279}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-244}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-202}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-49}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(c \cdot y2 - b \cdot j\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+155}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+244}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+117}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-58}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-205}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-280}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-198}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-101}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+142}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+241}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* x (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0)))))))
   (if (<= x -4.8e+117)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= x -1.4e-58)
       (* y0 (* y2 (- (* x c) (* k y5))))
       (if (<= x -3.2e-205)
         (*
          z
          (+ (* k (- (* b y0) (* i y1))) (- (* a (* y1 y3)) (* a (* t b)))))
         (if (<= x -7.5e-280)
           (* (* t j) (- (* b y4) (* i y5)))
           (if (<= x 3.8e-198)
             (* j (* y3 (- (* y0 y5) (* y1 y4))))
             (if (<= x 2.6e-101)
               (* y3 (* y (- (* c y4) (* a y5))))
               (if (<= x 6.8e+27)
                 t_1
                 (if (<= x 2.4e+142)
                   (* b (* y (- (* x a) (* k y4))))
                   (if (<= x 4.4e+241)
                     t_1
                     (* b (* x (- (* y a) (* j y0)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (x <= -4.8e+117) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (x <= -1.4e-58) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (x <= -3.2e-205) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (x <= -7.5e-280) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 3.8e-198) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (x <= 2.6e-101) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (x <= 6.8e+27) {
		tmp = t_1;
	} else if (x <= 2.4e+142) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (x <= 4.4e+241) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
    if (x <= (-4.8d+117)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (x <= (-1.4d-58)) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (x <= (-3.2d-205)) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))))
    else if (x <= (-7.5d-280)) then
        tmp = (t * j) * ((b * y4) - (i * y5))
    else if (x <= 3.8d-198) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (x <= 2.6d-101) then
        tmp = y3 * (y * ((c * y4) - (a * y5)))
    else if (x <= 6.8d+27) then
        tmp = t_1
    else if (x <= 2.4d+142) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (x <= 4.4d+241) then
        tmp = t_1
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (x <= -4.8e+117) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (x <= -1.4e-58) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (x <= -3.2e-205) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	} else if (x <= -7.5e-280) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 3.8e-198) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (x <= 2.6e-101) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (x <= 6.8e+27) {
		tmp = t_1;
	} else if (x <= 2.4e+142) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (x <= 4.4e+241) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if x <= -4.8e+117:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif x <= -1.4e-58:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif x <= -3.2e-205:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))))
	elif x <= -7.5e-280:
		tmp = (t * j) * ((b * y4) - (i * y5))
	elif x <= 3.8e-198:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif x <= 2.6e-101:
		tmp = y3 * (y * ((c * y4) - (a * y5)))
	elif x <= 6.8e+27:
		tmp = t_1
	elif x <= 2.4e+142:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif x <= 4.4e+241:
		tmp = t_1
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (x <= -4.8e+117)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (x <= -1.4e-58)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (x <= -3.2e-205)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(a * Float64(y1 * y3)) - Float64(a * Float64(t * b)))));
	elseif (x <= -7.5e-280)
		tmp = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)));
	elseif (x <= 3.8e-198)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (x <= 2.6e-101)
		tmp = Float64(y3 * Float64(y * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (x <= 6.8e+27)
		tmp = t_1;
	elseif (x <= 2.4e+142)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (x <= 4.4e+241)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (x <= -4.8e+117)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (x <= -1.4e-58)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (x <= -3.2e-205)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((a * (y1 * y3)) - (a * (t * b))));
	elseif (x <= -7.5e-280)
		tmp = (t * j) * ((b * y4) - (i * y5));
	elseif (x <= 3.8e-198)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (x <= 2.6e-101)
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	elseif (x <= 6.8e+27)
		tmp = t_1;
	elseif (x <= 2.4e+142)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (x <= 4.4e+241)
		tmp = t_1;
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+117], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.4e-58], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e-205], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e-280], N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e-198], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e-101], N[(y3 * N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e+27], t$95$1, If[LessEqual[x, 2.4e+142], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e+241], t$95$1, N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -4.7999999999999998e117

   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 b around inf 40.6%

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

      1. fma-define 43.3%

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

      2. *-commutative 43.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 43.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 43.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 53.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -4.7999999999999998e117 < x < -1.4e-58

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 60.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 60.3%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 60.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 60.3%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 60.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 60.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 60.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 60.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 60.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 57.5%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   if -1.4e-58 < x < -3.20000000000000009e-205

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf 36.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in c around 0 50.8%

      \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(-1 \cdot \left(a \cdot \left(y1 \cdot y3\right)\right) + a \cdot \left(b \cdot t\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   if -3.20000000000000009e-205 < x < -7.4999999999999999e-280

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 51.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 51.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 51.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 51.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 70.1%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 69.6%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(b \cdot y4 - i \cdot y5\right)} \]

      2. *-commutative 69.6%

         \[\leadsto \left(j \cdot t\right) \cdot \left(\color{blue}{y4 \cdot b} - i \cdot y5\right) \]

      3. *-commutative 69.6%

         \[\leadsto \left(j \cdot t\right) \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right) \]

   8. Simplified 69.6%

      \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)} \]

   if -7.4999999999999999e-280 < x < 3.8000000000000002e-198

   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 j around inf 50.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 50.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 50.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 50.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 59.6%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if 3.8000000000000002e-198 < x < 2.6000000000000001e-101

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 50.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y around inf 53.2%

      \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(y \cdot \left(a \cdot y5 - c \cdot y4\right)\right)}\right) \]

   if 2.6000000000000001e-101 < x < 6.8e27 or 2.3999999999999999e142 < x < 4.4e241

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 51.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 65.8%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 65.8%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 65.8%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   6. Simplified 65.8%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if 6.8e27 < x < 2.3999999999999999e142

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 33.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 39.3%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 39.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 39.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 39.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 39.3%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y around inf 50.7%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

   if 4.4e241 < x

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 60.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 60.1%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 60.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 60.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 60.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 60.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 73.5%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+117}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-58}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-205}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(a \cdot \left(y1 \cdot y3\right) - a \cdot \left(t \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-280}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-198}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-101}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+142}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+241}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;i \leq -1.4 \cdot 10^{+254}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{+40}:\\ \;\;\;\;\left(t \cdot j\right) \cdot t\_2\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-215}:\\ \;\;\;\;j \cdot \left(t \cdot t\_2 + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+140}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          b
          (+
           (+ (* (- (* t j) (* y k)) y4) (* a (- (* x y) (* z t))))
           (* y0 (- (* z k) (* x j))))))
        (t_2 (- (* b y4) (* i y5))))
   (if (<= i -1.4e+254)
     (* k (* (* i y1) (- z)))
     (if (<= i -3e+148)
       (* j (* y5 (- (* y0 y3) (* t i))))
       (if (<= i -2.6e+54)
         (* x (* y (- (* a b) (* c i))))
         (if (<= i -2.15e+40)
           (* (* t j) t_2)
           (if (<= i -1e-100)
             t_1
             (if (<= i -6e-215)
               (* j (+ (* t t_2) (- (* y0 (* y3 y5)) (* y0 (* x b)))))
               (if (<= i 1.25e+101)
                 t_1
                 (if (<= i 1.8e+140)
                   (* y3 (* y (- (* c y4) (* a y5))))
                   (*
                    x
                    (+
                     (* y2 (- (* c y0) (* a y1)))
                     (* j (- (* i y1) (* b y0)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double t_2 = (b * y4) - (i * y5);
	double tmp;
	if (i <= -1.4e+254) {
		tmp = k * ((i * y1) * -z);
	} else if (i <= -3e+148) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (i <= -2.6e+54) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (i <= -2.15e+40) {
		tmp = (t * j) * t_2;
	} else if (i <= -1e-100) {
		tmp = t_1;
	} else if (i <= -6e-215) {
		tmp = j * ((t * t_2) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	} else if (i <= 1.25e+101) {
		tmp = t_1;
	} else if (i <= 1.8e+140) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
    t_2 = (b * y4) - (i * y5)
    if (i <= (-1.4d+254)) then
        tmp = k * ((i * y1) * -z)
    else if (i <= (-3d+148)) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (i <= (-2.6d+54)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (i <= (-2.15d+40)) then
        tmp = (t * j) * t_2
    else if (i <= (-1d-100)) then
        tmp = t_1
    else if (i <= (-6d-215)) then
        tmp = j * ((t * t_2) + ((y0 * (y3 * y5)) - (y0 * (x * b))))
    else if (i <= 1.25d+101) then
        tmp = t_1
    else if (i <= 1.8d+140) then
        tmp = y3 * (y * ((c * y4) - (a * y5)))
    else
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	double t_2 = (b * y4) - (i * y5);
	double tmp;
	if (i <= -1.4e+254) {
		tmp = k * ((i * y1) * -z);
	} else if (i <= -3e+148) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (i <= -2.6e+54) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (i <= -2.15e+40) {
		tmp = (t * j) * t_2;
	} else if (i <= -1e-100) {
		tmp = t_1;
	} else if (i <= -6e-215) {
		tmp = j * ((t * t_2) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	} else if (i <= 1.25e+101) {
		tmp = t_1;
	} else if (i <= 1.8e+140) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))))
	t_2 = (b * y4) - (i * y5)
	tmp = 0
	if i <= -1.4e+254:
		tmp = k * ((i * y1) * -z)
	elif i <= -3e+148:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif i <= -2.6e+54:
		tmp = x * (y * ((a * b) - (c * i)))
	elif i <= -2.15e+40:
		tmp = (t * j) * t_2
	elif i <= -1e-100:
		tmp = t_1
	elif i <= -6e-215:
		tmp = j * ((t * t_2) + ((y0 * (y3 * y5)) - (y0 * (x * b))))
	elif i <= 1.25e+101:
		tmp = t_1
	elif i <= 1.8e+140:
		tmp = y3 * (y * ((c * y4) - (a * y5)))
	else:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(Float64(Float64(Float64(Float64(t * j) - Float64(y * k)) * y4) + Float64(a * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (i <= -1.4e+254)
		tmp = Float64(k * Float64(Float64(i * y1) * Float64(-z)));
	elseif (i <= -3e+148)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (i <= -2.6e+54)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (i <= -2.15e+40)
		tmp = Float64(Float64(t * j) * t_2);
	elseif (i <= -1e-100)
		tmp = t_1;
	elseif (i <= -6e-215)
		tmp = Float64(j * Float64(Float64(t * t_2) + Float64(Float64(y0 * Float64(y3 * y5)) - Float64(y0 * Float64(x * b)))));
	elseif (i <= 1.25e+101)
		tmp = t_1;
	elseif (i <= 1.8e+140)
		tmp = Float64(y3 * Float64(y * Float64(Float64(c * y4) - Float64(a * y5))));
	else
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (((((t * j) - (y * k)) * y4) + (a * ((x * y) - (z * t)))) + (y0 * ((z * k) - (x * j))));
	t_2 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (i <= -1.4e+254)
		tmp = k * ((i * y1) * -z);
	elseif (i <= -3e+148)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (i <= -2.6e+54)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (i <= -2.15e+40)
		tmp = (t * j) * t_2;
	elseif (i <= -1e-100)
		tmp = t_1;
	elseif (i <= -6e-215)
		tmp = j * ((t * t_2) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	elseif (i <= 1.25e+101)
		tmp = t_1;
	elseif (i <= 1.8e+140)
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	else
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(N[(N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision] + N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $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[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.4e+254], N[(k * N[(N[(i * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3e+148], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.6e+54], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.15e+40], N[(N[(t * j), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[i, -1e-100], t$95$1, If[LessEqual[i, -6e-215], N[(j * N[(N[(t * t$95$2), $MachinePrecision] + N[(N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.25e+101], t$95$1, If[LessEqual[i, 1.8e+140], N[(y3 * N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -1.39999999999999991e254

   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 26.7%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 26.7%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 26.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 26.7%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 26.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 26.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 26.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 26.7%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 73.3%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 73.3%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 73.4%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 73.4%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-i \cdot y1\right)}\right) \]

       2. distribute-lft-neg-out 73.4%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(\left(-i\right) \cdot y1\right)}\right) \]

       3. *-commutative 73.4%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   11. Simplified 73.4%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   if -1.39999999999999991e254 < i < -3.00000000000000015e148

   1. Initial program 13.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 40.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 40.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 40.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 40.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 40.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y5 around -inf 80.4%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 80.4%

         \[\leadsto j \cdot \color{blue}{\left(-y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)} \]

      2. *-commutative 80.4%

         \[\leadsto j \cdot \left(-y5 \cdot \left(\color{blue}{t \cdot i} - y0 \cdot y3\right)\right) \]

      3. *-commutative 80.4%

         \[\leadsto j \cdot \left(-y5 \cdot \left(t \cdot i - \color{blue}{y3 \cdot y0}\right)\right) \]

   8. Simplified 80.4%

      \[\leadsto j \cdot \color{blue}{\left(-y5 \cdot \left(t \cdot i - y3 \cdot y0\right)\right)} \]

   if -3.00000000000000015e148 < i < -2.60000000000000007e54

   1. Initial program 41.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 65.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if -2.60000000000000007e54 < i < -2.1500000000000001e40

   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 j around inf 60.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 60.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 60.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 60.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 60.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 60.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 80.9%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 61.8%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(b \cdot y4 - i \cdot y5\right)} \]

      2. *-commutative 61.8%

         \[\leadsto \left(j \cdot t\right) \cdot \left(\color{blue}{y4 \cdot b} - i \cdot y5\right) \]

      3. *-commutative 61.8%

         \[\leadsto \left(j \cdot t\right) \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right) \]

   8. Simplified 61.8%

      \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)} \]

   if -2.1500000000000001e40 < i < -1e-100 or -6.00000000000000051e-215 < i < 1.24999999999999997e101

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if -1e-100 < i < -6.00000000000000051e-215

   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 j around inf 42.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 42.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 42.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 42.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 42.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y1 around 0 53.5%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(-1 \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right) + b \cdot \left(x \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 53.5%

         \[\leadsto j \cdot \left(t \cdot \left(\color{blue}{y4 \cdot b} - i \cdot y5\right) - \left(-1 \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right) + b \cdot \left(x \cdot y0\right)\right)\right) \]

      2. *-commutative 53.5%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right) - \left(-1 \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right) + b \cdot \left(x \cdot y0\right)\right)\right) \]

      3. +-commutative 53.5%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \color{blue}{\left(b \cdot \left(x \cdot y0\right) + -1 \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\right)}\right) \]

      4. mul-1-neg 53.5%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \left(b \cdot \left(x \cdot y0\right) + \color{blue}{\left(-y0 \cdot \left(y3 \cdot y5\right)\right)}\right)\right) \]

      5. unsub-neg 53.5%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \color{blue}{\left(b \cdot \left(x \cdot y0\right) - y0 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      6. associate-*r* 53.5%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \left(\color{blue}{\left(b \cdot x\right) \cdot y0} - y0 \cdot \left(y3 \cdot y5\right)\right)\right) \]

   8. Simplified 53.5%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \left(\left(b \cdot x\right) \cdot y0 - y0 \cdot \left(y3 \cdot y5\right)\right)\right)} \]

   if 1.24999999999999997e101 < i < 1.8e140

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf 50.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y around inf 72.1%

