Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.4% → 40.4%

Time: 1.8min

Alternatives: 38

Speedup: 4.5×

• 88.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.4% 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: 40.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y3 - x \cdot y2\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := a \cdot y1 - c \cdot y0\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := c \cdot y4 - a \cdot y5\\ t_6 := b \cdot \left(t \cdot j - y \cdot k\right)\\ t_7 := y1 \cdot y4 - y0 \cdot y5\\ t_8 := b \cdot y0 - i \cdot y1\\ t_9 := k \cdot \left(\left(y2 \cdot t_7 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot t_8\right)\\ t_10 := k \cdot y2 - j \cdot y3\\ t_11 := t_10 \cdot t_7\\ \mathbf{if}\;k \leq -3.55 \cdot 10^{+146}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;k \leq -3.5 \cdot 10^{+113}:\\ \;\;\;\;y3 \cdot \left(y \cdot t_5 + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot t_4\right)\right)\\ \mathbf{elif}\;k \leq -4 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot \left(i \cdot j\right) - j \cdot \left(y3 \cdot y4\right)\right) + \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right) + a \cdot t_1\right)\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-158}:\\ \;\;\;\;t_11 + c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot t_2\right)\\ \mathbf{elif}\;k \leq 2.85 \cdot 10^{-131}:\\ \;\;\;\;y2 \cdot \left(x \cdot t_4\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-123}:\\ \;\;\;\;\left(y \cdot \left(-a\right)\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{-97}:\\ \;\;\;\;t_11 + \left(\left(z \cdot y3\right) \cdot t_3 + t_5 \cdot t_2\right)\\ \mathbf{elif}\;k \leq 10^{-29}:\\ \;\;\;\;y4 \cdot \left(t_6 + c \cdot t_2\right)\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{+71}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;k \leq 1.02 \cdot 10^{+152}:\\ \;\;\;\;z \cdot \left(k \cdot t_8 + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot t_3\right)\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{+161}:\\ \;\;\;\;t_11 + y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - c \cdot t_1\right)\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{+167}:\\ \;\;\;\;y4 \cdot \left(t_6 + y1 \cdot t_10\right)\\ \mathbf{else}:\\ \;\;\;\;t_9\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z y3) (* x y2)))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (- (* a y1) (* c y0)))
        (t_4 (- (* c y0) (* a y1)))
        (t_5 (- (* c y4) (* a y5)))
        (t_6 (* b (- (* t j) (* y k))))
        (t_7 (- (* y1 y4) (* y0 y5)))
        (t_8 (- (* b y0) (* i y1)))
        (t_9 (* k (+ (+ (* y2 t_7) (* y (- (* i y5) (* b y4)))) (* z t_8))))
        (t_10 (- (* k y2) (* j y3)))
        (t_11 (* t_10 t_7)))
   (if (<= k -3.55e+146)
     t_9
     (if (<= k -3.5e+113)
       (* y3 (+ (* y t_5) (- (* j (- (* y0 y5) (* y1 y4))) (* z t_4))))
       (if (<= k -4e-254)
         (*
          y1
          (+
           (- (* x (* i j)) (* j (* y3 y4)))
           (+ (* k (- (* y2 y4) (* z i))) (* a t_1))))
         (if (<= k 2.4e-158)
           (+
            t_11
            (*
             c
             (+
              (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
              (* y4 t_2))))
           (if (<= k 2.85e-131)
             (* y2 (* x t_4))
             (if (<= k 3.8e-123)
               (* (* y (- a)) (* y3 y5))
               (if (<= k 2.2e-97)
                 (+ t_11 (+ (* (* z y3) t_3) (* t_5 t_2)))
                 (if (<= k 1e-29)
                   (* y4 (+ t_6 (* c t_2)))
                   (if (<= k 3.9e+71)
                     t_9
                     (if (<= k 1.02e+152)
                       (*
                        z
                        (+ (* k t_8) (+ (* t (- (* c i) (* a b))) (* y3 t_3))))
                       (if (<= k 3.2e+161)
                         (+
                          t_11
                          (* y0 (- (* b (- (* z k) (* x j))) (* c t_1))))
                         (if (<= k 3.6e+167)
                           (* y4 (+ t_6 (* y1 t_10)))
                           t_9))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) - (x * y2);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (a * y1) - (c * y0);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (c * y4) - (a * y5);
	double t_6 = b * ((t * j) - (y * k));
	double t_7 = (y1 * y4) - (y0 * y5);
	double t_8 = (b * y0) - (i * y1);
	double t_9 = k * (((y2 * t_7) + (y * ((i * y5) - (b * y4)))) + (z * t_8));
	double t_10 = (k * y2) - (j * y3);
	double t_11 = t_10 * t_7;
	double tmp;
	if (k <= -3.55e+146) {
		tmp = t_9;
	} else if (k <= -3.5e+113) {
		tmp = y3 * ((y * t_5) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)));
	} else if (k <= -4e-254) {
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)));
	} else if (k <= 2.4e-158) {
		tmp = t_11 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2)));
	} else if (k <= 2.85e-131) {
		tmp = y2 * (x * t_4);
	} else if (k <= 3.8e-123) {
		tmp = (y * -a) * (y3 * y5);
	} else if (k <= 2.2e-97) {
		tmp = t_11 + (((z * y3) * t_3) + (t_5 * t_2));
	} else if (k <= 1e-29) {
		tmp = y4 * (t_6 + (c * t_2));
	} else if (k <= 3.9e+71) {
		tmp = t_9;
	} else if (k <= 1.02e+152) {
		tmp = z * ((k * t_8) + ((t * ((c * i) - (a * b))) + (y3 * t_3)));
	} else if (k <= 3.2e+161) {
		tmp = t_11 + (y0 * ((b * ((z * k) - (x * j))) - (c * t_1)));
	} else if (k <= 3.6e+167) {
		tmp = y4 * (t_6 + (y1 * t_10));
	} else {
		tmp = t_9;
	}
	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_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 = (z * y3) - (x * y2)
    t_2 = (y * y3) - (t * y2)
    t_3 = (a * y1) - (c * y0)
    t_4 = (c * y0) - (a * y1)
    t_5 = (c * y4) - (a * y5)
    t_6 = b * ((t * j) - (y * k))
    t_7 = (y1 * y4) - (y0 * y5)
    t_8 = (b * y0) - (i * y1)
    t_9 = k * (((y2 * t_7) + (y * ((i * y5) - (b * y4)))) + (z * t_8))
    t_10 = (k * y2) - (j * y3)
    t_11 = t_10 * t_7
    if (k <= (-3.55d+146)) then
        tmp = t_9
    else if (k <= (-3.5d+113)) then
        tmp = y3 * ((y * t_5) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)))
    else if (k <= (-4d-254)) then
        tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)))
    else if (k <= 2.4d-158) then
        tmp = t_11 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2)))
    else if (k <= 2.85d-131) then
        tmp = y2 * (x * t_4)
    else if (k <= 3.8d-123) then
        tmp = (y * -a) * (y3 * y5)
    else if (k <= 2.2d-97) then
        tmp = t_11 + (((z * y3) * t_3) + (t_5 * t_2))
    else if (k <= 1d-29) then
        tmp = y4 * (t_6 + (c * t_2))
    else if (k <= 3.9d+71) then
        tmp = t_9
    else if (k <= 1.02d+152) then
        tmp = z * ((k * t_8) + ((t * ((c * i) - (a * b))) + (y3 * t_3)))
    else if (k <= 3.2d+161) then
        tmp = t_11 + (y0 * ((b * ((z * k) - (x * j))) - (c * t_1)))
    else if (k <= 3.6d+167) then
        tmp = y4 * (t_6 + (y1 * t_10))
    else
        tmp = t_9