      \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(y \cdot \left(a \cdot y5 - c \cdot y4\right)\right)}\right) \]

   if 1.8e140 < i

   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 x around inf 46.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 51.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 51.5%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 51.5%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   6. Simplified 51.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+254}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{+40}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-100}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-215}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+101}:\\ \;\;\;\;b \cdot \left(\left(\left(t \cdot j - y \cdot k\right) \cdot y4 + a \cdot \left(x \cdot y - z \cdot t\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+140}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b - c \cdot i\\ t_2 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ t_3 := a \cdot y1 - c \cdot y0\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+217}:\\ \;\;\;\;z \cdot \left(y3 \cdot t\_3 - t \cdot t\_1\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+95}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \left(t \cdot c - k \cdot y1\right)\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-94}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(y \cdot t\_1\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+158}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+177}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(z \cdot t\_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a b) (* c i)))
        (t_2 (* y3 (* y (- (* c y4) (* a y5)))))
        (t_3 (- (* a y1) (* c y0))))
   (if (<= z -4.3e+217)
     (* z (- (* y3 t_3) (* t t_1)))
     (if (<= z -2.1e+95)
       (* (* z i) (- (* t c) (* k y1)))
       (if (<= z -1.56e+29)
         t_2
         (if (<= z -2.05e+17)
           (* (* z k) (- (* b y0) (* i y1)))
           (if (<= z -3.9e-94)
             (* b (* j (- (* t y4) (* x y0))))
             (if (<= z -3.6e-132)
               (* x (* y t_1))
               (if (<= z 2.2e-151)
                 (*
                  x
                  (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0)))))
                 (if (<= z 4.1e+34)
                   (*
                    j
                    (+
                     (* t (- (* b y4) (* i y5)))
                     (- (* y0 (* y3 y5)) (* y0 (* x b)))))
                   (if (<= z 1.35e+158)
                     t_2
                     (if (<= z 1.05e+177)
                       (* a (* x (- (* y b) (* y1 y2))))
                       (* y3 (* z t_3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * b) - (c * i);
	double t_2 = y3 * (y * ((c * y4) - (a * y5)));
	double t_3 = (a * y1) - (c * y0);
	double tmp;
	if (z <= -4.3e+217) {
		tmp = z * ((y3 * t_3) - (t * t_1));
	} else if (z <= -2.1e+95) {
		tmp = (z * i) * ((t * c) - (k * y1));
	} else if (z <= -1.56e+29) {
		tmp = t_2;
	} else if (z <= -2.05e+17) {
		tmp = (z * k) * ((b * y0) - (i * y1));
	} else if (z <= -3.9e-94) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (z <= -3.6e-132) {
		tmp = x * (y * t_1);
	} else if (z <= 2.2e-151) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (z <= 4.1e+34) {
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	} else if (z <= 1.35e+158) {
		tmp = t_2;
	} else if (z <= 1.05e+177) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else {
		tmp = y3 * (z * t_3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) - (c * i)
    t_2 = y3 * (y * ((c * y4) - (a * y5)))
    t_3 = (a * y1) - (c * y0)
    if (z <= (-4.3d+217)) then
        tmp = z * ((y3 * t_3) - (t * t_1))
    else if (z <= (-2.1d+95)) then
        tmp = (z * i) * ((t * c) - (k * y1))
    else if (z <= (-1.56d+29)) then
        tmp = t_2
    else if (z <= (-2.05d+17)) then
        tmp = (z * k) * ((b * y0) - (i * y1))
    else if (z <= (-3.9d-94)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (z <= (-3.6d-132)) then
        tmp = x * (y * t_1)
    else if (z <= 2.2d-151) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
    else if (z <= 4.1d+34) then
        tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))))
    else if (z <= 1.35d+158) then
        tmp = t_2
    else if (z <= 1.05d+177) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else
        tmp = y3 * (z * t_3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * b) - (c * i);
	double t_2 = y3 * (y * ((c * y4) - (a * y5)));
	double t_3 = (a * y1) - (c * y0);
	double tmp;
	if (z <= -4.3e+217) {
		tmp = z * ((y3 * t_3) - (t * t_1));
	} else if (z <= -2.1e+95) {
		tmp = (z * i) * ((t * c) - (k * y1));
	} else if (z <= -1.56e+29) {
		tmp = t_2;
	} else if (z <= -2.05e+17) {
		tmp = (z * k) * ((b * y0) - (i * y1));
	} else if (z <= -3.9e-94) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (z <= -3.6e-132) {
		tmp = x * (y * t_1);
	} else if (z <= 2.2e-151) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (z <= 4.1e+34) {
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	} else if (z <= 1.35e+158) {
		tmp = t_2;
	} else if (z <= 1.05e+177) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else {
		tmp = y3 * (z * t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * b) - (c * i)
	t_2 = y3 * (y * ((c * y4) - (a * y5)))
	t_3 = (a * y1) - (c * y0)
	tmp = 0
	if z <= -4.3e+217:
		tmp = z * ((y3 * t_3) - (t * t_1))
	elif z <= -2.1e+95:
		tmp = (z * i) * ((t * c) - (k * y1))
	elif z <= -1.56e+29:
		tmp = t_2
	elif z <= -2.05e+17:
		tmp = (z * k) * ((b * y0) - (i * y1))
	elif z <= -3.9e-94:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif z <= -3.6e-132:
		tmp = x * (y * t_1)
	elif z <= 2.2e-151:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
	elif z <= 4.1e+34:
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))))
	elif z <= 1.35e+158:
		tmp = t_2
	elif z <= 1.05e+177:
		tmp = a * (x * ((y * b) - (y1 * y2)))
	else:
		tmp = y3 * (z * t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * b) - Float64(c * i))
	t_2 = Float64(y3 * Float64(y * Float64(Float64(c * y4) - Float64(a * y5))))
	t_3 = Float64(Float64(a * y1) - Float64(c * y0))
	tmp = 0.0
	if (z <= -4.3e+217)
		tmp = Float64(z * Float64(Float64(y3 * t_3) - Float64(t * t_1)));
	elseif (z <= -2.1e+95)
		tmp = Float64(Float64(z * i) * Float64(Float64(t * c) - Float64(k * y1)));
	elseif (z <= -1.56e+29)
		tmp = t_2;
	elseif (z <= -2.05e+17)
		tmp = Float64(Float64(z * k) * Float64(Float64(b * y0) - Float64(i * y1)));
	elseif (z <= -3.9e-94)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (z <= -3.6e-132)
		tmp = Float64(x * Float64(y * t_1));
	elseif (z <= 2.2e-151)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (z <= 4.1e+34)
		tmp = Float64(j * Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(Float64(y0 * Float64(y3 * y5)) - Float64(y0 * Float64(x * b)))));
	elseif (z <= 1.35e+158)
		tmp = t_2;
	elseif (z <= 1.05e+177)
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	else
		tmp = Float64(y3 * Float64(z * t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * b) - (c * i);
	t_2 = y3 * (y * ((c * y4) - (a * y5)));
	t_3 = (a * y1) - (c * y0);
	tmp = 0.0;
	if (z <= -4.3e+217)
		tmp = z * ((y3 * t_3) - (t * t_1));
	elseif (z <= -2.1e+95)
		tmp = (z * i) * ((t * c) - (k * y1));
	elseif (z <= -1.56e+29)
		tmp = t_2;
	elseif (z <= -2.05e+17)
		tmp = (z * k) * ((b * y0) - (i * y1));
	elseif (z <= -3.9e-94)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (z <= -3.6e-132)
		tmp = x * (y * t_1);
	elseif (z <= 2.2e-151)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	elseif (z <= 4.1e+34)
		tmp = j * ((t * ((b * y4) - (i * y5))) + ((y0 * (y3 * y5)) - (y0 * (x * b))));
	elseif (z <= 1.35e+158)
		tmp = t_2;
	elseif (z <= 1.05e+177)
		tmp = a * (x * ((y * b) - (y1 * y2)));
	else
		tmp = y3 * (z * t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y3 * N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+217], N[(z * N[(N[(y3 * t$95$3), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e+95], N[(N[(z * i), $MachinePrecision] * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.56e+29], t$95$2, If[LessEqual[z, -2.05e+17], N[(N[(z * k), $MachinePrecision] * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-94], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-132], N[(x * N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-151], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+34], N[(j * N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+158], t$95$2, If[LessEqual[z, 1.05e+177], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(z * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if z < -4.3000000000000001e217

   1. Initial program 25.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf 68.8%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in k around 0 68.8%

      \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)} \]

   if -4.3000000000000001e217 < z < -2.1e95

   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 z around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around -inf 51.1%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.1%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)\right)} \]

      2. associate-*r* 68.4%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(i \cdot z\right) \cdot \left(c \cdot t - k \cdot y1\right)}\right) \]

      3. *-commutative 68.4%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(z \cdot i\right)} \cdot \left(c \cdot t - k \cdot y1\right)\right) \]

      4. *-commutative 68.4%

         \[\leadsto -1 \cdot \left(-\left(z \cdot i\right) \cdot \left(\color{blue}{t \cdot c} - k \cdot y1\right)\right) \]

   6. Simplified 68.4%

      \[\leadsto -1 \cdot \color{blue}{\left(-\left(z \cdot i\right) \cdot \left(t \cdot c - k \cdot y1\right)\right)} \]

   if -2.1e95 < z < -1.5599999999999999e29 or 4.0999999999999998e34 < z < 1.34999999999999989e158

   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 y3 around -inf 44.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y around inf 59.3%

      \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(y \cdot \left(a \cdot y5 - c \cdot y4\right)\right)}\right) \]

   if -1.5599999999999999e29 < z < -2.05e17

   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 k around inf 57.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 57.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 57.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 57.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 57.1%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 57.2%

         \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

      2. *-commutative 57.2%

         \[\leadsto \color{blue}{\left(z \cdot k\right)} \cdot \left(b \cdot y0 - i \cdot y1\right) \]

      3. *-commutative 57.2%

         \[\leadsto \left(z \cdot k\right) \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right) \]

   8. Simplified 57.2%

      \[\leadsto \color{blue}{\left(z \cdot k\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)} \]

   if -2.05e17 < z < -3.9000000000000002e-94

   1. Initial program 44.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 64.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 68.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 68.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 68.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 68.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 68.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 57.4%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -3.9000000000000002e-94 < z < -3.60000000000000007e-132

   1. Initial program 34.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 77.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if -3.60000000000000007e-132 < z < 2.1999999999999999e-151

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 41.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 52.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 52.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 52.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   6. Simplified 52.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if 2.1999999999999999e-151 < z < 4.0999999999999998e34

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 49.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 49.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 49.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 49.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 49.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y1 around 0 47.5%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(-1 \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right) + b \cdot \left(x \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.5%

         \[\leadsto j \cdot \left(t \cdot \left(\color{blue}{y4 \cdot b} - i \cdot y5\right) - \left(-1 \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right) + b \cdot \left(x \cdot y0\right)\right)\right) \]

      2. *-commutative 47.5%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right) - \left(-1 \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right) + b \cdot \left(x \cdot y0\right)\right)\right) \]

      3. +-commutative 47.5%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \color{blue}{\left(b \cdot \left(x \cdot y0\right) + -1 \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\right)}\right) \]

      4. mul-1-neg 47.5%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \left(b \cdot \left(x \cdot y0\right) + \color{blue}{\left(-y0 \cdot \left(y3 \cdot y5\right)\right)}\right)\right) \]

      5. unsub-neg 47.5%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \color{blue}{\left(b \cdot \left(x \cdot y0\right) - y0 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      6. associate-*r* 49.6%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \left(\color{blue}{\left(b \cdot x\right) \cdot y0} - y0 \cdot \left(y3 \cdot y5\right)\right)\right) \]

   8. Simplified 49.6%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y4 \cdot b - y5 \cdot i\right) - \left(\left(b \cdot x\right) \cdot y0 - y0 \cdot \left(y3 \cdot y5\right)\right)\right)} \]

   if 1.34999999999999989e158 < z < 1.05000000000000006e177

   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 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 a around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)} \]

      2. mul-1-neg 100.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]

      3. mul-1-neg 100.0%

         \[\leadsto \left(-a\right) \cdot \left(x \cdot \left(\color{blue}{\left(-b \cdot y\right)} + y1 \cdot y2\right)\right) \]

      4. distribute-lft-neg-out 100.0%

         \[\leadsto \left(-a\right) \cdot \left(x \cdot \left(\color{blue}{\left(-b\right) \cdot y} + y1 \cdot y2\right)\right) \]

      5. +-commutative 100.0%

         \[\leadsto \left(-a\right) \cdot \left(x \cdot \color{blue}{\left(y1 \cdot y2 + \left(-b\right) \cdot y\right)}\right) \]

      6. cancel-sign-sub-inv 100.0%

         \[\leadsto \left(-a\right) \cdot \left(x \cdot \color{blue}{\left(y1 \cdot y2 - b \cdot y\right)}\right) \]

      7. *-commutative 100.0%

         \[\leadsto \left(-a\right) \cdot \left(x \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   if 1.05000000000000006e177 < z

   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 z around -inf 50.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y3 around inf 62.6%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+217}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) - t \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+95}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \left(t \cdot c - k \cdot y1\right)\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+29}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-94}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \left(y0 \cdot \left(y3 \cdot y5\right) - y0 \cdot \left(x \cdot b\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+158}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+177}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b - c \cdot i\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+217}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) - t \cdot t\_1\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+95}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \left(t \cdot c - k \cdot y1\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+31}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-94}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(y \cdot t\_1\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a b) (* c i))))
   (if (<= z -4.3e+217)
     (* z (- (* y3 (- (* a y1) (* c y0))) (* t t_1)))
     (if (<= z -1.2e+95)
       (* (* z i) (- (* t c) (* k y1)))
       (if (<= z -4.3e+31)
         (* y3 (* y (- (* c y4) (* a y5))))
         (if (<= z -1.06e+17)
           (* (* z k) (- (* b y0) (* i y1)))
           (if (<= z -3.9e-94)
             (* b (* j (- (* t y4) (* x y0))))
             (if (<= z -1.8e-132)
               (* x (* y t_1))
               (if (<= z 1.7e+58)
                 (*
                  x
                  (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0)))))
                 (if (<= z 2.4e+161)
                   (* b (* x (- (* y a) (* j y0))))
                   (* y1 (* z (- (* a y3) (* i 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 * b) - (c * i);
	double tmp;
	if (z <= -4.3e+217) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) - (t * t_1));
	} else if (z <= -1.2e+95) {
		tmp = (z * i) * ((t * c) - (k * y1));
	} else if (z <= -4.3e+31) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (z <= -1.06e+17) {
		tmp = (z * k) * ((b * y0) - (i * y1));
	} else if (z <= -3.9e-94) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (z <= -1.8e-132) {
		tmp = x * (y * t_1);
	} else if (z <= 1.7e+58) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (z <= 2.4e+161) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = y1 * (z * ((a * y3) - (i * 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 * b) - (c * i)
    if (z <= (-4.3d+217)) then
        tmp = z * ((y3 * ((a * y1) - (c * y0))) - (t * t_1))
    else if (z <= (-1.2d+95)) then
        tmp = (z * i) * ((t * c) - (k * y1))
    else if (z <= (-4.3d+31)) then
        tmp = y3 * (y * ((c * y4) - (a * y5)))
    else if (z <= (-1.06d+17)) then
        tmp = (z * k) * ((b * y0) - (i * y1))
    else if (z <= (-3.9d-94)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (z <= (-1.8d-132)) then
        tmp = x * (y * t_1)
    else if (z <= 1.7d+58) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
    else if (z <= 2.4d+161) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else
        tmp = y1 * (z * ((a * y3) - (i * 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 * b) - (c * i);
	double tmp;
	if (z <= -4.3e+217) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) - (t * t_1));
	} else if (z <= -1.2e+95) {
		tmp = (z * i) * ((t * c) - (k * y1));
	} else if (z <= -4.3e+31) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (z <= -1.06e+17) {
		tmp = (z * k) * ((b * y0) - (i * y1));
	} else if (z <= -3.9e-94) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (z <= -1.8e-132) {
		tmp = x * (y * t_1);
	} else if (z <= 1.7e+58) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (z <= 2.4e+161) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = y1 * (z * ((a * y3) - (i * 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 * b) - (c * i)
	tmp = 0
	if z <= -4.3e+217:
		tmp = z * ((y3 * ((a * y1) - (c * y0))) - (t * t_1))
	elif z <= -1.2e+95:
		tmp = (z * i) * ((t * c) - (k * y1))
	elif z <= -4.3e+31:
		tmp = y3 * (y * ((c * y4) - (a * y5)))
	elif z <= -1.06e+17:
		tmp = (z * k) * ((b * y0) - (i * y1))
	elif z <= -3.9e-94:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif z <= -1.8e-132:
		tmp = x * (y * t_1)
	elif z <= 1.7e+58:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
	elif z <= 2.4e+161:
		tmp = b * (x * ((y * a) - (j * y0)))
	else:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * b) - Float64(c * i))
	tmp = 0.0
	if (z <= -4.3e+217)
		tmp = Float64(z * Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) - Float64(t * t_1)));
	elseif (z <= -1.2e+95)
		tmp = Float64(Float64(z * i) * Float64(Float64(t * c) - Float64(k * y1)));
	elseif (z <= -4.3e+31)
		tmp = Float64(y3 * Float64(y * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (z <= -1.06e+17)
		tmp = Float64(Float64(z * k) * Float64(Float64(b * y0) - Float64(i * y1)));
	elseif (z <= -3.9e-94)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (z <= -1.8e-132)
		tmp = Float64(x * Float64(y * t_1));
	elseif (z <= 1.7e+58)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (z <= 2.4e+161)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	else
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * 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 * b) - (c * i);
	tmp = 0.0;
	if (z <= -4.3e+217)
		tmp = z * ((y3 * ((a * y1) - (c * y0))) - (t * t_1));
	elseif (z <= -1.2e+95)
		tmp = (z * i) * ((t * c) - (k * y1));
	elseif (z <= -4.3e+31)
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	elseif (z <= -1.06e+17)
		tmp = (z * k) * ((b * y0) - (i * y1));
	elseif (z <= -3.9e-94)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (z <= -1.8e-132)
		tmp = x * (y * t_1);
	elseif (z <= 1.7e+58)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	elseif (z <= 2.4e+161)
		tmp = b * (x * ((y * a) - (j * y0)));
	else
		tmp = y1 * (z * ((a * y3) - (i * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+217], N[(z * N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e+95], N[(N[(z * i), $MachinePrecision] * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.3e+31], N[(y3 * N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.06e+17], N[(N[(z * k), $MachinePrecision] * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-94], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-132], N[(x * N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+58], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+161], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -4.3000000000000001e217

   1. Initial program 25.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf 68.8%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in k around 0 68.8%

      \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)} \]

   if -4.3000000000000001e217 < z < -1.2e95

   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 z around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around -inf 51.1%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.1%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)\right)} \]