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) - (x * y2);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (a * y1) - (c * y0);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (c * y4) - (a * y5);
	double t_6 = b * ((t * j) - (y * k));
	double t_7 = (y1 * y4) - (y0 * y5);
	double t_8 = (b * y0) - (i * y1);
	double t_9 = k * (((y2 * t_7) + (y * ((i * y5) - (b * y4)))) + (z * t_8));
	double t_10 = (k * y2) - (j * y3);
	double t_11 = t_10 * t_7;
	double tmp;
	if (k <= -3.55e+146) {
		tmp = t_9;
	} else if (k <= -3.5e+113) {
		tmp = y3 * ((y * t_5) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)));
	} else if (k <= -4e-254) {
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)));
	} else if (k <= 2.4e-158) {
		tmp = t_11 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2)));
	} else if (k <= 2.85e-131) {
		tmp = y2 * (x * t_4);
	} else if (k <= 3.8e-123) {
		tmp = (y * -a) * (y3 * y5);
	} else if (k <= 2.2e-97) {
		tmp = t_11 + (((z * y3) * t_3) + (t_5 * t_2));
	} else if (k <= 1e-29) {
		tmp = y4 * (t_6 + (c * t_2));
	} else if (k <= 3.9e+71) {
		tmp = t_9;
	} else if (k <= 1.02e+152) {
		tmp = z * ((k * t_8) + ((t * ((c * i) - (a * b))) + (y3 * t_3)));
	} else if (k <= 3.2e+161) {
		tmp = t_11 + (y0 * ((b * ((z * k) - (x * j))) - (c * t_1)));
	} else if (k <= 3.6e+167) {
		tmp = y4 * (t_6 + (y1 * t_10));
	} else {
		tmp = t_9;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (z * y3) - (x * y2)
	t_2 = (y * y3) - (t * y2)
	t_3 = (a * y1) - (c * y0)
	t_4 = (c * y0) - (a * y1)
	t_5 = (c * y4) - (a * y5)
	t_6 = b * ((t * j) - (y * k))
	t_7 = (y1 * y4) - (y0 * y5)
	t_8 = (b * y0) - (i * y1)
	t_9 = k * (((y2 * t_7) + (y * ((i * y5) - (b * y4)))) + (z * t_8))
	t_10 = (k * y2) - (j * y3)
	t_11 = t_10 * t_7
	tmp = 0
	if k <= -3.55e+146:
		tmp = t_9
	elif k <= -3.5e+113:
		tmp = y3 * ((y * t_5) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)))
	elif k <= -4e-254:
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)))
	elif k <= 2.4e-158:
		tmp = t_11 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2)))
	elif k <= 2.85e-131:
		tmp = y2 * (x * t_4)
	elif k <= 3.8e-123:
		tmp = (y * -a) * (y3 * y5)
	elif k <= 2.2e-97:
		tmp = t_11 + (((z * y3) * t_3) + (t_5 * t_2))
	elif k <= 1e-29:
		tmp = y4 * (t_6 + (c * t_2))
	elif k <= 3.9e+71:
		tmp = t_9
	elif k <= 1.02e+152:
		tmp = z * ((k * t_8) + ((t * ((c * i) - (a * b))) + (y3 * t_3)))
	elif k <= 3.2e+161:
		tmp = t_11 + (y0 * ((b * ((z * k) - (x * j))) - (c * t_1)))
	elif k <= 3.6e+167:
		tmp = y4 * (t_6 + (y1 * t_10))
	else:
		tmp = t_9
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * y3) - Float64(x * y2))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(Float64(a * y1) - Float64(c * y0))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(Float64(c * y4) - Float64(a * y5))
	t_6 = Float64(b * Float64(Float64(t * j) - Float64(y * k)))
	t_7 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_8 = Float64(Float64(b * y0) - Float64(i * y1))
	t_9 = Float64(k * Float64(Float64(Float64(y2 * t_7) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * t_8)))
	t_10 = Float64(Float64(k * y2) - Float64(j * y3))
	t_11 = Float64(t_10 * t_7)
	tmp = 0.0
	if (k <= -3.55e+146)
		tmp = t_9;
	elseif (k <= -3.5e+113)
		tmp = Float64(y3 * Float64(Float64(y * t_5) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(z * t_4))));
	elseif (k <= -4e-254)
		tmp = Float64(y1 * Float64(Float64(Float64(x * Float64(i * j)) - Float64(j * Float64(y3 * y4))) + Float64(Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))) + Float64(a * t_1))));
	elseif (k <= 2.4e-158)
		tmp = Float64(t_11 + Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * t_2))));
	elseif (k <= 2.85e-131)
		tmp = Float64(y2 * Float64(x * t_4));
	elseif (k <= 3.8e-123)
		tmp = Float64(Float64(y * Float64(-a)) * Float64(y3 * y5));
	elseif (k <= 2.2e-97)
		tmp = Float64(t_11 + Float64(Float64(Float64(z * y3) * t_3) + Float64(t_5 * t_2)));
	elseif (k <= 1e-29)
		tmp = Float64(y4 * Float64(t_6 + Float64(c * t_2)));
	elseif (k <= 3.9e+71)
		tmp = t_9;
	elseif (k <= 1.02e+152)
		tmp = Float64(z * Float64(Float64(k * t_8) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * t_3))));
	elseif (k <= 3.2e+161)
		tmp = Float64(t_11 + Float64(y0 * Float64(Float64(b * Float64(Float64(z * k) - Float64(x * j))) - Float64(c * t_1))));
	elseif (k <= 3.6e+167)
		tmp = Float64(y4 * Float64(t_6 + Float64(y1 * t_10)));
	else
		tmp = t_9;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * y3) - (x * y2);
	t_2 = (y * y3) - (t * y2);
	t_3 = (a * y1) - (c * y0);
	t_4 = (c * y0) - (a * y1);
	t_5 = (c * y4) - (a * y5);
	t_6 = b * ((t * j) - (y * k));
	t_7 = (y1 * y4) - (y0 * y5);
	t_8 = (b * y0) - (i * y1);
	t_9 = k * (((y2 * t_7) + (y * ((i * y5) - (b * y4)))) + (z * t_8));
	t_10 = (k * y2) - (j * y3);
	t_11 = t_10 * t_7;
	tmp = 0.0;
	if (k <= -3.55e+146)
		tmp = t_9;
	elseif (k <= -3.5e+113)
		tmp = y3 * ((y * t_5) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)));
	elseif (k <= -4e-254)
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)));
	elseif (k <= 2.4e-158)
		tmp = t_11 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2)));
	elseif (k <= 2.85e-131)
		tmp = y2 * (x * t_4);
	elseif (k <= 3.8e-123)
		tmp = (y * -a) * (y3 * y5);
	elseif (k <= 2.2e-97)
		tmp = t_11 + (((z * y3) * t_3) + (t_5 * t_2));
	elseif (k <= 1e-29)
		tmp = y4 * (t_6 + (c * t_2));
	elseif (k <= 3.9e+71)
		tmp = t_9;
	elseif (k <= 1.02e+152)
		tmp = z * ((k * t_8) + ((t * ((c * i) - (a * b))) + (y3 * t_3)));
	elseif (k <= 3.2e+161)
		tmp = t_11 + (y0 * ((b * ((z * k) - (x * j))) - (c * t_1)));
	elseif (k <= 3.6e+167)
		tmp = y4 * (t_6 + (y1 * t_10));
	else
		tmp = t_9;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(k * N[(N[(N[(y2 * t$95$7), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$10 * t$95$7), $MachinePrecision]}, If[LessEqual[k, -3.55e+146], t$95$9, If[LessEqual[k, -3.5e+113], N[(y3 * N[(N[(y * t$95$5), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4e-254], N[(y1 * N[(N[(N[(x * N[(i * j), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.4e-158], N[(t$95$11 + N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.85e-131], N[(y2 * N[(x * t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.8e-123], N[(N[(y * (-a)), $MachinePrecision] * N[(y3 * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.2e-97], N[(t$95$11 + N[(N[(N[(z * y3), $MachinePrecision] * t$95$3), $MachinePrecision] + N[(t$95$5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1e-29], N[(y4 * N[(t$95$6 + N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.9e+71], t$95$9, If[LessEqual[k, 1.02e+152], N[(z * N[(N[(k * t$95$8), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.2e+161], N[(t$95$11 + N[(y0 * N[(N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.6e+167], N[(y4 * N[(t$95$6 + N[(y1 * t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$9]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if k < -3.55e146 or 9.99999999999999943e-30 < k < 3.9000000000000001e71 or 3.60000000000000024e167 < k