      2. associate-*r* 68.4%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(i \cdot z\right) \cdot \left(c \cdot t - k \cdot y1\right)}\right) \]

      3. *-commutative 68.4%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(z \cdot i\right)} \cdot \left(c \cdot t - k \cdot y1\right)\right) \]

      4. *-commutative 68.4%

         \[\leadsto -1 \cdot \left(-\left(z \cdot i\right) \cdot \left(\color{blue}{t \cdot c} - k \cdot y1\right)\right) \]

   6. Simplified 68.4%

      \[\leadsto -1 \cdot \color{blue}{\left(-\left(z \cdot i\right) \cdot \left(t \cdot c - k \cdot y1\right)\right)} \]

   if -1.2e95 < z < -4.29999999999999989e31

   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 y3 around -inf 43.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y around inf 65.0%

      \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(y \cdot \left(a \cdot y5 - c \cdot y4\right)\right)}\right) \]

   if -4.29999999999999989e31 < z < -1.06e17

   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 k around inf 57.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 57.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 57.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 57.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 57.1%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 57.2%

         \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

      2. *-commutative 57.2%

         \[\leadsto \color{blue}{\left(z \cdot k\right)} \cdot \left(b \cdot y0 - i \cdot y1\right) \]

      3. *-commutative 57.2%

         \[\leadsto \left(z \cdot k\right) \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right) \]

   8. Simplified 57.2%

      \[\leadsto \color{blue}{\left(z \cdot k\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)} \]

   if -1.06e17 < z < -3.9000000000000002e-94

   1. Initial program 44.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 64.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 68.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 68.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 68.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 68.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 68.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 57.4%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -3.9000000000000002e-94 < z < -1.80000000000000004e-132

   1. Initial program 34.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 77.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if -1.80000000000000004e-132 < z < 1.7e58

   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 x around inf 42.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 45.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 45.5%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 45.5%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   6. Simplified 45.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if 1.7e58 < z < 2.3999999999999999e161

   1. Initial program 17.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. Step-by-step derivation

      1. fma-define 43.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 2.3999999999999999e161 < z

   1. Initial program 14.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y1 around -inf 56.2%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+217}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) - t \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+95}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \left(t \cdot c - k \cdot y1\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+31}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-94}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{if}\;k \leq -1.06 \cdot 10^{+58}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2.35 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{-231}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{+48}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+130}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+221}:\\ \;\;\;\;\left(y \cdot k\right) \cdot \left(i \cdot y5 - b \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (- (* y a) (* j y0))))))
   (if (<= k -1.06e+58)
     (* k (* y2 (- (* y1 y4) (* y0 y5))))
     (if (<= k -2.35e-153)
       t_1
       (if (<= k 3.1e-231)
         (* j (* y3 (- (* y0 y5) (* y1 y4))))
         (if (<= k 1.6e-197)
           t_1
           (if (<= k 3.4e-32)
             (* x (* y (- (* a b) (* c i))))
             (if (<= k 4.1e+48)
               (* (* x y2) (- (* c y0) (* a y1)))
               (if (<= k 7.8e+130)
                 (* y0 (* y5 (- (* j y3) (* k y2))))
                 (if (<= k 8e+221)
                   (* (* y k) (- (* i y5) (* b y4)))
                   (* k (* y0 (- (* z b) (* y2 y5))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (k <= -1.06e+58) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -2.35e-153) {
		tmp = t_1;
	} else if (k <= 3.1e-231) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 1.6e-197) {
		tmp = t_1;
	} else if (k <= 3.4e-32) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (k <= 4.1e+48) {
		tmp = (x * y2) * ((c * y0) - (a * y1));
	} else if (k <= 7.8e+130) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (k <= 8e+221) {
		tmp = (y * k) * ((i * y5) - (b * y4));
	} else {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (x * ((y * a) - (j * y0)))
    if (k <= (-1.06d+58)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (k <= (-2.35d-153)) then
        tmp = t_1
    else if (k <= 3.1d-231) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (k <= 1.6d-197) then
        tmp = t_1
    else if (k <= 3.4d-32) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (k <= 4.1d+48) then
        tmp = (x * y2) * ((c * y0) - (a * y1))
    else if (k <= 7.8d+130) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (k <= 8d+221) then
        tmp = (y * k) * ((i * y5) - (b * y4))
    else
        tmp = k * (y0 * ((z * b) - (y2 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (k <= -1.06e+58) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -2.35e-153) {
		tmp = t_1;
	} else if (k <= 3.1e-231) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 1.6e-197) {
		tmp = t_1;
	} else if (k <= 3.4e-32) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (k <= 4.1e+48) {
		tmp = (x * y2) * ((c * y0) - (a * y1));
	} else if (k <= 7.8e+130) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (k <= 8e+221) {
		tmp = (y * k) * ((i * y5) - (b * y4));
	} else {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (x * ((y * a) - (j * y0)))
	tmp = 0
	if k <= -1.06e+58:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif k <= -2.35e-153:
		tmp = t_1
	elif k <= 3.1e-231:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif k <= 1.6e-197:
		tmp = t_1
	elif k <= 3.4e-32:
		tmp = x * (y * ((a * b) - (c * i)))
	elif k <= 4.1e+48:
		tmp = (x * y2) * ((c * y0) - (a * y1))
	elif k <= 7.8e+130:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif k <= 8e+221:
		tmp = (y * k) * ((i * y5) - (b * y4))
	else:
		tmp = k * (y0 * ((z * b) - (y2 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))))
	tmp = 0.0
	if (k <= -1.06e+58)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (k <= -2.35e-153)
		tmp = t_1;
	elseif (k <= 3.1e-231)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (k <= 1.6e-197)
		tmp = t_1;
	elseif (k <= 3.4e-32)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (k <= 4.1e+48)
		tmp = Float64(Float64(x * y2) * Float64(Float64(c * y0) - Float64(a * y1)));
	elseif (k <= 7.8e+130)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (k <= 8e+221)
		tmp = Float64(Float64(y * k) * Float64(Float64(i * y5) - Float64(b * y4)));
	else
		tmp = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (x * ((y * a) - (j * y0)));
	tmp = 0.0;
	if (k <= -1.06e+58)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (k <= -2.35e-153)
		tmp = t_1;
	elseif (k <= 3.1e-231)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (k <= 1.6e-197)
		tmp = t_1;
	elseif (k <= 3.4e-32)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (k <= 4.1e+48)
		tmp = (x * y2) * ((c * y0) - (a * y1));
	elseif (k <= 7.8e+130)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (k <= 8e+221)
		tmp = (y * k) * ((i * y5) - (b * y4));
	else
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.06e+58], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.35e-153], t$95$1, If[LessEqual[k, 3.1e-231], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.6e-197], t$95$1, If[LessEqual[k, 3.4e-32], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.1e+48], N[(N[(x * y2), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.8e+130], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8e+221], N[(N[(y * k), $MachinePrecision] * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -1.05999999999999997e58

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto k \cdot \left(y2 \cdot \left(\color{blue}{y4 \cdot y1} - y0 \cdot y5\right)\right) \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]

   if -1.05999999999999997e58 < k < -2.35e-153 or 3.09999999999999988e-231 < k < 1.5999999999999999e-197

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 63.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 63.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 54.0%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -2.35e-153 < k < 3.09999999999999988e-231

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 37.5%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if 1.5999999999999999e-197 < k < 3.39999999999999978e-32

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 44.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 48.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if 3.39999999999999978e-32 < k < 4.1000000000000003e48

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 41.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 41.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 46.2%

         \[\leadsto \color{blue}{\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)} \]

   6. Simplified 46.2%

      \[\leadsto \color{blue}{\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)} \]

   if 4.1000000000000003e48 < k < 7.8000000000000004e130

   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 y0 around inf 33.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 33.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 33.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 33.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y5 around inf 67.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)} \]

   if 7.8000000000000004e130 < k < 8.0000000000000004e221

   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 k around inf 43.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 43.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 43.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 43.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 43.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 43.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 43.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around -inf 51.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.0%

         \[\leadsto \color{blue}{-k \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

      2. associate-*r* 51.0%

         \[\leadsto -\color{blue}{\left(k \cdot y\right) \cdot \left(b \cdot y4 - i \cdot y5\right)} \]

      3. *-commutative 51.0%

         \[\leadsto -\color{blue}{\left(y \cdot k\right)} \cdot \left(b \cdot y4 - i \cdot y5\right) \]

      4. *-commutative 51.0%

         \[\leadsto -\left(y \cdot k\right) \cdot \left(b \cdot y4 - \color{blue}{y5 \cdot i}\right) \]

   8. Simplified 51.0%

      \[\leadsto \color{blue}{-\left(y \cdot k\right) \cdot \left(b \cdot y4 - y5 \cdot i\right)} \]

   if 8.0000000000000004e221 < k

   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 k around inf 66.7%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.7%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 66.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 66.7%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 66.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 66.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 66.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y0 around -inf 75.0%

      \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 75.0%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

      2. neg-mul-1 75.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(y2 \cdot y5 - b \cdot z\right)\right) \]

   8. Simplified 75.0%

      \[\leadsto k \cdot \color{blue}{\left(\left(-y0\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.06 \cdot 10^{+58}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2.35 \cdot 10^{-153}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{-231}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{-197}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{+48}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+130}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+221}:\\ \;\;\;\;\left(y \cdot k\right) \cdot \left(i \cdot y5 - b \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{if}\;k \leq -1.7 \cdot 10^{+58}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2.3 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{-230}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+131}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{+211}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (- (* y a) (* j y0))))))
   (if (<= k -1.7e+58)
     (* k (* y2 (- (* y1 y4) (* y0 y5))))
     (if (<= k -2.3e-147)
       t_1
       (if (<= k 1.9e-230)
         (* j (* y3 (- (* y0 y5) (* y1 y4))))
         (if (<= k 2e-194)
           t_1
           (if (<= k 6.2e-29)
             (* x (* y (- (* a b) (* c i))))
             (if (<= k 2.7e+48)
               (* b (* j (- (* t y4) (* x y0))))
               (if (<= k 7.5e+131)
                 (* y0 (* y5 (- (* j y3) (* k y2))))
                 (if (<= k 1.55e+211)
                   (* k (* y (- (* i y5) (* b y4))))
                   (* k (* z (- (* b y0) (* i y1))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (k <= -1.7e+58) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -2.3e-147) {
		tmp = t_1;
	} else if (k <= 1.9e-230) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 2e-194) {
		tmp = t_1;
	} else if (k <= 6.2e-29) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (k <= 2.7e+48) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (k <= 7.5e+131) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (k <= 1.55e+211) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else {
		tmp = k * (z * ((b * y0) - (i * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (x * ((y * a) - (j * y0)))
    if (k <= (-1.7d+58)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (k <= (-2.3d-147)) then
        tmp = t_1
    else if (k <= 1.9d-230) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (k <= 2d-194) then
        tmp = t_1
    else if (k <= 6.2d-29) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (k <= 2.7d+48) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (k <= 7.5d+131) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (k <= 1.55d+211) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else
        tmp = k * (z * ((b * y0) - (i * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (k <= -1.7e+58) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -2.3e-147) {
		tmp = t_1;
	} else if (k <= 1.9e-230) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 2e-194) {
		tmp = t_1;
	} else if (k <= 6.2e-29) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (k <= 2.7e+48) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (k <= 7.5e+131) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (k <= 1.55e+211) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else {
		tmp = k * (z * ((b * y0) - (i * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (x * ((y * a) - (j * y0)))
	tmp = 0
	if k <= -1.7e+58:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif k <= -2.3e-147:
		tmp = t_1
	elif k <= 1.9e-230:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif k <= 2e-194:
		tmp = t_1
	elif k <= 6.2e-29:
		tmp = x * (y * ((a * b) - (c * i)))
	elif k <= 2.7e+48:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif k <= 7.5e+131:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif k <= 1.55e+211:
		tmp = k * (y * ((i * y5) - (b * y4)))
	else:
		tmp = k * (z * ((b * y0) - (i * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))))
	tmp = 0.0
	if (k <= -1.7e+58)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (k <= -2.3e-147)
		tmp = t_1;
	elseif (k <= 1.9e-230)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (k <= 2e-194)
		tmp = t_1;
	elseif (k <= 6.2e-29)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (k <= 2.7e+48)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (k <= 7.5e+131)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (k <= 1.55e+211)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	else
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (x * ((y * a) - (j * y0)));
	tmp = 0.0;
	if (k <= -1.7e+58)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (k <= -2.3e-147)
		tmp = t_1;
	elseif (k <= 1.9e-230)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (k <= 2e-194)
		tmp = t_1;
	elseif (k <= 6.2e-29)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (k <= 2.7e+48)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (k <= 7.5e+131)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (k <= 1.55e+211)
		tmp = k * (y * ((i * y5) - (b * y4)));
	else
		tmp = k * (z * ((b * y0) - (i * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.7e+58], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.3e-147], t$95$1, If[LessEqual[k, 1.9e-230], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2e-194], t$95$1, If[LessEqual[k, 6.2e-29], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.7e+48], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.5e+131], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.55e+211], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -1.7e58

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto k \cdot \left(y2 \cdot \left(\color{blue}{y4 \cdot y1} - y0 \cdot y5\right)\right) \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]

   if -1.7e58 < k < -2.2999999999999999e-147 or 1.8999999999999999e-230 < k < 2.00000000000000004e-194

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 63.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 63.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 54.0%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -2.2999999999999999e-147 < k < 1.8999999999999999e-230

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 37.5%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if 2.00000000000000004e-194 < k < 6.20000000000000052e-29

   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 x around inf 46.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 47.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if 6.20000000000000052e-29 < k < 2.70000000000000004e48

   1. Initial program 38.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 43.1%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 43.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 43.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 43.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 2.70000000000000004e48 < k < 7.4999999999999995e131

   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 y0 around inf 33.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 33.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 33.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 33.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y5 around inf 67.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)} \]

   if 7.4999999999999995e131 < k < 1.5500000000000001e211

   1. Initial program 10.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 20.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 20.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 20.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 20.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 20.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 20.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 20.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 20.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 50.4%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]

   if 1.5500000000000001e211 < k

   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 k around inf 75.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 75.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 75.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 75.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 75.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 75.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 75.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 56.6%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 56.6%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 56.6%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.7 \cdot 10^{+58}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2.3 \cdot 10^{-147}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{-230}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+131}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{+211}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+94}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \left(t \cdot c - k \cdot y1\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+30}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-94}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -2.4e+94)
   (* (* z i) (- (* t c) (* k y1)))
   (if (<= z -1.2e+30)
     (* y3 (* y (- (* c y4) (* a y5))))
     (if (<= z -1.55e+17)
       (* (* z k) (- (* b y0) (* i y1)))
       (if (<= z -3.9e-94)
         (* b (* j (- (* t y4) (* x y0))))
         (if (<= z -5.5e-132)
           (* x (* y (- (* a b) (* c i))))
           (if (<= z 4e+59)
             (* x (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0)))))
             (if (<= z 2.8e+161)
               (* b (* x (- (* y a) (* j y0))))
               (* y1 (* z (- (* a y3) (* i 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 tmp;
	if (z <= -2.4e+94) {
		tmp = (z * i) * ((t * c) - (k * y1));
	} else if (z <= -1.2e+30) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (z <= -1.55e+17) {
		tmp = (z * k) * ((b * y0) - (i * y1));
	} else if (z <= -3.9e-94) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (z <= -5.5e-132) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (z <= 4e+59) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (z <= 2.8e+161) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = y1 * (z * ((a * y3) - (i * 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) :: tmp
    if (z <= (-2.4d+94)) then
        tmp = (z * i) * ((t * c) - (k * y1))
    else if (z <= (-1.2d+30)) then
        tmp = y3 * (y * ((c * y4) - (a * y5)))
    else if (z <= (-1.55d+17)) then
        tmp = (z * k) * ((b * y0) - (i * y1))
    else if (z <= (-3.9d-94)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (z <= (-5.5d-132)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (z <= 4d+59) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
    else if (z <= 2.8d+161) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else
        tmp = y1 * (z * ((a * y3) - (i * 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 tmp;
	if (z <= -2.4e+94) {
		tmp = (z * i) * ((t * c) - (k * y1));
	} else if (z <= -1.2e+30) {
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	} else if (z <= -1.55e+17) {
		tmp = (z * k) * ((b * y0) - (i * y1));
	} else if (z <= -3.9e-94) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (z <= -5.5e-132) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (z <= 4e+59) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (z <= 2.8e+161) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	}
	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 <= -2.4e+94:
		tmp = (z * i) * ((t * c) - (k * y1))
	elif z <= -1.2e+30:
		tmp = y3 * (y * ((c * y4) - (a * y5)))
	elif z <= -1.55e+17:
		tmp = (z * k) * ((b * y0) - (i * y1))
	elif z <= -3.9e-94:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif z <= -5.5e-132:
		tmp = x * (y * ((a * b) - (c * i)))
	elif z <= 4e+59:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
	elif z <= 2.8e+161:
		tmp = b * (x * ((y * a) - (j * y0)))
	else:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	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 <= -2.4e+94)
		tmp = Float64(Float64(z * i) * Float64(Float64(t * c) - Float64(k * y1)));
	elseif (z <= -1.2e+30)
		tmp = Float64(y3 * Float64(y * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (z <= -1.55e+17)
		tmp = Float64(Float64(z * k) * Float64(Float64(b * y0) - Float64(i * y1)));
	elseif (z <= -3.9e-94)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (z <= -5.5e-132)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (z <= 4e+59)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (z <= 2.8e+161)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	else
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * 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)
	tmp = 0.0;
	if (z <= -2.4e+94)
		tmp = (z * i) * ((t * c) - (k * y1));
	elseif (z <= -1.2e+30)
		tmp = y3 * (y * ((c * y4) - (a * y5)));
	elseif (z <= -1.55e+17)
		tmp = (z * k) * ((b * y0) - (i * y1));
	elseif (z <= -3.9e-94)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (z <= -5.5e-132)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (z <= 4e+59)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	elseif (z <= 2.8e+161)
		tmp = b * (x * ((y * a) - (j * y0)));
	else
		tmp = y1 * (z * ((a * y3) - (i * k)));
	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, -2.4e+94], N[(N[(z * i), $MachinePrecision] * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e+30], N[(y3 * N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e+17], N[(N[(z * k), $MachinePrecision] * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-94], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-132], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+59], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+161], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if z < -2.39999999999999983e94

   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 z around -inf 59.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in i around -inf 48.3%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.3%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)\right)} \]

      2. associate-*r* 55.5%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(i \cdot z\right) \cdot \left(c \cdot t - k \cdot y1\right)}\right) \]

      3. *-commutative 55.5%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(z \cdot i\right)} \cdot \left(c \cdot t - k \cdot y1\right)\right) \]

      4. *-commutative 55.5%

         \[\leadsto -1 \cdot \left(-\left(z \cdot i\right) \cdot \left(\color{blue}{t \cdot c} - k \cdot y1\right)\right) \]

   6. Simplified 55.5%

      \[\leadsto -1 \cdot \color{blue}{\left(-\left(z \cdot i\right) \cdot \left(t \cdot c - k \cdot y1\right)\right)} \]

   if -2.39999999999999983e94 < z < -1.2e30

   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 y3 around -inf 43.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y around inf 65.0%

      \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(y \cdot \left(a \cdot y5 - c \cdot y4\right)\right)}\right) \]

   if -1.2e30 < z < -1.55e17

   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 k around inf 57.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 57.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 57.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 57.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 57.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 57.1%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 57.2%

         \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

      2. *-commutative 57.2%

         \[\leadsto \color{blue}{\left(z \cdot k\right)} \cdot \left(b \cdot y0 - i \cdot y1\right) \]

      3. *-commutative 57.2%

         \[\leadsto \left(z \cdot k\right) \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right) \]

   8. Simplified 57.2%

      \[\leadsto \color{blue}{\left(z \cdot k\right) \cdot \left(b \cdot y0 - y1 \cdot i\right)} \]

   if -1.55e17 < z < -3.9000000000000002e-94

   1. Initial program 44.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 64.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 68.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 68.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 68.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 68.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 68.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 57.4%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -3.9000000000000002e-94 < z < -5.4999999999999999e-132

   1. Initial program 34.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 77.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if -5.4999999999999999e-132 < z < 3.99999999999999989e59

   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 x around inf 42.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 45.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 45.5%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 45.5%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   6. Simplified 45.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if 3.99999999999999989e59 < z < 2.80000000000000021e161

   1. Initial program 17.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. Step-by-step derivation

      1. fma-define 43.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 2.80000000000000021e161 < z

   1. Initial program 14.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y1 around -inf 56.2%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+94}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \left(t \cdot c - k \cdot y1\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+30}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-94}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{if}\;k \leq -9 \cdot 10^{+57}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-235}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{-194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.08 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (- (* y a) (* j y0))))))
   (if (<= k -9e+57)
     (* k (* y2 (- (* y1 y4) (* y0 y5))))
     (if (<= k -2e-154)
       t_1
       (if (<= k 2.9e-235)
         (* j (* y3 (- (* y0 y5) (* y1 y4))))
         (if (<= k 1.4e-194)
           t_1
           (if (<= k 1.08e-31)
             (* x (* y (- (* a b) (* c i))))
             (if (<= k 8.5e+27)
               (* (* x y2) (- (* c y0) (* a y1)))
               (* b (* (- (* t j) (* y k)) 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 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (k <= -9e+57) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -2e-154) {
		tmp = t_1;
	} else if (k <= 2.9e-235) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 1.4e-194) {
		tmp = t_1;
	} else if (k <= 1.08e-31) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (k <= 8.5e+27) {
		tmp = (x * y2) * ((c * y0) - (a * y1));
	} else {
		tmp = b * (((t * j) - (y * k)) * 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 = b * (x * ((y * a) - (j * y0)))
    if (k <= (-9d+57)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (k <= (-2d-154)) then
        tmp = t_1
    else if (k <= 2.9d-235) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (k <= 1.4d-194) then
        tmp = t_1
    else if (k <= 1.08d-31) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (k <= 8.5d+27) then
        tmp = (x * y2) * ((c * y0) - (a * y1))
    else
        tmp = b * (((t * j) - (y * k)) * 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 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (k <= -9e+57) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -2e-154) {
		tmp = t_1;
	} else if (k <= 2.9e-235) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 1.4e-194) {
		tmp = t_1;
	} else if (k <= 1.08e-31) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (k <= 8.5e+27) {
		tmp = (x * y2) * ((c * y0) - (a * y1));
	} else {
		tmp = b * (((t * j) - (y * k)) * y4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (x * ((y * a) - (j * y0)))
	tmp = 0
	if k <= -9e+57:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif k <= -2e-154:
		tmp = t_1
	elif k <= 2.9e-235:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif k <= 1.4e-194:
		tmp = t_1
	elif k <= 1.08e-31:
		tmp = x * (y * ((a * b) - (c * i)))
	elif k <= 8.5e+27:
		tmp = (x * y2) * ((c * y0) - (a * y1))
	else:
		tmp = b * (((t * j) - (y * k)) * 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(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))))
	tmp = 0.0
	if (k <= -9e+57)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (k <= -2e-154)
		tmp = t_1;
	elseif (k <= 2.9e-235)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (k <= 1.4e-194)
		tmp = t_1;
	elseif (k <= 1.08e-31)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (k <= 8.5e+27)
		tmp = Float64(Float64(x * y2) * Float64(Float64(c * y0) - Float64(a * y1)));
	else
		tmp = Float64(b * Float64(Float64(Float64(t * j) - Float64(y * k)) * 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 = b * (x * ((y * a) - (j * y0)));
	tmp = 0.0;
	if (k <= -9e+57)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (k <= -2e-154)
		tmp = t_1;
	elseif (k <= 2.9e-235)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (k <= 1.4e-194)
		tmp = t_1;
	elseif (k <= 1.08e-31)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (k <= 8.5e+27)
		tmp = (x * y2) * ((c * y0) - (a * y1));
	else
		tmp = b * (((t * j) - (y * k)) * 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[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -9e+57], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2e-154], t$95$1, If[LessEqual[k, 2.9e-235], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.4e-194], t$95$1, If[LessEqual[k, 1.08e-31], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.5e+27], N[(N[(x * y2), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -8.99999999999999991e57

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto k \cdot \left(y2 \cdot \left(\color{blue}{y4 \cdot y1} - y0 \cdot y5\right)\right) \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]

   if -8.99999999999999991e57 < k < -1.9999999999999999e-154 or 2.90000000000000009e-235 < k < 1.40000000000000006e-194

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 63.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 63.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 54.0%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -1.9999999999999999e-154 < k < 2.90000000000000009e-235

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 37.5%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if 1.40000000000000006e-194 < k < 1.07999999999999992e-31

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 44.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 48.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if 1.07999999999999992e-31 < k < 8.5e27

   1. Initial program 37.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 32.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 44.6%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 44.5%

         \[\leadsto \color{blue}{\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)} \]

   6. Simplified 44.5%

      \[\leadsto \color{blue}{\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)} \]

   if 8.5e27 < k

   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 b around inf 34.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 38.9%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 38.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 38.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 38.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 38.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf 43.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.9%

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) \]

      2. *-commutative 43.9%

         \[\leadsto b \cdot \left(y4 \cdot \left(t \cdot j - \color{blue}{y \cdot k}\right)\right) \]

   8. Simplified 43.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9 \cdot 10^{+57}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-235}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.08 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{if}\;k \leq -9.5 \cdot 10^{+57}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -4.2 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-233}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2.05 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{+28}:\\ \;\;\;\;\left(-a\right) \cdot \left(z \cdot \left(t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (- (* y a) (* j y0))))))
   (if (<= k -9.5e+57)
     (* k (* y2 (- (* y1 y4) (* y0 y5))))
     (if (<= k -4.2e-147)
       t_1
       (if (<= k 2.7e-233)
         (* j (* y3 (- (* y0 y5) (* y1 y4))))
         (if (<= k 2.05e-193)
           t_1
           (if (<= k 2.2e-29)
             (* x (* y (- (* a b) (* c i))))
             (if (<= k 1.2e+28)
               (* (- a) (* z (* t b)))
               (* b (* (- (* t j) (* y k)) 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 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (k <= -9.5e+57) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -4.2e-147) {
		tmp = t_1;
	} else if (k <= 2.7e-233) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 2.05e-193) {
		tmp = t_1;
	} else if (k <= 2.2e-29) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (k <= 1.2e+28) {
		tmp = -a * (z * (t * b));
	} else {
		tmp = b * (((t * j) - (y * k)) * 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 = b * (x * ((y * a) - (j * y0)))
    if (k <= (-9.5d+57)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (k <= (-4.2d-147)) then
        tmp = t_1
    else if (k <= 2.7d-233) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (k <= 2.05d-193) then
        tmp = t_1
    else if (k <= 2.2d-29) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (k <= 1.2d+28) then
        tmp = -a * (z * (t * b))
    else
        tmp = b * (((t * j) - (y * k)) * 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 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (k <= -9.5e+57) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -4.2e-147) {
		tmp = t_1;
	} else if (k <= 2.7e-233) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 2.05e-193) {
		tmp = t_1;
	} else if (k <= 2.2e-29) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (k <= 1.2e+28) {
		tmp = -a * (z * (t * b));
	} else {
		tmp = b * (((t * j) - (y * k)) * y4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (x * ((y * a) - (j * y0)))
	tmp = 0
	if k <= -9.5e+57:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif k <= -4.2e-147:
		tmp = t_1
	elif k <= 2.7e-233:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif k <= 2.05e-193:
		tmp = t_1
	elif k <= 2.2e-29:
		tmp = x * (y * ((a * b) - (c * i)))
	elif k <= 1.2e+28:
		tmp = -a * (z * (t * b))
	else:
		tmp = b * (((t * j) - (y * k)) * 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(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))))
	tmp = 0.0
	if (k <= -9.5e+57)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (k <= -4.2e-147)
		tmp = t_1;
	elseif (k <= 2.7e-233)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (k <= 2.05e-193)
		tmp = t_1;
	elseif (k <= 2.2e-29)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (k <= 1.2e+28)
		tmp = Float64(Float64(-a) * Float64(z * Float64(t * b)));
	else
		tmp = Float64(b * Float64(Float64(Float64(t * j) - Float64(y * k)) * 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 = b * (x * ((y * a) - (j * y0)));
	tmp = 0.0;
	if (k <= -9.5e+57)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (k <= -4.2e-147)
		tmp = t_1;
	elseif (k <= 2.7e-233)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (k <= 2.05e-193)
		tmp = t_1;
	elseif (k <= 2.2e-29)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (k <= 1.2e+28)
		tmp = -a * (z * (t * b));
	else
		tmp = b * (((t * j) - (y * k)) * 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[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -9.5e+57], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.2e-147], t$95$1, If[LessEqual[k, 2.7e-233], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.05e-193], t$95$1, If[LessEqual[k, 2.2e-29], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.2e+28], N[((-a) * N[(z * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -9.4999999999999997e57

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto k \cdot \left(y2 \cdot \left(\color{blue}{y4 \cdot y1} - y0 \cdot y5\right)\right) \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]

   if -9.4999999999999997e57 < k < -4.2e-147 or 2.6999999999999999e-233 < k < 2.05000000000000001e-193

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 63.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 63.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 63.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 54.0%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -4.2e-147 < k < 2.6999999999999999e-233

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 37.5%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if 2.05000000000000001e-193 < k < 2.1999999999999999e-29

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 44.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 48.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if 2.1999999999999999e-29 < k < 1.19999999999999991e28

   1. Initial program 37.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 37.8%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 37.8%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 37.8%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 37.8%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 37.8%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 31.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   7. Taylor expanded in x around 0 32.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 32.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. neg-mul-1 32.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

      3. associate-*r* 38.0%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(b \cdot t\right) \cdot z\right)} \]

   9. Simplified 38.0%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(\left(b \cdot t\right) \cdot z\right)} \]

   if 1.19999999999999991e28 < k

   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 b around inf 34.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 38.9%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 38.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 38.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 38.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 38.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf 43.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.9%

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) \]

      2. *-commutative 43.9%

         \[\leadsto b \cdot \left(y4 \cdot \left(t \cdot j - \color{blue}{y \cdot k}\right)\right) \]

   8. Simplified 43.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9.5 \cdot 10^{+57}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -4.2 \cdot 10^{-147}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-233}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2.05 \cdot 10^{-193}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{+28}:\\ \;\;\;\;\left(-a\right) \cdot \left(z \cdot \left(t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{if}\;k \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2.6 \cdot 10^{-148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.46 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{-42}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (- (* y a) (* j y0))))))
   (if (<= k -1.4e+58)
     (* k (* y2 (- (* y1 y4) (* y0 y5))))
     (if (<= k -2.6e-148)
       t_1
       (if (<= k 2.8e-234)
         (* j (* y3 (- (* y0 y5) (* y1 y4))))
         (if (<= k 1.46e-186)
           t_1
           (if (<= k 1.25e-42)
             (* k (* z (- (* b y0) (* i y1))))
             (if (<= k 1.35e+48)
               (* b (* j (- (* t y4) (* x y0))))
               (* b (* (- (* t j) (* y k)) 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 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (k <= -1.4e+58) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -2.6e-148) {
		tmp = t_1;
	} else if (k <= 2.8e-234) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 1.46e-186) {
		tmp = t_1;
	} else if (k <= 1.25e-42) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (k <= 1.35e+48) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = b * (((t * j) - (y * k)) * 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 = b * (x * ((y * a) - (j * y0)))
    if (k <= (-1.4d+58)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (k <= (-2.6d-148)) then
        tmp = t_1
    else if (k <= 2.8d-234) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (k <= 1.46d-186) then
        tmp = t_1
    else if (k <= 1.25d-42) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (k <= 1.35d+48) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = b * (((t * j) - (y * k)) * 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 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (k <= -1.4e+58) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -2.6e-148) {
		tmp = t_1;
	} else if (k <= 2.8e-234) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 1.46e-186) {
		tmp = t_1;
	} else if (k <= 1.25e-42) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (k <= 1.35e+48) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = b * (((t * j) - (y * k)) * y4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (x * ((y * a) - (j * y0)))
	tmp = 0
	if k <= -1.4e+58:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif k <= -2.6e-148:
		tmp = t_1
	elif k <= 2.8e-234:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif k <= 1.46e-186:
		tmp = t_1
	elif k <= 1.25e-42:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif k <= 1.35e+48:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = b * (((t * j) - (y * k)) * 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(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))))
	tmp = 0.0
	if (k <= -1.4e+58)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (k <= -2.6e-148)
		tmp = t_1;
	elseif (k <= 2.8e-234)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (k <= 1.46e-186)
		tmp = t_1;
	elseif (k <= 1.25e-42)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (k <= 1.35e+48)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(b * Float64(Float64(Float64(t * j) - Float64(y * k)) * 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 = b * (x * ((y * a) - (j * y0)));
	tmp = 0.0;
	if (k <= -1.4e+58)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (k <= -2.6e-148)
		tmp = t_1;
	elseif (k <= 2.8e-234)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (k <= 1.46e-186)
		tmp = t_1;
	elseif (k <= 1.25e-42)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (k <= 1.35e+48)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = b * (((t * j) - (y * k)) * 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[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.4e+58], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.6e-148], t$95$1, If[LessEqual[k, 2.8e-234], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.46e-186], t$95$1, If[LessEqual[k, 1.25e-42], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.35e+48], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -1.3999999999999999e58

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto k \cdot \left(y2 \cdot \left(\color{blue}{y4 \cdot y1} - y0 \cdot y5\right)\right) \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]

   if -1.3999999999999999e58 < k < -2.60000000000000008e-148 or 2.7999999999999999e-234 < k < 1.46e-186

   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 b around inf 61.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 65.1%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 65.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 65.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 65.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 65.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 53.9%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -2.60000000000000008e-148 < k < 2.7999999999999999e-234

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 37.5%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if 1.46e-186 < k < 1.25000000000000001e-42