   1. Initial program 29.9%

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

   2. Taylor expanded in k around inf 73.2%

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

      1. sub-neg 73.2%

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

      2. +-commutative 73.2%

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

      3. mul-1-neg 73.2%

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

      4. unsub-neg 73.2%

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

      5. *-commutative 73.2%

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

      6. mul-1-neg 73.2%

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

      7. remove-double-neg 73.2%

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

   4. Simplified 73.2%

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

   if -3.55e146 < k < -3.5000000000000001e113

   1. Initial program 30.0%

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

   2. Taylor expanded in y3 around -inf 100.0%

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

   if -3.5000000000000001e113 < k < -3.9999999999999996e-254

   1. Initial program 26.9%

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

   2. Taylor expanded in y1 around -inf 52.0%

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

      1. mul-1-neg 52.0%

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

      2. *-commutative 52.0%

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

      3. distribute-rgt-neg-in 52.0%

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

   4. Simplified 52.0%

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

   5. Taylor expanded in k around 0 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

      4. *-commutative 58.6%

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

      5. *-commutative 58.6%

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

      6. *-commutative 58.6%

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

      7. +-commutative 58.6%

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

      8. mul-1-neg 58.6%

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

      9. unsub-neg 58.6%

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

      10. *-commutative 58.6%

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

      11. +-commutative 58.6%

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

      12. mul-1-neg 58.6%

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

   7. Simplified 60.3%

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

   if -3.9999999999999996e-254 < k < 2.40000000000000007e-158

   1. Initial program 40.9%

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

   2. Taylor expanded in c around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. *-commutative 62.9%

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

      6. *-commutative 62.9%

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

      7. *-commutative 62.9%

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

   4. Simplified 62.9%

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

   if 2.40000000000000007e-158 < k < 2.8500000000000001e-131

   1. Initial program 42.9%

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

   2. Taylor expanded in y2 around inf 44.1%

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

   3. Taylor expanded in x around inf 72.2%

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

   if 2.8500000000000001e-131 < k < 3.79999999999999996e-123

   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. Taylor expanded in y4 around inf 0.0%

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

      1. *-commutative 0.0%

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

   4. Simplified 0.0%

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

   5. Taylor expanded in a around inf 68.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 68.1%

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

      2. *-commutative 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in y2 around 0 68.1%

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

      1. associate-*r* 68.1%

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

      2. associate-*r* 68.8%

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

      3. neg-mul-1 68.8%

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

   10. Simplified 68.8%

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

   if 3.79999999999999996e-123 < k < 2.1999999999999999e-97

   1. Initial program 72.7%

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

   2. Taylor expanded in y3 around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. associate-*r* 73.4%

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

      3. *-commutative 73.4%

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

   4. Simplified 73.4%

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

   if 2.1999999999999999e-97 < k < 9.99999999999999943e-30

   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. Taylor expanded in y4 around inf 64.8%

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

   3. Taylor expanded in y1 around 0 65.2%

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

      1. *-commutative 65.2%

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

      2. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   if 3.9000000000000001e71 < k < 1.01999999999999999e152

   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. Taylor expanded in z around -inf 57.4%

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

   3. Taylor expanded in z around inf 63.0%

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

   if 1.01999999999999999e152 < k < 3.20000000000000002e161

   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. Taylor expanded in y0 around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. *-commutative 75.0%

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

      3. *-commutative 75.0%

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

   4. Simplified 75.0%

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

   if 3.20000000000000002e161 < k < 3.60000000000000024e167

   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. Taylor expanded in y4 around inf 25.0%

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

   3. Taylor expanded in c around 0 75.0%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.55 \cdot 10^{+146}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -3.5 \cdot 10^{+113}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;k \leq -4 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot \left(i \cdot j\right) - j \cdot \left(y3 \cdot y4\right)\right) + \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-158}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + 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}\;k \leq 2.85 \cdot 10^{-131}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-123}:\\ \;\;\;\;\left(y \cdot \left(-a\right)\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{-97}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 10^{-29}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{+71}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 1.02 \cdot 10^{+152}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{+161}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{+167}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]

Alternative 2: 53.0% accurate, 0.5× speedup

Math

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

FPCore

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

Java

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.2%

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

   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. Taylor expanded in k around inf 39.4%

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

      1. sub-neg 39.4%

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

      2. +-commutative 39.4%

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

      3. mul-1-neg 39.4%

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

      4. unsub-neg 39.4%

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

      5. *-commutative 39.4%

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

      6. mul-1-neg 39.4%

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

      7. remove-double-neg 39.4%

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

   4. Simplified 39.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.0%

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

Alternative 3: 40.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y3 - x \cdot y2\\ t_2 := a \cdot b - c \cdot i\\ t_3 := c \cdot y4 - a \cdot y5\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := y \cdot y3 - t \cdot y2\\ t_6 := t \cdot j - y \cdot k\\ t_7 := y1 \cdot y4 - y0 \cdot y5\\ t_8 := k \cdot \left(\left(y2 \cdot t_7 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_9 := k \cdot y2 - j \cdot y3\\ t_10 := t_9 \cdot t_7\\ \mathbf{if}\;k \leq -1.25 \cdot 10^{+147}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;k \leq -7 \cdot 10^{+113}:\\ \;\;\;\;y3 \cdot \left(y \cdot t_3 + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot t_4\right)\right)\\ \mathbf{elif}\;k \leq -1.65 \cdot 10^{-255}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot \left(i \cdot j\right) - j \cdot \left(y3 \cdot y4\right)\right) + \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right) + a \cdot t_1\right)\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-182}:\\ \;\;\;\;t_10 + c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot t_5\right)\\ \mathbf{elif}\;k \leq 1.18 \cdot 10^{-122}:\\ \;\;\;\;t_10 + x \cdot \left(\left(y \cdot t_2 + y2 \cdot t_4\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.56 \cdot 10^{-74}:\\ \;\;\;\;\left(a \cdot \left(y1 \cdot t_1\right) + \left(y1 \cdot \left(y4 \cdot t_9\right) + \left(\left(x \cdot y - z \cdot t\right) \cdot t_2 + \left(b \cdot y4 - i \cdot y5\right) \cdot t_6\right)\right)\right) + \left(i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right) + t_3 \cdot t_5\right)\\ \mathbf{elif}\;k \leq 10^{-29}:\\ \;\;\;\;y4 \cdot \left(b \cdot t_6 + c \cdot t_5\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+71} \lor \neg \left(k \leq 1.1 \cdot 10^{+147}\right):\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot t_6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z y3) (* x y2)))
        (t_2 (- (* a b) (* c i)))
        (t_3 (- (* c y4) (* a y5)))
        (t_4 (- (* c y0) (* a y1)))
        (t_5 (- (* y y3) (* t y2)))
        (t_6 (- (* t j) (* y k)))
        (t_7 (- (* y1 y4) (* y0 y5)))
        (t_8
         (*
          k
          (+
           (+ (* y2 t_7) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1))))))
        (t_9 (- (* k y2) (* j y3)))
        (t_10 (* t_9 t_7)))
   (if (<= k -1.25e+147)
     t_8
     (if (<= k -7e+113)
       (* y3 (+ (* y t_3) (- (* j (- (* y0 y5) (* y1 y4))) (* z t_4))))
       (if (<= k -1.65e-255)
         (*
          y1
          (+
           (- (* x (* i j)) (* j (* y3 y4)))
           (+ (* k (- (* y2 y4) (* z i))) (* a t_1))))
         (if (<= k 1.55e-182)
           (+
            t_10
            (*
             c
             (+
              (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
              (* y4 t_5))))
           (if (<= k 1.18e-122)
             (+
              t_10
              (* x (+ (+ (* y t_2) (* y2 t_4)) (* j (- (* i y1) (* b y0))))))
             (if (<= k 1.56e-74)
               (+
                (+
                 (* a (* y1 t_1))
                 (+
                  (* y1 (* y4 t_9))
                  (+
                   (* (- (* x y) (* z t)) t_2)
                   (* (- (* b y4) (* i y5)) t_6))))
                (+ (* i (* y1 (- (* x j) (* z k)))) (* t_3 t_5)))
               (if (<= k 1e-29)
                 (* y4 (+ (* b t_6) (* c t_5)))
                 (if (or (<= k 7.5e+71) (not (<= k 1.1e+147)))
                   t_8
                   (* y5 (- (* y0 (- (* j y3) (* k y2))) (* i t_6)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) - (x * y2);
	double t_2 = (a * b) - (c * i);
	double t_3 = (c * y4) - (a * y5);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (y * y3) - (t * y2);
	double t_6 = (t * j) - (y * k);
	double t_7 = (y1 * y4) - (y0 * y5);
	double t_8 = k * (((y2 * t_7) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_9 = (k * y2) - (j * y3);
	double t_10 = t_9 * t_7;
	double tmp;
	if (k <= -1.25e+147) {
		tmp = t_8;
	} else if (k <= -7e+113) {
		tmp = y3 * ((y * t_3) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)));
	} else if (k <= -1.65e-255) {
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)));
	} else if (k <= 1.55e-182) {
		tmp = t_10 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_5)));
	} else if (k <= 1.18e-122) {
		tmp = t_10 + (x * (((y * t_2) + (y2 * t_4)) + (j * ((i * y1) - (b * y0)))));
	} else if (k <= 1.56e-74) {
		tmp = ((a * (y1 * t_1)) + ((y1 * (y4 * t_9)) + ((((x * y) - (z * t)) * t_2) + (((b * y4) - (i * y5)) * t_6)))) + ((i * (y1 * ((x * j) - (z * k)))) + (t_3 * t_5));
	} else if (k <= 1e-29) {
		tmp = y4 * ((b * t_6) + (c * t_5));
	} else if ((k <= 7.5e+71) || !(k <= 1.1e+147)) {
		tmp = t_8;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_6));
	}
	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_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 = (z * y3) - (x * y2)
    t_2 = (a * b) - (c * i)
    t_3 = (c * y4) - (a * y5)
    t_4 = (c * y0) - (a * y1)
    t_5 = (y * y3) - (t * y2)
    t_6 = (t * j) - (y * k)
    t_7 = (y1 * y4) - (y0 * y5)
    t_8 = k * (((y2 * t_7) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    t_9 = (k * y2) - (j * y3)
    t_10 = t_9 * t_7
    if (k <= (-1.25d+147)) then
        tmp = t_8
    else if (k <= (-7d+113)) then
        tmp = y3 * ((y * t_3) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)))
    else if (k <= (-1.65d-255)) then
        tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)))
    else if (k <= 1.55d-182) then
        tmp = t_10 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_5)))
    else if (k <= 1.18d-122) then
        tmp = t_10 + (x * (((y * t_2) + (y2 * t_4)) + (j * ((i * y1) - (b * y0)))))
    else if (k <= 1.56d-74) then
        tmp = ((a * (y1 * t_1)) + ((y1 * (y4 * t_9)) + ((((x * y) - (z * t)) * t_2) + (((b * y4) - (i * y5)) * t_6)))) + ((i * (y1 * ((x * j) - (z * k)))) + (t_3 * t_5))
    else if (k <= 1d-29) then
        tmp = y4 * ((b * t_6) + (c * t_5))
    else if ((k <= 7.5d+71) .or. (.not. (k <= 1.1d+147))) then
        tmp = t_8
    else
        tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_6))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) - (x * y2);
	double t_2 = (a * b) - (c * i);
	double t_3 = (c * y4) - (a * y5);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (y * y3) - (t * y2);
	double t_6 = (t * j) - (y * k);
	double t_7 = (y1 * y4) - (y0 * y5);
	double t_8 = k * (((y2 * t_7) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_9 = (k * y2) - (j * y3);
	double t_10 = t_9 * t_7;
	double tmp;
	if (k <= -1.25e+147) {
		tmp = t_8;
	} else if (k <= -7e+113) {
		tmp = y3 * ((y * t_3) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)));
	} else if (k <= -1.65e-255) {
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)));
	} else if (k <= 1.55e-182) {
		tmp = t_10 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_5)));
	} else if (k <= 1.18e-122) {
		tmp = t_10 + (x * (((y * t_2) + (y2 * t_4)) + (j * ((i * y1) - (b * y0)))));
	} else if (k <= 1.56e-74) {
		tmp = ((a * (y1 * t_1)) + ((y1 * (y4 * t_9)) + ((((x * y) - (z * t)) * t_2) + (((b * y4) - (i * y5)) * t_6)))) + ((i * (y1 * ((x * j) - (z * k)))) + (t_3 * t_5));
	} else if (k <= 1e-29) {
		tmp = y4 * ((b * t_6) + (c * t_5));
	} else if ((k <= 7.5e+71) || !(k <= 1.1e+147)) {
		tmp = t_8;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_6));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (z * y3) - (x * y2)
	t_2 = (a * b) - (c * i)
	t_3 = (c * y4) - (a * y5)
	t_4 = (c * y0) - (a * y1)
	t_5 = (y * y3) - (t * y2)
	t_6 = (t * j) - (y * k)
	t_7 = (y1 * y4) - (y0 * y5)
	t_8 = k * (((y2 * t_7) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	t_9 = (k * y2) - (j * y3)
	t_10 = t_9 * t_7
	tmp = 0
	if k <= -1.25e+147:
		tmp = t_8
	elif k <= -7e+113:
		tmp = y3 * ((y * t_3) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)))
	elif k <= -1.65e-255:
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)))
	elif k <= 1.55e-182:
		tmp = t_10 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_5)))
	elif k <= 1.18e-122:
		tmp = t_10 + (x * (((y * t_2) + (y2 * t_4)) + (j * ((i * y1) - (b * y0)))))
	elif k <= 1.56e-74:
		tmp = ((a * (y1 * t_1)) + ((y1 * (y4 * t_9)) + ((((x * y) - (z * t)) * t_2) + (((b * y4) - (i * y5)) * t_6)))) + ((i * (y1 * ((x * j) - (z * k)))) + (t_3 * t_5))
	elif k <= 1e-29:
		tmp = y4 * ((b * t_6) + (c * t_5))
	elif (k <= 7.5e+71) or not (k <= 1.1e+147):
		tmp = t_8
	else:
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_6))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * y3) - Float64(x * y2))
	t_2 = Float64(Float64(a * b) - Float64(c * i))
	t_3 = Float64(Float64(c * y4) - Float64(a * y5))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(Float64(y * y3) - Float64(t * y2))
	t_6 = Float64(Float64(t * j) - Float64(y * k))
	t_7 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_8 = Float64(k * Float64(Float64(Float64(y2 * t_7) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_9 = Float64(Float64(k * y2) - Float64(j * y3))
	t_10 = Float64(t_9 * t_7)
	tmp = 0.0
	if (k <= -1.25e+147)
		tmp = t_8;
	elseif (k <= -7e+113)
		tmp = Float64(y3 * Float64(Float64(y * t_3) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(z * t_4))));
	elseif (k <= -1.65e-255)
		tmp = Float64(y1 * Float64(Float64(Float64(x * Float64(i * j)) - Float64(j * Float64(y3 * y4))) + Float64(Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))) + Float64(a * t_1))));
	elseif (k <= 1.55e-182)
		tmp = Float64(t_10 + Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * t_5))));
	elseif (k <= 1.18e-122)
		tmp = Float64(t_10 + Float64(x * Float64(Float64(Float64(y * t_2) + Float64(y2 * t_4)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0))))));
	elseif (k <= 1.56e-74)
		tmp = Float64(Float64(Float64(a * Float64(y1 * t_1)) + Float64(Float64(y1 * Float64(y4 * t_9)) + Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * t_2) + Float64(Float64(Float64(b * y4) - Float64(i * y5)) * t_6)))) + Float64(Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k)))) + Float64(t_3 * t_5)));
	elseif (k <= 1e-29)
		tmp = Float64(y4 * Float64(Float64(b * t_6) + Float64(c * t_5)));
	elseif ((k <= 7.5e+71) || !(k <= 1.1e+147))
		tmp = t_8;
	else
		tmp = Float64(y5 * Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(i * t_6)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * y3) - (x * y2);
	t_2 = (a * b) - (c * i);
	t_3 = (c * y4) - (a * y5);
	t_4 = (c * y0) - (a * y1);
	t_5 = (y * y3) - (t * y2);
	t_6 = (t * j) - (y * k);
	t_7 = (y1 * y4) - (y0 * y5);
	t_8 = k * (((y2 * t_7) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	t_9 = (k * y2) - (j * y3);
	t_10 = t_9 * t_7;
	tmp = 0.0;
	if (k <= -1.25e+147)
		tmp = t_8;
	elseif (k <= -7e+113)
		tmp = y3 * ((y * t_3) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)));
	elseif (k <= -1.65e-255)
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)));
	elseif (k <= 1.55e-182)
		tmp = t_10 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_5)));
	elseif (k <= 1.18e-122)
		tmp = t_10 + (x * (((y * t_2) + (y2 * t_4)) + (j * ((i * y1) - (b * y0)))));
	elseif (k <= 1.56e-74)
		tmp = ((a * (y1 * t_1)) + ((y1 * (y4 * t_9)) + ((((x * y) - (z * t)) * t_2) + (((b * y4) - (i * y5)) * t_6)))) + ((i * (y1 * ((x * j) - (z * k)))) + (t_3 * t_5));
	elseif (k <= 1e-29)
		tmp = y4 * ((b * t_6) + (c * t_5));
	elseif ((k <= 7.5e+71) || ~((k <= 1.1e+147)))
		tmp = t_8;
	else
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_6));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(k * N[(N[(N[(y2 * t$95$7), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(t$95$9 * t$95$7), $MachinePrecision]}, If[LessEqual[k, -1.25e+147], t$95$8, If[LessEqual[k, -7e+113], N[(y3 * N[(N[(y * t$95$3), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.65e-255], N[(y1 * N[(N[(N[(x * N[(i * j), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.55e-182], N[(t$95$10 + N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.18e-122], N[(t$95$10 + N[(x * N[(N[(N[(y * t$95$2), $MachinePrecision] + N[(y2 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.56e-74], N[(N[(N[(a * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(y1 * N[(y4 * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1e-29], N[(y4 * N[(N[(b * t$95$6), $MachinePrecision] + N[(c * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 7.5e+71], N[Not[LessEqual[k, 1.1e+147]], $MachinePrecision]], t$95$8, N[(y5 * N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -1.2500000000000001e147 or 9.99999999999999943e-30 < k < 7.50000000000000007e71 or 1.1000000000000001e147 < k