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 22.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 22.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 22.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 22.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 22.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 22.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 22.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 22.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 47.6%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.6%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 47.6%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   if 1.25000000000000001e-42 < k < 1.35000000000000002e48

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 43.0%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 43.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 43.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 43.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 44.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 1.35000000000000002e48 < k

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 29.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 34.5%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 34.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf 40.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) \]

      2. *-commutative 40.3%

         \[\leadsto b \cdot \left(y4 \cdot \left(t \cdot j - \color{blue}{y \cdot k}\right)\right) \]

   8. Simplified 40.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2.6 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.46 \cdot 10^{-186}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{-42}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ t_2 := b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \mathbf{if}\;y3 \leq -9 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -6.5 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -3.9 \cdot 10^{-168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y3 \leq -1.6 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 9 \cdot 10^{-131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3)))))
        (t_2 (* b (* (- (* t j) (* y k)) y4))))
   (if (<= y3 -9e+198)
     t_1
     (if (<= y3 -6.5e+107)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= y3 -3.9e-168)
         t_2
         (if (<= y3 -1.6e-305)
           (* b (* x (- (* y a) (* j y0))))
           (if (<= y3 9e-131)
             t_2
             (if (<= y3 1.1e+50) (* b (* y0 (- (* z k) (* x 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 = c * (y0 * ((x * y2) - (z * y3)));
	double t_2 = b * (((t * j) - (y * k)) * y4);
	double tmp;
	if (y3 <= -9e+198) {
		tmp = t_1;
	} else if (y3 <= -6.5e+107) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y3 <= -3.9e-168) {
		tmp = t_2;
	} else if (y3 <= -1.6e-305) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y3 <= 9e-131) {
		tmp = t_2;
	} else if (y3 <= 1.1e+50) {
		tmp = b * (y0 * ((z * k) - (x * 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) :: t_2
    real(8) :: tmp
    t_1 = c * (y0 * ((x * y2) - (z * y3)))
    t_2 = b * (((t * j) - (y * k)) * y4)
    if (y3 <= (-9d+198)) then
        tmp = t_1
    else if (y3 <= (-6.5d+107)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y3 <= (-3.9d-168)) then
        tmp = t_2
    else if (y3 <= (-1.6d-305)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y3 <= 9d-131) then
        tmp = t_2
    else if (y3 <= 1.1d+50) then
        tmp = b * (y0 * ((z * k) - (x * 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 = c * (y0 * ((x * y2) - (z * y3)));
	double t_2 = b * (((t * j) - (y * k)) * y4);
	double tmp;
	if (y3 <= -9e+198) {
		tmp = t_1;
	} else if (y3 <= -6.5e+107) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y3 <= -3.9e-168) {
		tmp = t_2;
	} else if (y3 <= -1.6e-305) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y3 <= 9e-131) {
		tmp = t_2;
	} else if (y3 <= 1.1e+50) {
		tmp = b * (y0 * ((z * k) - (x * 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 = c * (y0 * ((x * y2) - (z * y3)))
	t_2 = b * (((t * j) - (y * k)) * y4)
	tmp = 0
	if y3 <= -9e+198:
		tmp = t_1
	elif y3 <= -6.5e+107:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y3 <= -3.9e-168:
		tmp = t_2
	elif y3 <= -1.6e-305:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y3 <= 9e-131:
		tmp = t_2
	elif y3 <= 1.1e+50:
		tmp = b * (y0 * ((z * k) - (x * 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(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	t_2 = Float64(b * Float64(Float64(Float64(t * j) - Float64(y * k)) * y4))
	tmp = 0.0
	if (y3 <= -9e+198)
		tmp = t_1;
	elseif (y3 <= -6.5e+107)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y3 <= -3.9e-168)
		tmp = t_2;
	elseif (y3 <= -1.6e-305)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y3 <= 9e-131)
		tmp = t_2;
	elseif (y3 <= 1.1e+50)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * 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 = c * (y0 * ((x * y2) - (z * y3)));
	t_2 = b * (((t * j) - (y * k)) * y4);
	tmp = 0.0;
	if (y3 <= -9e+198)
		tmp = t_1;
	elseif (y3 <= -6.5e+107)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y3 <= -3.9e-168)
		tmp = t_2;
	elseif (y3 <= -1.6e-305)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y3 <= 9e-131)
		tmp = t_2;
	elseif (y3 <= 1.1e+50)
		tmp = b * (y0 * ((z * k) - (x * 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[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -9e+198], t$95$1, If[LessEqual[y3, -6.5e+107], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -3.9e-168], t$95$2, If[LessEqual[y3, -1.6e-305], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 9e-131], t$95$2, If[LessEqual[y3, 1.1e+50], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -9.00000000000000003e198 or 1.10000000000000008e50 < y3

   1. Initial program 18.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 42.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.6%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 42.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 42.6%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 42.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 42.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 42.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 42.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 45.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -9.00000000000000003e198 < y3 < -6.5000000000000006e107

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 47.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 53.6%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 53.6%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 53.6%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 53.6%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 48.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -6.5000000000000006e107 < y3 < -3.90000000000000012e-168 or -1.60000000000000004e-305 < y3 < 9.0000000000000004e-131

   1. Initial program 40.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 43.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf 39.7%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) \]

      2. *-commutative 39.7%

         \[\leadsto b \cdot \left(y4 \cdot \left(t \cdot j - \color{blue}{y \cdot k}\right)\right) \]

   8. Simplified 39.7%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)} \]

   if -3.90000000000000012e-168 < y3 < -1.60000000000000004e-305

   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 52.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 56.4%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 56.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 56.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 56.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 56.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 50.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 9.0000000000000004e-131 < y3 < 1.10000000000000008e50

   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 39.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 42.3%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 42.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 42.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 42.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.3%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf 40.2%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto b \cdot \left(y0 \cdot \left(\color{blue}{z \cdot k} - j \cdot x\right)\right) \]

      2. *-commutative 40.2%

         \[\leadsto b \cdot \left(y0 \cdot \left(z \cdot k - \color{blue}{x \cdot j}\right)\right) \]

   8. Simplified 40.2%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -9 \cdot 10^{+198}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -6.5 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -3.9 \cdot 10^{-168}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \mathbf{elif}\;y3 \leq -1.6 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 9 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \mathbf{elif}\;y3 \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{if}\;k \leq -1.9 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -6.2 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -6.2 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y3 (- (* y0 y5) (* y1 y4))))))
   (if (<= k -1.9e+147)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= k -6.2e+30)
       t_1
       (if (<= k -6.2e-155)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= k 5.6e-236)
           t_1
           (if (<= k 2.4e+48)
             (* b (* j (- (* t y4) (* x y0))))
             (* b (* (- (* t j) (* y k)) 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 * (y3 * ((y0 * y5) - (y1 * y4)));
	double tmp;
	if (k <= -1.9e+147) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (k <= -6.2e+30) {
		tmp = t_1;
	} else if (k <= -6.2e-155) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 5.6e-236) {
		tmp = t_1;
	} else if (k <= 2.4e+48) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = b * (((t * j) - (y * k)) * 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 * (y3 * ((y0 * y5) - (y1 * y4)))
    if (k <= (-1.9d+147)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (k <= (-6.2d+30)) then
        tmp = t_1
    else if (k <= (-6.2d-155)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (k <= 5.6d-236) then
        tmp = t_1
    else if (k <= 2.4d+48) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = b * (((t * j) - (y * k)) * 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 * (y3 * ((y0 * y5) - (y1 * y4)));
	double tmp;
	if (k <= -1.9e+147) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (k <= -6.2e+30) {
		tmp = t_1;
	} else if (k <= -6.2e-155) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 5.6e-236) {
		tmp = t_1;
	} else if (k <= 2.4e+48) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = b * (((t * j) - (y * k)) * 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 * (y3 * ((y0 * y5) - (y1 * y4)))
	tmp = 0
	if k <= -1.9e+147:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif k <= -6.2e+30:
		tmp = t_1
	elif k <= -6.2e-155:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif k <= 5.6e-236:
		tmp = t_1
	elif k <= 2.4e+48:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = b * (((t * j) - (y * k)) * 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(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))))
	tmp = 0.0
	if (k <= -1.9e+147)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (k <= -6.2e+30)
		tmp = t_1;
	elseif (k <= -6.2e-155)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (k <= 5.6e-236)
		tmp = t_1;
	elseif (k <= 2.4e+48)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(b * Float64(Float64(Float64(t * j) - Float64(y * k)) * 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 * (y3 * ((y0 * y5) - (y1 * y4)));
	tmp = 0.0;
	if (k <= -1.9e+147)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (k <= -6.2e+30)
		tmp = t_1;
	elseif (k <= -6.2e-155)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (k <= 5.6e-236)
		tmp = t_1;
	elseif (k <= 2.4e+48)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = b * (((t * j) - (y * k)) * 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[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.9e+147], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -6.2e+30], t$95$1, If[LessEqual[k, -6.2e-155], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.6e-236], t$95$1, If[LessEqual[k, 2.4e+48], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -1.89999999999999985e147

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 44.6%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 44.6%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 44.6%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 44.6%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 44.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf 45.3%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 45.3%

         \[\leadsto b \cdot \left(y0 \cdot \left(\color{blue}{z \cdot k} - j \cdot x\right)\right) \]

      2. *-commutative 45.3%

         \[\leadsto b \cdot \left(y0 \cdot \left(z \cdot k - \color{blue}{x \cdot j}\right)\right) \]

   8. Simplified 45.3%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)} \]

   if -1.89999999999999985e147 < k < -6.1999999999999995e30 or -6.2e-155 < k < 5.59999999999999973e-236

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 40.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 40.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 40.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 40.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 40.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 40.3%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -6.1999999999999995e30 < k < -6.2e-155

   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 b around inf 56.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 59.5%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 59.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 59.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 59.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 59.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 45.7%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 5.59999999999999973e-236 < k < 2.4000000000000001e48

   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 b around inf 48.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 48.9%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 48.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 48.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 48.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 43.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 2.4000000000000001e48 < k

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 29.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 34.5%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 34.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf 40.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) \]

      2. *-commutative 40.3%

         \[\leadsto b \cdot \left(y4 \cdot \left(t \cdot j - \color{blue}{y \cdot k}\right)\right) \]

   8. Simplified 40.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.9 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -6.2 \cdot 10^{+30}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -6.2 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 21.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-105}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-58}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{+96}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(c \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{+204}:\\ \;\;\;\;\left(-a\right) \cdot \left(z \cdot \left(t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(b \cdot \left(-y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -4.5e+114)
   (* a (* b (* x y)))
   (if (<= b 1.3e-105)
     (* k (* (* i y1) (- z)))
     (if (<= b 1.55e-58)
       (* k (* y1 (* y2 y4)))
       (if (<= b 7.4e+96)
         (* y3 (* z (* c (- y0))))
         (if (<= b 9.4e+204)
           (* (- a) (* z (* t b)))
           (* k (* y4 (* b (- y))))))))))

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 (b <= -4.5e+114) {
		tmp = a * (b * (x * y));
	} else if (b <= 1.3e-105) {
		tmp = k * ((i * y1) * -z);
	} else if (b <= 1.55e-58) {
		tmp = k * (y1 * (y2 * y4));
	} else if (b <= 7.4e+96) {
		tmp = y3 * (z * (c * -y0));
	} else if (b <= 9.4e+204) {
		tmp = -a * (z * (t * b));
	} else {
		tmp = k * (y4 * (b * -y));
	}
	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 (b <= (-4.5d+114)) then
        tmp = a * (b * (x * y))
    else if (b <= 1.3d-105) then
        tmp = k * ((i * y1) * -z)
    else if (b <= 1.55d-58) then
        tmp = k * (y1 * (y2 * y4))
    else if (b <= 7.4d+96) then
        tmp = y3 * (z * (c * -y0))
    else if (b <= 9.4d+204) then
        tmp = -a * (z * (t * b))
    else
        tmp = k * (y4 * (b * -y))
    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 (b <= -4.5e+114) {
		tmp = a * (b * (x * y));
	} else if (b <= 1.3e-105) {
		tmp = k * ((i * y1) * -z);
	} else if (b <= 1.55e-58) {
		tmp = k * (y1 * (y2 * y4));
	} else if (b <= 7.4e+96) {
		tmp = y3 * (z * (c * -y0));
	} else if (b <= 9.4e+204) {
		tmp = -a * (z * (t * b));
	} else {
		tmp = k * (y4 * (b * -y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -4.5e+114:
		tmp = a * (b * (x * y))
	elif b <= 1.3e-105:
		tmp = k * ((i * y1) * -z)
	elif b <= 1.55e-58:
		tmp = k * (y1 * (y2 * y4))
	elif b <= 7.4e+96:
		tmp = y3 * (z * (c * -y0))
	elif b <= 9.4e+204:
		tmp = -a * (z * (t * b))
	else:
		tmp = k * (y4 * (b * -y))
	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 (b <= -4.5e+114)
		tmp = Float64(a * Float64(b * Float64(x * y)));
	elseif (b <= 1.3e-105)
		tmp = Float64(k * Float64(Float64(i * y1) * Float64(-z)));
	elseif (b <= 1.55e-58)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (b <= 7.4e+96)
		tmp = Float64(y3 * Float64(z * Float64(c * Float64(-y0))));
	elseif (b <= 9.4e+204)
		tmp = Float64(Float64(-a) * Float64(z * Float64(t * b)));
	else
		tmp = Float64(k * Float64(y4 * Float64(b * Float64(-y))));
	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 (b <= -4.5e+114)
		tmp = a * (b * (x * y));
	elseif (b <= 1.3e-105)
		tmp = k * ((i * y1) * -z);
	elseif (b <= 1.55e-58)
		tmp = k * (y1 * (y2 * y4));
	elseif (b <= 7.4e+96)
		tmp = y3 * (z * (c * -y0));
	elseif (b <= 9.4e+204)
		tmp = -a * (z * (t * b));
	else
		tmp = k * (y4 * (b * -y));
	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[b, -4.5e+114], N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3e-105], N[(k * N[(N[(i * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e-58], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.4e+96], N[(y3 * N[(z * N[(c * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.4e+204], N[((-a) * N[(z * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y4 * N[(b * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.5000000000000001e114

   1. Initial program 17.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 60.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 60.0%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 60.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 60.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 60.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 60.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 41.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 38.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 38.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x\right)\right)} \]

   if -4.5000000000000001e114 < b < 1.2999999999999999e-105

   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 k around inf 41.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 41.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 41.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 41.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 41.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 41.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 41.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 31.7%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 31.7%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 31.7%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 27.1%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 27.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-i \cdot y1\right)}\right) \]

       2. distribute-lft-neg-out 27.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(\left(-i\right) \cdot y1\right)}\right) \]

       3. *-commutative 27.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   11. Simplified 27.1%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   if 1.2999999999999999e-105 < b < 1.55e-58

   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 k around inf 73.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 73.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 73.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 73.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 73.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 73.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 73.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 73.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y4 around inf 47.6%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y1 \cdot y2 - b \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.6%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   8. Simplified 47.6%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   9. Taylor expanded in y2 around inf 47.8%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 1.55e-58 < b < 7.39999999999999982e96

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf 50.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y3 around inf 42.5%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in c around inf 38.1%

      \[\leadsto -1 \cdot \left(y3 \cdot \left(z \cdot \color{blue}{\left(c \cdot y0\right)}\right)\right) \]

   if 7.39999999999999982e96 < b < 9.4000000000000003e204

   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 63.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 63.8%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 63.8%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 63.8%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 63.8%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 63.8%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 34.2%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   7. Taylor expanded in x around 0 37.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 37.5%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. neg-mul-1 37.5%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

      3. associate-*r* 45.2%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(b \cdot t\right) \cdot z\right)} \]

   9. Simplified 45.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(\left(b \cdot t\right) \cdot z\right)} \]

   if 9.4000000000000003e204 < b

   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 k around inf 32.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 32.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 32.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 32.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 32.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 32.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 32.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 32.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y4 around inf 37.3%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y1 \cdot y2 - b \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   8. Simplified 37.3%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   9. Taylor expanded in y2 around 0 48.1%

      \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 48.1%

          \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(-b \cdot y\right)}\right) \]

       2. *-commutative 48.1%

          \[\leadsto k \cdot \left(y4 \cdot \left(-\color{blue}{y \cdot b}\right)\right) \]

       3. distribute-lft-neg-in 48.1%

          \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(\left(-y\right) \cdot b\right)}\right) \]

   11. Simplified 48.1%

       \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(\left(-y\right) \cdot b\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-105}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-58}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{+96}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(c \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{+204}:\\ \;\;\;\;\left(-a\right) \cdot \left(z \cdot \left(t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(b \cdot \left(-y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 31.1% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -2 \cdot 10^{+58}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -1.5 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -2e+58)
   (* k (* y2 (- (* y1 y4) (* y0 y5))))
   (if (<= k -1.5e-155)
     (* b (* x (- (* y a) (* j y0))))
     (if (<= k 3.1e-236)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= k 4.1e+48)
         (* b (* j (- (* t y4) (* x y0))))
         (* b (* (- (* t j) (* y k)) 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 (k <= -2e+58) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -1.5e-155) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 3.1e-236) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 4.1e+48) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = b * (((t * j) - (y * k)) * 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 (k <= (-2d+58)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (k <= (-1.5d-155)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (k <= 3.1d-236) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (k <= 4.1d+48) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = b * (((t * j) - (y * k)) * 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 (k <= -2e+58) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (k <= -1.5e-155) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 3.1e-236) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 4.1e+48) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = b * (((t * j) - (y * k)) * 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 k <= -2e+58:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif k <= -1.5e-155:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif k <= 3.1e-236:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif k <= 4.1e+48:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = b * (((t * j) - (y * k)) * 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 (k <= -2e+58)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (k <= -1.5e-155)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (k <= 3.1e-236)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (k <= 4.1e+48)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(b * Float64(Float64(Float64(t * j) - Float64(y * k)) * 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 (k <= -2e+58)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (k <= -1.5e-155)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (k <= 3.1e-236)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (k <= 4.1e+48)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = b * (((t * j) - (y * k)) * 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[k, -2e+58], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.5e-155], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.1e-236], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.1e+48], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -1.99999999999999989e58

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 67.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 67.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 67.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto k \cdot \left(y2 \cdot \left(\color{blue}{y4 \cdot y1} - y0 \cdot y5\right)\right) \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]

   if -1.99999999999999989e58 < k < -1.49999999999999992e-155

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 52.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 57.2%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 57.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 57.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 57.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 45.1%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -1.49999999999999992e-155 < k < 3.0999999999999998e-236

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 37.5%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if 3.0999999999999998e-236 < k < 4.1000000000000003e48

   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 b around inf 48.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 48.9%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 48.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 48.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 48.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 43.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 4.1000000000000003e48 < k

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 29.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 34.5%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 34.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf 40.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) \]

      2. *-commutative 40.3%

         \[\leadsto b \cdot \left(y4 \cdot \left(t \cdot j - \color{blue}{y \cdot k}\right)\right) \]

   8. Simplified 40.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2 \cdot 10^{+58}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -1.5 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 31.2% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -6.6 \cdot 10^{+89}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -4.8 \cdot 10^{-150}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -6.6e+89)
   (* k (* y (- (* i y5) (* b y4))))
   (if (<= k -4.8e-150)
     (* b (* x (- (* y a) (* j y0))))
     (if (<= k 4e-232)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= k 8e+48)
         (* b (* j (- (* t y4) (* x y0))))
         (* b (* (- (* t j) (* y k)) 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 (k <= -6.6e+89) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (k <= -4.8e-150) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 4e-232) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 8e+48) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = b * (((t * j) - (y * k)) * 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 (k <= (-6.6d+89)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (k <= (-4.8d-150)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (k <= 4d-232) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (k <= 8d+48) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = b * (((t * j) - (y * k)) * 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 (k <= -6.6e+89) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (k <= -4.8e-150) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 4e-232) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= 8e+48) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = b * (((t * j) - (y * k)) * 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 k <= -6.6e+89:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif k <= -4.8e-150:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif k <= 4e-232:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif k <= 8e+48:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = b * (((t * j) - (y * k)) * 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 (k <= -6.6e+89)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (k <= -4.8e-150)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (k <= 4e-232)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (k <= 8e+48)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(b * Float64(Float64(Float64(t * j) - Float64(y * k)) * 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 (k <= -6.6e+89)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (k <= -4.8e-150)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (k <= 4e-232)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (k <= 8e+48)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = b * (((t * j) - (y * k)) * 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[k, -6.6e+89], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.8e-150], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4e-232], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8e+48], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -6.59999999999999948e89

   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 k around inf 69.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 69.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 69.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 69.5%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 69.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 69.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 69.5%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 69.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 43.7%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]

   if -6.59999999999999948e89 < k < -4.8e-150

   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 b around inf 45.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 52.2%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 52.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 52.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 52.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 52.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -4.8e-150 < k < 4.0000000000000001e-232

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 35.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 35.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 35.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 37.5%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if 4.0000000000000001e-232 < k < 8.00000000000000035e48

   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 b around inf 48.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 48.9%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 48.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 48.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 48.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 43.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 8.00000000000000035e48 < k

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 29.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 34.5%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 34.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 34.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf 40.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) \]

      2. *-commutative 40.3%

         \[\leadsto b \cdot \left(y4 \cdot \left(t \cdot j - \color{blue}{y \cdot k}\right)\right) \]

   8. Simplified 40.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6.6 \cdot 10^{+89}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -4.8 \cdot 10^{-150}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 28.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;j \leq -1.02 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-172}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{+244}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t))))))
   (if (<= j -1.02e+37)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= j -6.2e-284)
       t_1
       (if (<= j 1.55e-172)
         (* k (* (* i y1) (- z)))
         (if (<= j 4.7e+244) t_1 (* b (* t (* 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 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (j <= -1.02e+37) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (j <= -6.2e-284) {
		tmp = t_1;
	} else if (j <= 1.55e-172) {
		tmp = k * ((i * y1) * -z);
	} else if (j <= 4.7e+244) {
		tmp = t_1;
	} else {
		tmp = b * (t * (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) :: tmp
    t_1 = b * (a * ((x * y) - (z * t)))
    if (j <= (-1.02d+37)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (j <= (-6.2d-284)) then
        tmp = t_1
    else if (j <= 1.55d-172) then
        tmp = k * ((i * y1) * -z)
    else if (j <= 4.7d+244) then
        tmp = t_1
    else
        tmp = b * (t * (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 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (j <= -1.02e+37) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (j <= -6.2e-284) {
		tmp = t_1;
	} else if (j <= 1.55e-172) {
		tmp = k * ((i * y1) * -z);
	} else if (j <= 4.7e+244) {
		tmp = t_1;
	} else {
		tmp = b * (t * (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 = b * (a * ((x * y) - (z * t)))
	tmp = 0
	if j <= -1.02e+37:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif j <= -6.2e-284:
		tmp = t_1
	elif j <= 1.55e-172:
		tmp = k * ((i * y1) * -z)
	elif j <= 4.7e+244:
		tmp = t_1
	else:
		tmp = b * (t * (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(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (j <= -1.02e+37)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (j <= -6.2e-284)
		tmp = t_1;
	elseif (j <= 1.55e-172)
		tmp = Float64(k * Float64(Float64(i * y1) * Float64(-z)));
	elseif (j <= 4.7e+244)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * 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 = b * (a * ((x * y) - (z * t)));
	tmp = 0.0;
	if (j <= -1.02e+37)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (j <= -6.2e-284)
		tmp = t_1;
	elseif (j <= 1.55e-172)
		tmp = k * ((i * y1) * -z);
	elseif (j <= 4.7e+244)
		tmp = t_1;
	else
		tmp = b * (t * (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[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.02e+37], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.2e-284], t$95$1, If[LessEqual[j, 1.55e-172], N[(k * N[(N[(i * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.7e+244], t$95$1, N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.01999999999999995e37

   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 b around inf 40.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 44.3%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 44.3%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 46.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -1.01999999999999995e37 < j < -6.1999999999999996e-284 or 1.5500000000000001e-172 < j < 4.70000000000000012e244

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 42.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 43.4%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 43.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 43.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 43.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 31.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -6.1999999999999996e-284 < j < 1.5500000000000001e-172

   1. Initial program 38.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 51.7%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.7%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 51.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 51.7%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 51.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 51.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 51.7%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 51.7%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 44.6%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 44.6%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 44.6%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 39.1%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 39.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-i \cdot y1\right)}\right) \]

       2. distribute-lft-neg-out 39.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(\left(-i\right) \cdot y1\right)}\right) \]

       3. *-commutative 39.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   11. Simplified 39.1%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   if 4.70000000000000012e244 < j

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 36.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 43.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 43.7%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf 50.5%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 57.6%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.02 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-172}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{+244}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 26.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-180}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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))))))
   (if (<= a -1.05e-96)
     t_1
     (if (<= a -1.35e-180)
       (* b (* j (* t y4)))
       (if (<= a 1.9e-154)
         (* b (* k (* z y0)))
         (if (<= a 2.4e+98) (* b (* t (* j 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)));
	double tmp;
	if (a <= -1.05e-96) {
		tmp = t_1;
	} else if (a <= -1.35e-180) {
		tmp = b * (j * (t * y4));
	} else if (a <= 1.9e-154) {
		tmp = b * (k * (z * y0));
	} else if (a <= 2.4e+98) {
		tmp = b * (t * (j * 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)))
    if (a <= (-1.05d-96)) then
        tmp = t_1
    else if (a <= (-1.35d-180)) then
        tmp = b * (j * (t * y4))
    else if (a <= 1.9d-154) then
        tmp = b * (k * (z * y0))
    else if (a <= 2.4d+98) then
        tmp = b * (t * (j * 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)));
	double tmp;
	if (a <= -1.05e-96) {
		tmp = t_1;
	} else if (a <= -1.35e-180) {
		tmp = b * (j * (t * y4));
	} else if (a <= 1.9e-154) {
		tmp = b * (k * (z * y0));
	} else if (a <= 2.4e+98) {
		tmp = b * (t * (j * 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)))
	tmp = 0
	if a <= -1.05e-96:
		tmp = t_1
	elif a <= -1.35e-180:
		tmp = b * (j * (t * y4))
	elif a <= 1.9e-154:
		tmp = b * (k * (z * y0))
	elif a <= 2.4e+98:
		tmp = b * (t * (j * 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(a * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (a <= -1.05e-96)
		tmp = t_1;
	elseif (a <= -1.35e-180)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (a <= 1.9e-154)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (a <= 2.4e+98)
		tmp = Float64(b * Float64(t * Float64(j * 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)));
	tmp = 0.0;
	if (a <= -1.05e-96)
		tmp = t_1;
	elseif (a <= -1.35e-180)
		tmp = b * (j * (t * y4));
	elseif (a <= 1.9e-154)
		tmp = b * (k * (z * y0));
	elseif (a <= 2.4e+98)
		tmp = b * (t * (j * 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[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e-96], t$95$1, If[LessEqual[a, -1.35e-180], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-154], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+98], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.05000000000000001e-96 or 2.3999999999999999e98 < a

   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 b around inf 43.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 47.1%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 47.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 47.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 47.1%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 47.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 39.4%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.05000000000000001e-96 < a < -1.35000000000000007e-180

   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 47.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 47.5%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 47.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 47.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 47.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 47.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf 47.7%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 47.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 47.9%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 47.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -1.35000000000000007e-180 < a < 1.90000000000000005e-154

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 44.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 44.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 44.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 44.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 44.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 44.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 44.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 38.6%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.6%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 38.6%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around inf 27.8%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if 1.90000000000000005e-154 < a < 2.3999999999999999e98

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 35.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 38.2%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 38.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 38.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 38.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 38.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf 29.6%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 27.1%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-96}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-180}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 21.4% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{-105}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-58}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+97}:\\ \;\;\;\;-c \cdot \left(y0 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -1.75e+116)
   (* a (* b (* x y)))
   (if (<= b 2.45e-105)
     (* k (* (* i y1) (- z)))
     (if (<= b 2.05e-58)
       (* k (* y1 (* y2 y4)))
       (if (<= b 1.06e+97) (- (* c (* y0 (* z y3)))) (* k (* z (* b y0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.75e+116) {
		tmp = a * (b * (x * y));
	} else if (b <= 2.45e-105) {
		tmp = k * ((i * y1) * -z);
	} else if (b <= 2.05e-58) {
		tmp = k * (y1 * (y2 * y4));
	} else if (b <= 1.06e+97) {
		tmp = -(c * (y0 * (z * y3)));
	} else {
		tmp = k * (z * (b * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-1.75d+116)) then
        tmp = a * (b * (x * y))
    else if (b <= 2.45d-105) then
        tmp = k * ((i * y1) * -z)
    else if (b <= 2.05d-58) then
        tmp = k * (y1 * (y2 * y4))
    else if (b <= 1.06d+97) then
        tmp = -(c * (y0 * (z * y3)))
    else
        tmp = k * (z * (b * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.75e+116) {
		tmp = a * (b * (x * y));
	} else if (b <= 2.45e-105) {
		tmp = k * ((i * y1) * -z);
	} else if (b <= 2.05e-58) {
		tmp = k * (y1 * (y2 * y4));
	} else if (b <= 1.06e+97) {
		tmp = -(c * (y0 * (z * y3)));
	} else {
		tmp = k * (z * (b * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -1.75e+116:
		tmp = a * (b * (x * y))
	elif b <= 2.45e-105:
		tmp = k * ((i * y1) * -z)
	elif b <= 2.05e-58:
		tmp = k * (y1 * (y2 * y4))
	elif b <= 1.06e+97:
		tmp = -(c * (y0 * (z * y3)))
	else:
		tmp = k * (z * (b * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -1.75e+116)
		tmp = Float64(a * Float64(b * Float64(x * y)));
	elseif (b <= 2.45e-105)
		tmp = Float64(k * Float64(Float64(i * y1) * Float64(-z)));
	elseif (b <= 2.05e-58)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (b <= 1.06e+97)
		tmp = Float64(-Float64(c * Float64(y0 * Float64(z * y3))));
	else
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -1.75e+116)
		tmp = a * (b * (x * y));
	elseif (b <= 2.45e-105)
		tmp = k * ((i * y1) * -z);
	elseif (b <= 2.05e-58)
		tmp = k * (y1 * (y2 * y4));
	elseif (b <= 1.06e+97)
		tmp = -(c * (y0 * (z * y3)));
	else
		tmp = k * (z * (b * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -1.75e+116], N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.45e-105], N[(k * N[(N[(i * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e-58], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.06e+97], (-N[(c * N[(y0 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.74999999999999998e116

   1. Initial program 17.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 60.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 60.0%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 60.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 60.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 60.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 60.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 41.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 38.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 38.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x\right)\right)} \]

   if -1.74999999999999998e116 < b < 2.45e-105

   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 k around inf 41.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 41.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 41.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 41.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 41.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 41.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 41.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 31.7%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 31.7%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 31.7%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 27.1%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 27.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-i \cdot y1\right)}\right) \]

       2. distribute-lft-neg-out 27.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(\left(-i\right) \cdot y1\right)}\right) \]

       3. *-commutative 27.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   11. Simplified 27.1%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   if 2.45e-105 < b < 2.05000000000000014e-58

   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 k around inf 73.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 73.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 73.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 73.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 73.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 73.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 73.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 73.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y4 around inf 47.6%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y1 \cdot y2 - b \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.6%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   8. Simplified 47.6%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   9. Taylor expanded in y2 around inf 47.8%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 2.05000000000000014e-58 < b < 1.05999999999999994e97

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf 50.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in y3 around inf 42.5%

      \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in c around inf 34.4%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]

   if 1.05999999999999994e97 < b

   1. Initial program 16.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 30.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 30.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 30.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 30.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 30.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 30.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 30.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 30.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 42.5%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 42.5%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 42.5%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around inf 35.8%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(b \cdot y0\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 35.8%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y0 \cdot b\right)}\right) \]

   11. Simplified 35.8%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y0 \cdot b\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{-105}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-58}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+97}:\\ \;\;\;\;-c \cdot \left(y0 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 21.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -4 \cdot 10^{+209}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -6.5 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -1.05 \cdot 10^{-262}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 3.6 \cdot 10^{+124}:\\ \;\;\;\;k \cdot \left(\left(-i\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* t (* j y4)))))
   (if (<= y4 -4e+209)
     (* k (* y1 (* y2 y4)))
     (if (<= y4 -6.5e+112)
       t_1
       (if (<= y4 -1.05e-262)
         (* k (* z (* b y0)))
         (if (<= y4 3.6e+124) (* k (* (- i) (* z y1))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (t * (j * y4));
	double tmp;
	if (y4 <= -4e+209) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y4 <= -6.5e+112) {
		tmp = t_1;
	} else if (y4 <= -1.05e-262) {
		tmp = k * (z * (b * y0));
	} else if (y4 <= 3.6e+124) {
		tmp = k * (-i * (z * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * (j * y4))
    if (y4 <= (-4d+209)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y4 <= (-6.5d+112)) then
        tmp = t_1
    else if (y4 <= (-1.05d-262)) then
        tmp = k * (z * (b * y0))
    else if (y4 <= 3.6d+124) then
        tmp = k * (-i * (z * y1))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (t * (j * y4));
	double tmp;
	if (y4 <= -4e+209) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y4 <= -6.5e+112) {
		tmp = t_1;
	} else if (y4 <= -1.05e-262) {
		tmp = k * (z * (b * y0));
	} else if (y4 <= 3.6e+124) {
		tmp = k * (-i * (z * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (t * (j * y4))
	tmp = 0
	if y4 <= -4e+209:
		tmp = k * (y1 * (y2 * y4))
	elif y4 <= -6.5e+112:
		tmp = t_1
	elif y4 <= -1.05e-262:
		tmp = k * (z * (b * y0))
	elif y4 <= 3.6e+124:
		tmp = k * (-i * (z * y1))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(t * Float64(j * y4)))
	tmp = 0.0
	if (y4 <= -4e+209)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y4 <= -6.5e+112)
		tmp = t_1;
	elseif (y4 <= -1.05e-262)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (y4 <= 3.6e+124)
		tmp = Float64(k * Float64(Float64(-i) * Float64(z * y1)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (t * (j * y4));
	tmp = 0.0;
	if (y4 <= -4e+209)
		tmp = k * (y1 * (y2 * y4));
	elseif (y4 <= -6.5e+112)
		tmp = t_1;
	elseif (y4 <= -1.05e-262)
		tmp = k * (z * (b * y0));
	elseif (y4 <= 3.6e+124)
		tmp = k * (-i * (z * y1));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4e+209], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -6.5e+112], t$95$1, If[LessEqual[y4, -1.05e-262], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.6e+124], N[(k * N[((-i) * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -4.0000000000000003e209