   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. Taylor expanded in k around inf 68.7%

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

      1. sub-neg 68.7%

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

      2. +-commutative 68.7%

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

      3. mul-1-neg 68.7%

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

      4. unsub-neg 68.7%

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

      5. *-commutative 68.7%

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

      6. mul-1-neg 68.7%

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

      7. remove-double-neg 68.7%

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

   4. Simplified 68.7%

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

   if -1.2500000000000001e147 < k < -7.0000000000000001e113

   1. Initial program 30.0%

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

   2. Taylor expanded in y3 around -inf 100.0%

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

   if -7.0000000000000001e113 < k < -1.64999999999999994e-255

   1. Initial program 26.9%

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

   2. Taylor expanded in y1 around -inf 52.0%

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

      1. mul-1-neg 52.0%

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

      2. *-commutative 52.0%

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

      3. distribute-rgt-neg-in 52.0%

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

   4. Simplified 52.0%

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

   5. Taylor expanded in k around 0 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

      4. *-commutative 58.6%

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

      5. *-commutative 58.6%

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

      6. *-commutative 58.6%

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

      7. +-commutative 58.6%

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

      8. mul-1-neg 58.6%

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

      9. unsub-neg 58.6%

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

      10. *-commutative 58.6%

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

      11. +-commutative 58.6%

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

      12. mul-1-neg 58.6%

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

   7. Simplified 60.3%

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

   if -1.64999999999999994e-255 < k < 1.55000000000000004e-182

   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. Taylor expanded in c around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

      4. *-commutative 66.0%

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

      5. *-commutative 66.0%

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

      6. *-commutative 66.0%

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

      7. *-commutative 66.0%

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

   4. Simplified 66.0%

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

   if 1.55000000000000004e-182 < k < 1.17999999999999998e-122

   1. Initial program 30.6%

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

   2. Taylor expanded in x around inf 61.8%

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

   if 1.17999999999999998e-122 < k < 1.5600000000000001e-74

   1. Initial program 60.0%

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

   2. Taylor expanded in y0 around 0 73.4%

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

   if 1.5600000000000001e-74 < k < 9.99999999999999943e-30

   1. Initial program 14.3%

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

   2. Taylor expanded in y4 around inf 72.8%

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

   3. Taylor expanded in y1 around 0 73.5%

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

      1. *-commutative 73.5%

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

      2. *-commutative 73.5%

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

   5. Simplified 73.5%

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

   if 7.50000000000000007e71 < k < 1.1000000000000001e147

   1. Initial program 30.8%

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

   2. Taylor expanded in i around -inf 40.1%

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

   3. Taylor expanded in y5 around -inf 63.1%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.25 \cdot 10^{+147}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -7 \cdot 10^{+113}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;k \leq -1.65 \cdot 10^{-255}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot \left(i \cdot j\right) - j \cdot \left(y3 \cdot y4\right)\right) + \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-182}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + 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}\;k \leq 1.18 \cdot 10^{-122}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.56 \cdot 10^{-74}:\\ \;\;\;\;\left(a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + \left(y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\right) + \left(i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 10^{-29}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+71} \lor \neg \left(k \leq 1.1 \cdot 10^{+147}\right):\\ \;\;\;\;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{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]

Alternative 4: 40.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y4 - a \cdot y5\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := k \cdot \left(\left(y2 \cdot t_3 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_5 := \left(k \cdot y2 - j \cdot y3\right) \cdot t_3\\ t_6 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;k \leq -7.4 \cdot 10^{+147}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq -6.6 \cdot 10^{+113}:\\ \;\;\;\;y3 \cdot \left(y \cdot t_1 + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot t_6\right)\right)\\ \mathbf{elif}\;k \leq -1.25 \cdot 10^{-256}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot \left(i \cdot j\right) - j \cdot \left(y3 \cdot y4\right)\right) + \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{-183}:\\ \;\;\;\;t_5 + c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot t_2\right)\\ \mathbf{elif}\;k \leq 7.4 \cdot 10^{-131}:\\ \;\;\;\;t_5 + x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_6\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 6.8 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{-96}:\\ \;\;\;\;t_5 + \left(\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right) + t_1 \cdot t_2\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-30}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y4) (* a y5)))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4
         (*
          k
          (+
           (+ (* y2 t_3) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1))))))
        (t_5 (* (- (* k y2) (* j y3)) t_3))
        (t_6 (- (* c y0) (* a y1))))
   (if (<= k -7.4e+147)
     t_4
     (if (<= k -6.6e+113)
       (* y3 (+ (* y t_1) (- (* j (- (* y0 y5) (* y1 y4))) (* z t_6))))
       (if (<= k -1.25e-256)
         (*
          y1
          (+
           (- (* x (* i j)) (* j (* y3 y4)))
           (+ (* k (- (* y2 y4) (* z i))) (* a (- (* z y3) (* x y2))))))
         (if (<= k 1.6e-183)
           (+
            t_5
            (*
             c
             (+
              (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
              (* y4 t_2))))
           (if (<= k 7.4e-131)
             (+
              t_5
              (*
               x
               (+
                (+ (* y (- (* a b) (* c i))) (* y2 t_6))
                (* j (- (* i y1) (* b y0))))))
             (if (<= k 6.8e-122)
               (* a (* z (- (* y1 y3) (* t b))))
               (if (<= k 4.4e-96)
                 (+ t_5 (+ (* (* z y3) (- (* a y1) (* c y0))) (* t_1 t_2)))
                 (if (<= k 9e-30)
                   (* j (* y1 (- (* x i) (* y3 y4))))
                   t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) - (a * y5);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_5 = ((k * y2) - (j * y3)) * t_3;
	double t_6 = (c * y0) - (a * y1);
	double tmp;
	if (k <= -7.4e+147) {
		tmp = t_4;
	} else if (k <= -6.6e+113) {
		tmp = y3 * ((y * t_1) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_6)));
	} else if (k <= -1.25e-256) {
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * ((z * y3) - (x * y2)))));
	} else if (k <= 1.6e-183) {
		tmp = t_5 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2)));
	} else if (k <= 7.4e-131) {
		tmp = t_5 + (x * (((y * ((a * b) - (c * i))) + (y2 * t_6)) + (j * ((i * y1) - (b * y0)))));
	} else if (k <= 6.8e-122) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 4.4e-96) {
		tmp = t_5 + (((z * y3) * ((a * y1) - (c * y0))) + (t_1 * t_2));
	} else if (k <= 9e-30) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (c * y4) - (a * y5)
    t_2 = (y * y3) - (t * y2)
    t_3 = (y1 * y4) - (y0 * y5)
    t_4 = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    t_5 = ((k * y2) - (j * y3)) * t_3
    t_6 = (c * y0) - (a * y1)
    if (k <= (-7.4d+147)) then
        tmp = t_4
    else if (k <= (-6.6d+113)) then
        tmp = y3 * ((y * t_1) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_6)))
    else if (k <= (-1.25d-256)) then
        tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * ((z * y3) - (x * y2)))))
    else if (k <= 1.6d-183) then
        tmp = t_5 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2)))
    else if (k <= 7.4d-131) then
        tmp = t_5 + (x * (((y * ((a * b) - (c * i))) + (y2 * t_6)) + (j * ((i * y1) - (b * y0)))))
    else if (k <= 6.8d-122) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (k <= 4.4d-96) then
        tmp = t_5 + (((z * y3) * ((a * y1) - (c * y0))) + (t_1 * t_2))
    else if (k <= 9d-30) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) - (a * y5);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_5 = ((k * y2) - (j * y3)) * t_3;
	double t_6 = (c * y0) - (a * y1);
	double tmp;
	if (k <= -7.4e+147) {
		tmp = t_4;
	} else if (k <= -6.6e+113) {
		tmp = y3 * ((y * t_1) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_6)));
	} else if (k <= -1.25e-256) {
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * ((z * y3) - (x * y2)))));
	} else if (k <= 1.6e-183) {
		tmp = t_5 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2)));
	} else if (k <= 7.4e-131) {
		tmp = t_5 + (x * (((y * ((a * b) - (c * i))) + (y2 * t_6)) + (j * ((i * y1) - (b * y0)))));
	} else if (k <= 6.8e-122) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 4.4e-96) {
		tmp = t_5 + (((z * y3) * ((a * y1) - (c * y0))) + (t_1 * t_2));
	} else if (k <= 9e-30) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y4) - (a * y5)
	t_2 = (y * y3) - (t * y2)
	t_3 = (y1 * y4) - (y0 * y5)
	t_4 = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	t_5 = ((k * y2) - (j * y3)) * t_3
	t_6 = (c * y0) - (a * y1)
	tmp = 0
	if k <= -7.4e+147:
		tmp = t_4
	elif k <= -6.6e+113:
		tmp = y3 * ((y * t_1) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_6)))
	elif k <= -1.25e-256:
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * ((z * y3) - (x * y2)))))
	elif k <= 1.6e-183:
		tmp = t_5 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2)))
	elif k <= 7.4e-131:
		tmp = t_5 + (x * (((y * ((a * b) - (c * i))) + (y2 * t_6)) + (j * ((i * y1) - (b * y0)))))
	elif k <= 6.8e-122:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif k <= 4.4e-96:
		tmp = t_5 + (((z * y3) * ((a * y1) - (c * y0))) + (t_1 * t_2))
	elif k <= 9e-30:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y4) - Float64(a * y5))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(k * Float64(Float64(Float64(y2 * t_3) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_5 = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_3)
	t_6 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (k <= -7.4e+147)
		tmp = t_4;
	elseif (k <= -6.6e+113)
		tmp = Float64(y3 * Float64(Float64(y * t_1) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(z * t_6))));
	elseif (k <= -1.25e-256)
		tmp = Float64(y1 * Float64(Float64(Float64(x * Float64(i * j)) - Float64(j * Float64(y3 * y4))) + Float64(Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))));
	elseif (k <= 1.6e-183)
		tmp = Float64(t_5 + Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * t_2))));
	elseif (k <= 7.4e-131)
		tmp = Float64(t_5 + Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_6)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0))))));
	elseif (k <= 6.8e-122)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (k <= 4.4e-96)
		tmp = Float64(t_5 + Float64(Float64(Float64(z * y3) * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(t_1 * t_2)));
	elseif (k <= 9e-30)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y4) - (a * y5);
	t_2 = (y * y3) - (t * y2);
	t_3 = (y1 * y4) - (y0 * y5);
	t_4 = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	t_5 = ((k * y2) - (j * y3)) * t_3;
	t_6 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (k <= -7.4e+147)
		tmp = t_4;
	elseif (k <= -6.6e+113)
		tmp = y3 * ((y * t_1) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_6)));
	elseif (k <= -1.25e-256)
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * ((z * y3) - (x * y2)))));
	elseif (k <= 1.6e-183)
		tmp = t_5 + (c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * t_2)));
	elseif (k <= 7.4e-131)
		tmp = t_5 + (x * (((y * ((a * b) - (c * i))) + (y2 * t_6)) + (j * ((i * y1) - (b * y0)))));
	elseif (k <= 6.8e-122)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (k <= 4.4e-96)
		tmp = t_5 + (((z * y3) * ((a * y1) - (c * y0))) + (t_1 * t_2));
	elseif (k <= 9e-30)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(k * N[(N[(N[(y2 * t$95$3), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -7.4e+147], t$95$4, If[LessEqual[k, -6.6e+113], N[(y3 * N[(N[(y * t$95$1), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.25e-256], N[(y1 * N[(N[(N[(x * N[(i * j), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.6e-183], N[(t$95$5 + N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.4e-131], N[(t$95$5 + N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.8e-122], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.4e-96], N[(t$95$5 + N[(N[(N[(z * y3), $MachinePrecision] * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9e-30], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -7.3999999999999999e147 or 8.99999999999999935e-30 < k