   1. Initial program 13.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 50.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 50.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y4 around inf 46.8%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y1 \cdot y2 - b \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   8. Simplified 46.8%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   9. Taylor expanded in y2 around inf 47.0%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if -4.0000000000000003e209 < y4 < -6.4999999999999998e112 or 3.59999999999999986e124 < y4

   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 47.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 52.9%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 52.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 52.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 52.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 52.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf 40.8%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 41.0%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]

   if -6.4999999999999998e112 < y4 < -1.05e-262

   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 k around inf 40.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 40.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 40.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 40.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 40.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 40.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 40.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 30.5%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.5%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 30.5%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around inf 21.5%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(b \cdot y0\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 21.5%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y0 \cdot b\right)}\right) \]

   11. Simplified 21.5%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y0 \cdot b\right)}\right) \]

   if -1.05e-262 < y4 < 3.59999999999999986e124

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 34.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 34.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 34.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 34.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 34.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 34.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 34.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 34.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 32.8%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 32.8%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 28.4%

      \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 28.4%

          \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot i\right) \cdot \left(y1 \cdot z\right)\right)} \]

       2. neg-mul-1 28.4%

          \[\leadsto k \cdot \left(\color{blue}{\left(-i\right)} \cdot \left(y1 \cdot z\right)\right) \]

       3. *-commutative 28.4%

          \[\leadsto k \cdot \left(\left(-i\right) \cdot \color{blue}{\left(z \cdot y1\right)}\right) \]

   11. Simplified 28.4%

       \[\leadsto k \cdot \color{blue}{\left(\left(-i\right) \cdot \left(z \cdot y1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4 \cdot 10^{+209}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -6.5 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.05 \cdot 10^{-262}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 3.6 \cdot 10^{+124}:\\ \;\;\;\;k \cdot \left(\left(-i\right) \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 22.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -2.7 \cdot 10^{+209}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -5.6 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -2.05 \cdot 10^{-255}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.25 \cdot 10^{+67}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* t (* j y4)))))
   (if (<= y4 -2.7e+209)
     (* k (* y1 (* y2 y4)))
     (if (<= y4 -5.6e+112)
       t_1
       (if (<= y4 -2.05e-255)
         (* k (* z (* b y0)))
         (if (<= y4 1.25e+67) (* k (* (* i y1) (- z))) 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 * (t * (j * y4));
	double tmp;
	if (y4 <= -2.7e+209) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y4 <= -5.6e+112) {
		tmp = t_1;
	} else if (y4 <= -2.05e-255) {
		tmp = k * (z * (b * y0));
	} else if (y4 <= 1.25e+67) {
		tmp = k * ((i * y1) * -z);
	} 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 * (t * (j * y4))
    if (y4 <= (-2.7d+209)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y4 <= (-5.6d+112)) then
        tmp = t_1
    else if (y4 <= (-2.05d-255)) then
        tmp = k * (z * (b * y0))
    else if (y4 <= 1.25d+67) then
        tmp = k * ((i * y1) * -z)
    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 * (t * (j * y4));
	double tmp;
	if (y4 <= -2.7e+209) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y4 <= -5.6e+112) {
		tmp = t_1;
	} else if (y4 <= -2.05e-255) {
		tmp = k * (z * (b * y0));
	} else if (y4 <= 1.25e+67) {
		tmp = k * ((i * y1) * -z);
	} 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 * (t * (j * y4))
	tmp = 0
	if y4 <= -2.7e+209:
		tmp = k * (y1 * (y2 * y4))
	elif y4 <= -5.6e+112:
		tmp = t_1
	elif y4 <= -2.05e-255:
		tmp = k * (z * (b * y0))
	elif y4 <= 1.25e+67:
		tmp = k * ((i * y1) * -z)
	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(t * Float64(j * y4)))
	tmp = 0.0
	if (y4 <= -2.7e+209)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y4 <= -5.6e+112)
		tmp = t_1;
	elseif (y4 <= -2.05e-255)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (y4 <= 1.25e+67)
		tmp = Float64(k * Float64(Float64(i * y1) * Float64(-z)));
	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 * (t * (j * y4));
	tmp = 0.0;
	if (y4 <= -2.7e+209)
		tmp = k * (y1 * (y2 * y4));
	elseif (y4 <= -5.6e+112)
		tmp = t_1;
	elseif (y4 <= -2.05e-255)
		tmp = k * (z * (b * y0));
	elseif (y4 <= 1.25e+67)
		tmp = k * ((i * y1) * -z);
	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[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.7e+209], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -5.6e+112], t$95$1, If[LessEqual[y4, -2.05e-255], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.25e+67], N[(k * N[(N[(i * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -2.7e209

   1. Initial program 13.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 50.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 50.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y4 around inf 46.8%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y1 \cdot y2 - b \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   8. Simplified 46.8%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   9. Taylor expanded in y2 around inf 47.0%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if -2.7e209 < y4 < -5.6000000000000003e112 or 1.24999999999999994e67 < y4

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 48.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 56.0%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 56.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 56.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 56.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 56.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf 40.4%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 40.8%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]

   if -5.6000000000000003e112 < y4 < -2.05e-255

   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 k around inf 41.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 41.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 41.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 41.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 41.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 41.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 41.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 30.8%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.8%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 30.8%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around inf 21.7%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(b \cdot y0\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 21.7%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y0 \cdot b\right)}\right) \]

   11. Simplified 21.7%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y0 \cdot b\right)}\right) \]

   if -2.05e-255 < y4 < 1.24999999999999994e67

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 34.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 34.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 34.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 34.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 34.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 34.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 34.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 34.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 32.3%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 32.3%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 32.3%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 26.3%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 26.3%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-i \cdot y1\right)}\right) \]

       2. distribute-lft-neg-out 26.3%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(\left(-i\right) \cdot y1\right)}\right) \]

       3. *-commutative 26.3%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   11. Simplified 26.3%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.7 \cdot 10^{+209}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -5.6 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -2.05 \cdot 10^{-255}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.25 \cdot 10^{+67}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 21.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -4 \cdot 10^{+209}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.3 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -3.3 \cdot 10^{-274}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(t \cdot \left(z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* t (* j y4)))))
   (if (<= y4 -4e+209)
     (* k (* y1 (* y2 y4)))
     (if (<= y4 -1.3e+113)
       t_1
       (if (<= y4 -3.3e-274)
         (* k (* z (* b y0)))
         (if (<= y4 4e+67) (* b (* t (* z (- a)))) 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 * (t * (j * y4));
	double tmp;
	if (y4 <= -4e+209) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y4 <= -1.3e+113) {
		tmp = t_1;
	} else if (y4 <= -3.3e-274) {
		tmp = k * (z * (b * y0));
	} else if (y4 <= 4e+67) {
		tmp = b * (t * (z * -a));
	} 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 * (t * (j * y4))
    if (y4 <= (-4d+209)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y4 <= (-1.3d+113)) then
        tmp = t_1
    else if (y4 <= (-3.3d-274)) then
        tmp = k * (z * (b * y0))
    else if (y4 <= 4d+67) then
        tmp = b * (t * (z * -a))
    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 * (t * (j * y4));
	double tmp;
	if (y4 <= -4e+209) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y4 <= -1.3e+113) {
		tmp = t_1;
	} else if (y4 <= -3.3e-274) {
		tmp = k * (z * (b * y0));
	} else if (y4 <= 4e+67) {
		tmp = b * (t * (z * -a));
	} 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 * (t * (j * y4))
	tmp = 0
	if y4 <= -4e+209:
		tmp = k * (y1 * (y2 * y4))
	elif y4 <= -1.3e+113:
		tmp = t_1
	elif y4 <= -3.3e-274:
		tmp = k * (z * (b * y0))
	elif y4 <= 4e+67:
		tmp = b * (t * (z * -a))
	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(t * Float64(j * y4)))
	tmp = 0.0
	if (y4 <= -4e+209)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y4 <= -1.3e+113)
		tmp = t_1;
	elseif (y4 <= -3.3e-274)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (y4 <= 4e+67)
		tmp = Float64(b * Float64(t * Float64(z * Float64(-a))));
	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 * (t * (j * y4));
	tmp = 0.0;
	if (y4 <= -4e+209)
		tmp = k * (y1 * (y2 * y4));
	elseif (y4 <= -1.3e+113)
		tmp = t_1;
	elseif (y4 <= -3.3e-274)
		tmp = k * (z * (b * y0));
	elseif (y4 <= 4e+67)
		tmp = b * (t * (z * -a));
	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[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4e+209], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.3e+113], t$95$1, If[LessEqual[y4, -3.3e-274], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4e+67], N[(b * N[(t * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -4.0000000000000003e209

   1. Initial program 13.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 50.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 50.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y4 around inf 46.8%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y1 \cdot y2 - b \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   8. Simplified 46.8%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   9. Taylor expanded in y2 around inf 47.0%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if -4.0000000000000003e209 < y4 < -1.3e113 or 3.99999999999999993e67 < y4

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 48.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 56.0%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 56.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 56.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 56.0%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 56.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf 40.4%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 40.8%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]

   if -1.3e113 < y4 < -3.2999999999999998e-274

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 41.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 41.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 41.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 41.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 41.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 41.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 41.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 30.4%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.4%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 30.4%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around inf 20.7%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(b \cdot y0\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 20.7%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y0 \cdot b\right)}\right) \]

   11. Simplified 20.7%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y0 \cdot b\right)}\right) \]

   if -3.2999999999999998e-274 < y4 < 3.99999999999999993e67

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 41.4%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 41.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 41.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 41.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 41.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf 31.4%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 27.4%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot z\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 27.4%

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-a \cdot z\right)}\right) \]

      2. distribute-rgt-neg-in 27.4%

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(a \cdot \left(-z\right)\right)}\right) \]

   9. Simplified 27.4%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(a \cdot \left(-z\right)\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4 \cdot 10^{+209}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.3 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -3.3 \cdot 10^{-274}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(t \cdot \left(z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 22.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+72}:\\ \;\;\;\;\left(-a\right) \cdot \left(z \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-268}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-211}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -3.4e+72)
   (* (- a) (* z (* t b)))
   (if (<= t 1.4e-268)
     (* k (* y4 (* y1 y2)))
     (if (<= t 2.8e-211)
       (* (* z y0) (* b k))
       (if (<= t 1.05e-77) (* b (* a (* x y))) (* b (* j (* t 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 (t <= -3.4e+72) {
		tmp = -a * (z * (t * b));
	} else if (t <= 1.4e-268) {
		tmp = k * (y4 * (y1 * y2));
	} else if (t <= 2.8e-211) {
		tmp = (z * y0) * (b * k);
	} else if (t <= 1.05e-77) {
		tmp = b * (a * (x * y));
	} else {
		tmp = b * (j * (t * 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 (t <= (-3.4d+72)) then
        tmp = -a * (z * (t * b))
    else if (t <= 1.4d-268) then
        tmp = k * (y4 * (y1 * y2))
    else if (t <= 2.8d-211) then
        tmp = (z * y0) * (b * k)
    else if (t <= 1.05d-77) then
        tmp = b * (a * (x * y))
    else
        tmp = b * (j * (t * 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 (t <= -3.4e+72) {
		tmp = -a * (z * (t * b));
	} else if (t <= 1.4e-268) {
		tmp = k * (y4 * (y1 * y2));
	} else if (t <= 2.8e-211) {
		tmp = (z * y0) * (b * k);
	} else if (t <= 1.05e-77) {
		tmp = b * (a * (x * y));
	} else {
		tmp = b * (j * (t * 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 t <= -3.4e+72:
		tmp = -a * (z * (t * b))
	elif t <= 1.4e-268:
		tmp = k * (y4 * (y1 * y2))
	elif t <= 2.8e-211:
		tmp = (z * y0) * (b * k)
	elif t <= 1.05e-77:
		tmp = b * (a * (x * y))
	else:
		tmp = b * (j * (t * 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 (t <= -3.4e+72)
		tmp = Float64(Float64(-a) * Float64(z * Float64(t * b)));
	elseif (t <= 1.4e-268)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (t <= 2.8e-211)
		tmp = Float64(Float64(z * y0) * Float64(b * k));
	elseif (t <= 1.05e-77)
		tmp = Float64(b * Float64(a * Float64(x * y)));
	else
		tmp = Float64(b * Float64(j * Float64(t * 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 (t <= -3.4e+72)
		tmp = -a * (z * (t * b));
	elseif (t <= 1.4e-268)
		tmp = k * (y4 * (y1 * y2));
	elseif (t <= 2.8e-211)
		tmp = (z * y0) * (b * k);
	elseif (t <= 1.05e-77)
		tmp = b * (a * (x * y));
	else
		tmp = b * (j * (t * 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[t, -3.4e+72], N[((-a) * N[(z * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-268], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-211], N[(N[(z * y0), $MachinePrecision] * N[(b * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-77], N[(b * N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.3999999999999998e72

   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 b around inf 46.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 48.4%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 48.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 48.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 48.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 41.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   7. Taylor expanded in x around 0 36.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. neg-mul-1 36.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(b \cdot \left(t \cdot z\right)\right) \]

      3. associate-*r* 40.0%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(\left(b \cdot t\right) \cdot z\right)} \]

   9. Simplified 40.0%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(\left(b \cdot t\right) \cdot z\right)} \]

   if -3.3999999999999998e72 < t < 1.40000000000000008e-268

   1. Initial program 38.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 44.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 44.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 44.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 44.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 44.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 44.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 44.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y4 around inf 32.5%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y1 \cdot y2 - b \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 32.5%

         \[\leadsto k \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right)\right) \]

   8. Simplified 32.5%

      \[\leadsto k \cdot \color{blue}{\left(y4 \cdot \left(y2 \cdot y1 - b \cdot y\right)\right)} \]

   9. Taylor expanded in y2 around inf 21.5%

      \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 21.5%

          \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   11. Simplified 21.5%

       \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   if 1.40000000000000008e-268 < t < 2.7999999999999998e-211

   1. Initial program 17.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 61.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 61.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 61.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 61.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 61.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 61.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 61.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 62.2%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 62.2%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 62.2%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around inf 51.2%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 61.3%

          \[\leadsto \color{blue}{\left(b \cdot k\right) \cdot \left(y0 \cdot z\right)} \]

       2. *-commutative 61.3%

          \[\leadsto \left(b \cdot k\right) \cdot \color{blue}{\left(z \cdot y0\right)} \]

   11. Simplified 61.3%

       \[\leadsto \color{blue}{\left(b \cdot k\right) \cdot \left(z \cdot y0\right)} \]

   if 2.7999999999999998e-211 < t < 1.05000000000000008e-77

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 55.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 55.2%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 55.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 55.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 55.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 55.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 36.3%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 36.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.9%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 36.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x\right)\right)} \]

   if 1.05000000000000008e-77 < t

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 39.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 41.2%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 41.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 41.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 41.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 41.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf 39.1%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 27.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 27.7%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 27.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+72}:\\ \;\;\;\;\left(-a\right) \cdot \left(z \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-268}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-211}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 28.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{if}\;y1 \leq -9.2 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 2.8 \cdot 10^{+104}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* (* i y1) (- z)))))
   (if (<= y1 -9.2e+151)
     t_1
     (if (<= y1 3.2e-41)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= y1 2.8e+104) (* b (* (- (* t j) (* y k)) 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 = k * ((i * y1) * -z);
	double tmp;
	if (y1 <= -9.2e+151) {
		tmp = t_1;
	} else if (y1 <= 3.2e-41) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y1 <= 2.8e+104) {
		tmp = b * (((t * j) - (y * k)) * 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 = k * ((i * y1) * -z)
    if (y1 <= (-9.2d+151)) then
        tmp = t_1
    else if (y1 <= 3.2d-41) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y1 <= 2.8d+104) then
        tmp = b * (((t * j) - (y * k)) * 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 = k * ((i * y1) * -z);
	double tmp;
	if (y1 <= -9.2e+151) {
		tmp = t_1;
	} else if (y1 <= 3.2e-41) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y1 <= 2.8e+104) {
		tmp = b * (((t * j) - (y * k)) * 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 = k * ((i * y1) * -z)
	tmp = 0
	if y1 <= -9.2e+151:
		tmp = t_1
	elif y1 <= 3.2e-41:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y1 <= 2.8e+104:
		tmp = b * (((t * j) - (y * k)) * 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(k * Float64(Float64(i * y1) * Float64(-z)))
	tmp = 0.0
	if (y1 <= -9.2e+151)
		tmp = t_1;
	elseif (y1 <= 3.2e-41)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y1 <= 2.8e+104)
		tmp = Float64(b * Float64(Float64(Float64(t * j) - Float64(y * k)) * 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 = k * ((i * y1) * -z);
	tmp = 0.0;
	if (y1 <= -9.2e+151)
		tmp = t_1;
	elseif (y1 <= 3.2e-41)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y1 <= 2.8e+104)
		tmp = b * (((t * j) - (y * k)) * 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[(k * N[(N[(i * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -9.2e+151], t$95$1, If[LessEqual[y1, 3.2e-41], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.8e+104], N[(b * N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -9.2000000000000003e151 or 2.8e104 < y1