   1. Initial program 27.8%

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

   2. Taylor expanded in k around inf 64.3%

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

      1. sub-neg 64.3%

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

      2. +-commutative 64.3%

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

      3. mul-1-neg 64.3%

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

      4. unsub-neg 64.3%

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

      5. *-commutative 64.3%

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

      6. mul-1-neg 64.3%

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

      7. remove-double-neg 64.3%

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

   4. Simplified 64.3%

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

   if -7.3999999999999999e147 < k < -6.6000000000000006e113

   1. Initial program 30.0%

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

   2. Taylor expanded in y3 around -inf 100.0%

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

   if -6.6000000000000006e113 < k < -1.25e-256

   1. Initial program 26.9%

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

   2. Taylor expanded in y1 around -inf 52.0%

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

      1. mul-1-neg 52.0%

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

      2. *-commutative 52.0%

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

      3. distribute-rgt-neg-in 52.0%

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

   4. Simplified 52.0%

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

   5. Taylor expanded in k around 0 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

      4. *-commutative 58.6%

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

      5. *-commutative 58.6%

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

      6. *-commutative 58.6%

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

      7. +-commutative 58.6%

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

      8. mul-1-neg 58.6%

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

      9. unsub-neg 58.6%

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

      10. *-commutative 58.6%

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

      11. +-commutative 58.6%

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

      12. mul-1-neg 58.6%

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

   7. Simplified 60.3%

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

   if -1.25e-256 < k < 1.6000000000000001e-183

   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. Taylor expanded in c around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

      4. *-commutative 66.0%

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

      5. *-commutative 66.0%

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

      6. *-commutative 66.0%

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

      7. *-commutative 66.0%

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

   4. Simplified 66.0%

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

   if 1.6000000000000001e-183 < k < 7.4000000000000004e-131

   1. Initial program 39.8%

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

   2. Taylor expanded in x around inf 70.4%

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

   if 7.4000000000000004e-131 < k < 6.7999999999999996e-122

   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. Taylor expanded in z around -inf 16.7%

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

   3. Taylor expanded in a around -inf 67.4%

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

      1. +-commutative 67.4%

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

      2. mul-1-neg 67.4%

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

      3. unsub-neg 67.4%

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

      4. *-commutative 67.4%

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

      5. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   if 6.7999999999999996e-122 < k < 4.39999999999999959e-96

   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. Taylor expanded in y3 around inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. associate-*r* 75.9%

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

      3. *-commutative 75.9%

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

   4. Simplified 75.9%

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

   if 4.39999999999999959e-96 < k < 8.99999999999999935e-30

   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. Taylor expanded in j around inf 60.0%

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

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

   4. Simplified 60.0%

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

   5. Taylor expanded in y1 around -inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

   7. Simplified 70.8%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -7.4 \cdot 10^{+147}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -6.6 \cdot 10^{+113}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;k \leq -1.25 \cdot 10^{-256}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot \left(i \cdot j\right) - j \cdot \left(y3 \cdot y4\right)\right) + \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{-183}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + 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}\;k \leq 7.4 \cdot 10^{-131}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 6.8 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{-96}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(z \cdot y3\right) \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-30}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]

Alternative 5: 40.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := k \cdot \left(\left(y2 \cdot t_2 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_4 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;k \leq -3.05 \cdot 10^{+146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -1.05 \cdot 10^{+126}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot t_4\right)\right)\\ \mathbf{elif}\;k \leq -2 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -3.9 \cdot 10^{-305}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 5.8 \cdot 10^{-133}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_4 + k \cdot t_2\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 3.5 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-30}:\\ \;\;\;\;y4 \cdot \left(b \cdot t_1 + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+71} \lor \neg \left(k \leq 1.9 \cdot 10^{+143}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (- (* y1 y4) (* y0 y5)))
        (t_3
         (*
          k
          (+
           (+ (* y2 t_2) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1))))))
        (t_4 (- (* c y0) (* a y1))))
   (if (<= k -3.05e+146)
     t_3
     (if (<= k -1.05e+126)
       (*
        y3
        (+
         (* y (- (* c y4) (* a y5)))
         (- (* j (- (* y0 y5) (* y1 y4))) (* z t_4))))
       (if (<= k -2e-241)
         (* y1 (+ (* i (- (* x j) (* z k))) (* a (- (* z y3) (* x y2)))))
         (if (<= k -3.9e-305)
           (* (* z t) (- (* c i) (* a b)))
           (if (<= k 5.8e-133)
             (* y2 (+ (+ (* x t_4) (* k t_2)) (* t (- (* a y5) (* c y4)))))
             (if (<= k 3.5e-103)
               (* a (* z (- (* y1 y3) (* t b))))
               (if (<= k 2.2e-97)
                 (* a (* y5 (- (* t y2) (* y y3))))
                 (if (<= k 9.5e-30)
                   (* y4 (+ (* b t_1) (* c (- (* y y3) (* t y2)))))
                   (if (or (<= k 7.8e+71) (not (<= k 1.9e+143)))
                     t_3
                     (*
                      y5
                      (- (* y0 (- (* j y3) (* k y2))) (* i t_1))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = k * (((y2 * t_2) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_4 = (c * y0) - (a * y1);
	double tmp;
	if (k <= -3.05e+146) {
		tmp = t_3;
	} else if (k <= -1.05e+126) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)));
	} else if (k <= -2e-241) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (k <= -3.9e-305) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 5.8e-133) {
		tmp = y2 * (((x * t_4) + (k * t_2)) + (t * ((a * y5) - (c * y4))));
	} else if (k <= 3.5e-103) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 2.2e-97) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 9.5e-30) {
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))));
	} else if ((k <= 7.8e+71) || !(k <= 1.9e+143)) {
		tmp = t_3;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * 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 = (t * j) - (y * k)
    t_2 = (y1 * y4) - (y0 * y5)
    t_3 = k * (((y2 * t_2) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    t_4 = (c * y0) - (a * y1)
    if (k <= (-3.05d+146)) then
        tmp = t_3
    else if (k <= (-1.05d+126)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)))
    else if (k <= (-2d-241)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
    else if (k <= (-3.9d-305)) then
        tmp = (z * t) * ((c * i) - (a * b))
    else if (k <= 5.8d-133) then
        tmp = y2 * (((x * t_4) + (k * t_2)) + (t * ((a * y5) - (c * y4))))
    else if (k <= 3.5d-103) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (k <= 2.2d-97) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (k <= 9.5d-30) then
        tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))))
    else if ((k <= 7.8d+71) .or. (.not. (k <= 1.9d+143))) then
        tmp = t_3
    else
        tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = k * (((y2 * t_2) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_4 = (c * y0) - (a * y1);
	double tmp;
	if (k <= -3.05e+146) {
		tmp = t_3;
	} else if (k <= -1.05e+126) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)));
	} else if (k <= -2e-241) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (k <= -3.9e-305) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 5.8e-133) {
		tmp = y2 * (((x * t_4) + (k * t_2)) + (t * ((a * y5) - (c * y4))));
	} else if (k <= 3.5e-103) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 2.2e-97) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 9.5e-30) {
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))));
	} else if ((k <= 7.8e+71) || !(k <= 1.9e+143)) {
		tmp = t_3;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = (y1 * y4) - (y0 * y5)
	t_3 = k * (((y2 * t_2) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	t_4 = (c * y0) - (a * y1)
	tmp = 0
	if k <= -3.05e+146:
		tmp = t_3
	elif k <= -1.05e+126:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)))
	elif k <= -2e-241:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
	elif k <= -3.9e-305:
		tmp = (z * t) * ((c * i) - (a * b))
	elif k <= 5.8e-133:
		tmp = y2 * (((x * t_4) + (k * t_2)) + (t * ((a * y5) - (c * y4))))
	elif k <= 3.5e-103:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif k <= 2.2e-97:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif k <= 9.5e-30:
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))))
	elif (k <= 7.8e+71) or not (k <= 1.9e+143):
		tmp = t_3
	else:
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(k * Float64(Float64(Float64(y2 * t_2) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (k <= -3.05e+146)
		tmp = t_3;
	elseif (k <= -1.05e+126)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(z * t_4))));
	elseif (k <= -2e-241)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (k <= -3.9e-305)
		tmp = Float64(Float64(z * t) * Float64(Float64(c * i) - Float64(a * b)));
	elseif (k <= 5.8e-133)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_4) + Float64(k * t_2)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (k <= 3.5e-103)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (k <= 2.2e-97)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (k <= 9.5e-30)
		tmp = Float64(y4 * Float64(Float64(b * t_1) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif ((k <= 7.8e+71) || !(k <= 1.9e+143))
		tmp = t_3;
	else
		tmp = Float64(y5 * Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(i * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = (y1 * y4) - (y0 * y5);
	t_3 = k * (((y2 * t_2) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	t_4 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (k <= -3.05e+146)
		tmp = t_3;
	elseif (k <= -1.05e+126)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_4)));
	elseif (k <= -2e-241)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	elseif (k <= -3.9e-305)
		tmp = (z * t) * ((c * i) - (a * b));
	elseif (k <= 5.8e-133)
		tmp = y2 * (((x * t_4) + (k * t_2)) + (t * ((a * y5) - (c * y4))));
	elseif (k <= 3.5e-103)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (k <= 2.2e-97)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (k <= 9.5e-30)
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))));
	elseif ((k <= 7.8e+71) || ~((k <= 1.9e+143)))
		tmp = t_3;
	else
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(N[(N[(y2 * t$95$2), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.05e+146], t$95$3, If[LessEqual[k, -1.05e+126], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2e-241], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.9e-305], N[(N[(z * t), $MachinePrecision] * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.8e-133], N[(y2 * N[(N[(N[(x * t$95$4), $MachinePrecision] + N[(k * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.5e-103], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.2e-97], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9.5e-30], N[(y4 * N[(N[(b * t$95$1), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 7.8e+71], N[Not[LessEqual[k, 1.9e+143]], $MachinePrecision]], t$95$3, N[(y5 * N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if k < -3.0499999999999999e146 or 9.49999999999999939e-30 < k < 7.8000000000000002e71 or 1.9e143 < k