   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 k around inf 32.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 32.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 32.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 32.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 32.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 32.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 32.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 32.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 40.3%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 40.3%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 40.2%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 40.2%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-i \cdot y1\right)}\right) \]

       2. distribute-lft-neg-out 40.2%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(\left(-i\right) \cdot y1\right)}\right) \]

       3. *-commutative 40.2%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   11. Simplified 40.2%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   if -9.2000000000000003e151 < y1 < 3.20000000000000012e-41

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 44.3%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 44.3%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 37.6%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 3.20000000000000012e-41 < y1 < 2.8e104

   1. Initial program 34.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. Step-by-step derivation

      1. fma-define 51.9%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 51.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 51.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 51.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 51.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf 46.7%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 46.7%

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) \]

      2. *-commutative 46.7%

         \[\leadsto b \cdot \left(y4 \cdot \left(t \cdot j - \color{blue}{y \cdot k}\right)\right) \]

   8. Simplified 46.7%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -9.2 \cdot 10^{+151}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 2.8 \cdot 10^{+104}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j - y \cdot k\right) \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 28.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{if}\;y1 \leq -3.5 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 4 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 9.5 \cdot 10^{+131}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* (* i y1) (- z)))))
   (if (<= y1 -3.5e+152)
     t_1
     (if (<= y1 4e-41)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= y1 9.5e+131) (* b (* y0 (- (* z k) (* x 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 = k * ((i * y1) * -z);
	double tmp;
	if (y1 <= -3.5e+152) {
		tmp = t_1;
	} else if (y1 <= 4e-41) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y1 <= 9.5e+131) {
		tmp = b * (y0 * ((z * k) - (x * 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 = k * ((i * y1) * -z)
    if (y1 <= (-3.5d+152)) then
        tmp = t_1
    else if (y1 <= 4d-41) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y1 <= 9.5d+131) then
        tmp = b * (y0 * ((z * k) - (x * 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 = k * ((i * y1) * -z);
	double tmp;
	if (y1 <= -3.5e+152) {
		tmp = t_1;
	} else if (y1 <= 4e-41) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y1 <= 9.5e+131) {
		tmp = b * (y0 * ((z * k) - (x * 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 = k * ((i * y1) * -z)
	tmp = 0
	if y1 <= -3.5e+152:
		tmp = t_1
	elif y1 <= 4e-41:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y1 <= 9.5e+131:
		tmp = b * (y0 * ((z * k) - (x * 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(k * Float64(Float64(i * y1) * Float64(-z)))
	tmp = 0.0
	if (y1 <= -3.5e+152)
		tmp = t_1;
	elseif (y1 <= 4e-41)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y1 <= 9.5e+131)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * 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 = k * ((i * y1) * -z);
	tmp = 0.0;
	if (y1 <= -3.5e+152)
		tmp = t_1;
	elseif (y1 <= 4e-41)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y1 <= 9.5e+131)
		tmp = b * (y0 * ((z * k) - (x * 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[(k * N[(N[(i * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -3.5e+152], t$95$1, If[LessEqual[y1, 4e-41], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9.5e+131], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -3.49999999999999981e152 or 9.50000000000000015e131 < y1

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 36.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 36.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 36.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 36.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 36.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 36.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 36.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 36.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 43.4%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.4%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 43.4%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 43.5%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 43.5%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-i \cdot y1\right)}\right) \]

       2. distribute-lft-neg-out 43.5%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(\left(-i\right) \cdot y1\right)}\right) \]

       3. *-commutative 43.5%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   11. Simplified 43.5%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   if -3.49999999999999981e152 < y1 < 4.00000000000000002e-41

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 44.3%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 44.3%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 37.6%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 4.00000000000000002e-41 < y1 < 9.50000000000000015e131

   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 43.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 47.4%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 47.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 47.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 47.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 47.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf 36.7%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto b \cdot \left(y0 \cdot \left(\color{blue}{z \cdot k} - j \cdot x\right)\right) \]

      2. *-commutative 36.7%

         \[\leadsto b \cdot \left(y0 \cdot \left(z \cdot k - \color{blue}{x \cdot j}\right)\right) \]

   8. Simplified 36.7%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.5 \cdot 10^{+152}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y1 \leq 4 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 9.5 \cdot 10^{+131}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 27.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{if}\;y1 \leq -1.36 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 1.2 \cdot 10^{-32}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 3.7 \cdot 10^{+54}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* (* i y1) (- z)))))
   (if (<= y1 -1.36e+152)
     t_1
     (if (<= y1 1.2e-32)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= y1 3.7e+54) (* (* z y0) (* b k)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * ((i * y1) * -z);
	double tmp;
	if (y1 <= -1.36e+152) {
		tmp = t_1;
	} else if (y1 <= 1.2e-32) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y1 <= 3.7e+54) {
		tmp = (z * y0) * (b * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * ((i * y1) * -z)
    if (y1 <= (-1.36d+152)) then
        tmp = t_1
    else if (y1 <= 1.2d-32) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y1 <= 3.7d+54) then
        tmp = (z * y0) * (b * k)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * ((i * y1) * -z);
	double tmp;
	if (y1 <= -1.36e+152) {
		tmp = t_1;
	} else if (y1 <= 1.2e-32) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y1 <= 3.7e+54) {
		tmp = (z * y0) * (b * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * ((i * y1) * -z)
	tmp = 0
	if y1 <= -1.36e+152:
		tmp = t_1
	elif y1 <= 1.2e-32:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y1 <= 3.7e+54:
		tmp = (z * y0) * (b * k)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(Float64(i * y1) * Float64(-z)))
	tmp = 0.0
	if (y1 <= -1.36e+152)
		tmp = t_1;
	elseif (y1 <= 1.2e-32)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y1 <= 3.7e+54)
		tmp = Float64(Float64(z * y0) * Float64(b * k));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * ((i * y1) * -z);
	tmp = 0.0;
	if (y1 <= -1.36e+152)
		tmp = t_1;
	elseif (y1 <= 1.2e-32)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y1 <= 3.7e+54)
		tmp = (z * y0) * (b * k);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(N[(i * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.36e+152], t$95$1, If[LessEqual[y1, 1.2e-32], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.7e+54], N[(N[(z * y0), $MachinePrecision] * N[(b * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -1.36e152 or 3.7000000000000002e54 < y1

   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 34.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 34.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 34.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 34.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 34.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 34.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 34.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 34.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 41.3%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 41.3%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 41.3%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around 0 40.1%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 40.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(-i \cdot y1\right)}\right) \]

       2. distribute-lft-neg-out 40.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(\left(-i\right) \cdot y1\right)}\right) \]

       3. *-commutative 40.1%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   11. Simplified 40.1%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y1 \cdot \left(-i\right)\right)}\right) \]

   if -1.36e152 < y1 < 1.2000000000000001e-32

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 43.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 44.3%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 44.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 44.3%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf 37.6%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 1.2000000000000001e-32 < y1 < 3.7000000000000002e54

   1. Initial program 45.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 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 z around inf 37.8%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.8%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 37.8%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around inf 28.7%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 32.7%

          \[\leadsto \color{blue}{\left(b \cdot k\right) \cdot \left(y0 \cdot z\right)} \]

       2. *-commutative 32.7%

          \[\leadsto \left(b \cdot k\right) \cdot \color{blue}{\left(z \cdot y0\right)} \]

   11. Simplified 32.7%

       \[\leadsto \color{blue}{\left(b \cdot k\right) \cdot \left(z \cdot y0\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.36 \cdot 10^{+152}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y1 \leq 1.2 \cdot 10^{-32}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 3.7 \cdot 10^{+54}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 39: 22.7% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 8.2 \cdot 10^{-232}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 9.2 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -1.6e+84)
   (* k (* z (* b y0)))
   (if (<= y0 8.2e-232)
     (* b (* j (* t y4)))
     (if (<= y0 9.2e+85) (* b (* a (* x y))) (* b (* k (* z y0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1.6e+84) {
		tmp = k * (z * (b * y0));
	} else if (y0 <= 8.2e-232) {
		tmp = b * (j * (t * y4));
	} else if (y0 <= 9.2e+85) {
		tmp = b * (a * (x * y));
	} else {
		tmp = b * (k * (z * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-1.6d+84)) then
        tmp = k * (z * (b * y0))
    else if (y0 <= 8.2d-232) then
        tmp = b * (j * (t * y4))
    else if (y0 <= 9.2d+85) then
        tmp = b * (a * (x * y))
    else
        tmp = b * (k * (z * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1.6e+84) {
		tmp = k * (z * (b * y0));
	} else if (y0 <= 8.2e-232) {
		tmp = b * (j * (t * y4));
	} else if (y0 <= 9.2e+85) {
		tmp = b * (a * (x * y));
	} else {
		tmp = b * (k * (z * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -1.6e+84:
		tmp = k * (z * (b * y0))
	elif y0 <= 8.2e-232:
		tmp = b * (j * (t * y4))
	elif y0 <= 9.2e+85:
		tmp = b * (a * (x * y))
	else:
		tmp = b * (k * (z * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -1.6e+84)
		tmp = Float64(k * Float64(z * Float64(b * y0)));
	elseif (y0 <= 8.2e-232)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y0 <= 9.2e+85)
		tmp = Float64(b * Float64(a * Float64(x * y)));
	else
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -1.6e+84)
		tmp = k * (z * (b * y0));
	elseif (y0 <= 8.2e-232)
		tmp = b * (j * (t * y4));
	elseif (y0 <= 9.2e+85)
		tmp = b * (a * (x * y));
	else
		tmp = b * (k * (z * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -1.6e+84], N[(k * N[(z * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8.2e-232], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9.2e+85], N[(b * N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -1.60000000000000005e84

   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 k around inf 42.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 42.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 42.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 48.7%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 48.7%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 48.7%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around inf 38.3%

      \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(b \cdot y0\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative 38.3%

          \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y0 \cdot b\right)}\right) \]

   11. Simplified 38.3%

       \[\leadsto k \cdot \left(z \cdot \color{blue}{\left(y0 \cdot b\right)}\right) \]

   if -1.60000000000000005e84 < y0 < 8.19999999999999945e-232

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 42.5%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf 32.4%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 29.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.1%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 29.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if 8.19999999999999945e-232 < y0 < 9.1999999999999996e85

   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 41.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 42.5%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 30.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 24.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 24.5%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 24.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x\right)\right)} \]

   if 9.1999999999999996e85 < y0

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 33.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 33.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 33.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 33.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 33.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 33.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 33.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 28.4%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 28.4%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 28.4%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around inf 22.3%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 28.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 8.2 \cdot 10^{-232}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 9.2 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 40: 22.8% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{if}\;y0 \leq -8.5 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{-233}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.02 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* k (* z y0)))))
   (if (<= y0 -8.5e+85)
     t_1
     (if (<= y0 6e-233)
       (* b (* j (* t y4)))
       (if (<= y0 1.02e+86) (* b (* a (* x y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (k * (z * y0));
	double tmp;
	if (y0 <= -8.5e+85) {
		tmp = t_1;
	} else if (y0 <= 6e-233) {
		tmp = b * (j * (t * y4));
	} else if (y0 <= 1.02e+86) {
		tmp = b * (a * (x * y));
	} 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 * (k * (z * y0))
    if (y0 <= (-8.5d+85)) then
        tmp = t_1
    else if (y0 <= 6d-233) then
        tmp = b * (j * (t * y4))
    else if (y0 <= 1.02d+86) then
        tmp = b * (a * (x * y))
    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 * (k * (z * y0));
	double tmp;
	if (y0 <= -8.5e+85) {
		tmp = t_1;
	} else if (y0 <= 6e-233) {
		tmp = b * (j * (t * y4));
	} else if (y0 <= 1.02e+86) {
		tmp = b * (a * (x * y));
	} 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 * (k * (z * y0))
	tmp = 0
	if y0 <= -8.5e+85:
		tmp = t_1
	elif y0 <= 6e-233:
		tmp = b * (j * (t * y4))
	elif y0 <= 1.02e+86:
		tmp = b * (a * (x * y))
	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(k * Float64(z * y0)))
	tmp = 0.0
	if (y0 <= -8.5e+85)
		tmp = t_1;
	elseif (y0 <= 6e-233)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y0 <= 1.02e+86)
		tmp = Float64(b * Float64(a * Float64(x * y)));
	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 * (k * (z * y0));
	tmp = 0.0;
	if (y0 <= -8.5e+85)
		tmp = t_1;
	elseif (y0 <= 6e-233)
		tmp = b * (j * (t * y4));
	elseif (y0 <= 1.02e+86)
		tmp = b * (a * (x * y));
	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[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -8.5e+85], t$95$1, If[LessEqual[y0, 6e-233], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.02e+86], N[(b * N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y0 < -8.4999999999999994e85 or 1.01999999999999996e86 < y0

   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 k around inf 37.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 37.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 37.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 37.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 37.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 37.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 37.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in z around inf 38.5%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.5%

         \[\leadsto k \cdot \left(z \cdot \left(b \cdot y0 - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 38.5%

      \[\leadsto k \cdot \color{blue}{\left(z \cdot \left(b \cdot y0 - y1 \cdot i\right)\right)} \]

   9. Taylor expanded in b around inf 28.3%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -8.4999999999999994e85 < y0 < 5.99999999999999997e-233

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 42.5%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf 32.4%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 29.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.1%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 29.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if 5.99999999999999997e-233 < y0 < 1.01999999999999996e86

   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 41.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 42.5%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 42.5%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 30.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 24.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 24.5%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 24.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -8.5 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{-233}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.02 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 41: 20.4% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x 7.2e-26) (* b (* j (* t y4))) (* b (* a (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= 7.2e-26) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = b * (a * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= 7.2d-26) then
        tmp = b * (j * (t * y4))
    else
        tmp = b * (a * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= 7.2e-26) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = b * (a * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= 7.2e-26:
		tmp = b * (j * (t * y4))
	else:
		tmp = b * (a * (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= 7.2e-26)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = Float64(b * Float64(a * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= 7.2e-26)
		tmp = b * (j * (t * y4));
	else
		tmp = b * (a * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, 7.2e-26], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.2000000000000003e-26

   1. Initial program 32.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. Step-by-step derivation

      1. fma-define 43.3%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 43.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 43.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 43.3%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf 31.1%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around 0 20.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 20.6%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 20.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if 7.2000000000000003e-26 < 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 b around inf 39.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. fma-define 42.2%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. *-commutative 42.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. *-commutative 42.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 42.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 34.3%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 29.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.7%

         \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   9. Simplified 29.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 42: 16.8% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot \left(x \cdot y\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* b (* a (* x y))))

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 b * (a * (x * y));
}

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 = b * (a * (x * y))
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 b * (a * (x * y));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return b * (a * (x * y))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(b * Float64(a * Float64(x * y)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = b * (a * (x * y));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(b * N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 29.5%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 40.6%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
4. Step-by-step derivation

   1. fma-define 43.0%

      \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   2. *-commutative 43.0%

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   3. *-commutative 43.0%

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   4. *-commutative 43.0%

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

5. Simplified 43.0%

   \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

6. Taylor expanded in a around inf 25.5%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

7. Taylor expanded in x around inf 17.4%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative 17.4%

      \[\leadsto b \cdot \left(a \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

9. Simplified 17.4%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x\right)\right)} \]

10. Final simplification 17.4%

    \[\leadsto b \cdot \left(a \cdot \left(x \cdot y\right)\right) \]
11. Add Preprocessing

Alternative 43: 16.8% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot \left(x \cdot y\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* b (* x y))))

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 * (b * (x * y));
}

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 * (b * (x * y))
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 * (b * (x * y));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (b * (x * y))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(b * Float64(x * y)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (b * (x * y));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 29.5%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 40.6%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
4. Step-by-step derivation

   1. fma-define 43.0%

      \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   2. *-commutative 43.0%

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   3. *-commutative 43.0%

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   4. *-commutative 43.0%

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

5. Simplified 43.0%

   \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

6. Taylor expanded in a around inf 25.5%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

7. Taylor expanded in x around inf 16.4%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative 16.4%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

9. Simplified 16.4%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x\right)\right)} \]

10. Final simplification 16.4%

    \[\leadsto a \cdot \left(b \cdot \left(x \cdot y\right)\right) \]
11. 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 2024087 
(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)))))