   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. Taylor expanded in k around inf 68.7%

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

      1. sub-neg 68.7%

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

      2. +-commutative 68.7%

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

      3. mul-1-neg 68.7%

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

      4. unsub-neg 68.7%

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

      5. *-commutative 68.7%

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

      6. mul-1-neg 68.7%

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

      7. remove-double-neg 68.7%

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

   4. Simplified 68.7%

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

   if -3.0499999999999999e146 < k < -1.05e126

   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. Taylor expanded in y3 around -inf 100.0%

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

   if -1.05e126 < k < -1.9999999999999999e-241

   1. Initial program 25.6%

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

   2. Taylor expanded in y1 around -inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. *-commutative 54.5%

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

      3. distribute-rgt-neg-in 54.5%

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

   4. Simplified 54.5%

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

   5. Taylor expanded in y4 around 0 60.1%

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

   if -1.9999999999999999e-241 < k < -3.90000000000000025e-305

   1. Initial program 46.2%

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

   2. Taylor expanded in z around -inf 69.5%

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

   3. Taylor expanded in t around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. associate-*r* 77.4%

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

      3. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   if -3.90000000000000025e-305 < k < 5.7999999999999997e-133

   1. Initial program 38.2%

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

   2. Taylor expanded in y2 around inf 42.7%

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

   if 5.7999999999999997e-133 < k < 3.50000000000000016e-103

   1. Initial program 50.0%

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

   2. Taylor expanded in z around -inf 30.4%

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

   3. Taylor expanded in a around -inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

      4. *-commutative 60.7%

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

      5. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   if 3.50000000000000016e-103 < k < 2.1999999999999999e-97

   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. Taylor expanded in y4 around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 2.1999999999999999e-97 < k < 9.49999999999999939e-30

   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. Taylor expanded in y4 around inf 64.8%

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

   3. Taylor expanded in y1 around 0 65.2%

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

      1. *-commutative 65.2%

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

      2. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   if 7.8000000000000002e71 < k < 1.9e143

   1. Initial program 30.8%

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

   2. Taylor expanded in i around -inf 40.1%

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

   3. Taylor expanded in y5 around -inf 63.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.05 \cdot 10^{+146}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -1.05 \cdot 10^{+126}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;k \leq -2 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -3.9 \cdot 10^{-305}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 5.8 \cdot 10^{-133}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 3.5 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-30}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+71} \lor \neg \left(k \leq 1.9 \cdot 10^{+143}\right):\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]

Alternative 6: 41.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := b \cdot y0 - i \cdot y1\\ t_5 := k \cdot \left(\left(y2 \cdot t_3 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot t_4\right)\\ \mathbf{if}\;k \leq -2.6 \cdot 10^{+147}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq -1.25 \cdot 10^{+113}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot t_2\right)\right)\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-134}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot \left(i \cdot j\right) - j \cdot \left(y3 \cdot y4\right)\right) + \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(k \cdot t_4 + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-122}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_2 + k \cdot t_3\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{-29}:\\ \;\;\;\;y4 \cdot \left(b \cdot t_1 + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+71} \lor \neg \left(k \leq 1.75 \cdot 10^{+143}\right):\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4 (- (* b y0) (* i y1)))
        (t_5 (* k (+ (+ (* y2 t_3) (* y (- (* i y5) (* b y4)))) (* z t_4)))))
   (if (<= k -2.6e+147)
     t_5
     (if (<= k -1.25e+113)
       (*
        y3
        (+
         (* y (- (* c y4) (* a y5)))
         (- (* j (- (* y0 y5) (* y1 y4))) (* z t_2))))
       (if (<= k -1.6e-134)
         (*
          y1
          (+
           (- (* x (* i j)) (* j (* y3 y4)))
           (+ (* k (- (* y2 y4) (* z i))) (* a (- (* z y3) (* x y2))))))
         (if (<= k 4.1e-236)
           (*
            z
            (+
             (* k t_4)
             (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0))))))
           (if (<= k 2.8e-122)
             (* y2 (+ (+ (* x t_2) (* k t_3)) (* t (- (* a y5) (* c y4)))))
             (if (<= k 2.8e-103)
               (* j (* y4 (- (* t b) (* y1 y3))))
               (if (<= k 5e-80)
                 (* a (* y5 (- (* t y2) (* y y3))))
                 (if (<= k 4.6e-29)
                   (* y4 (+ (* b t_1) (* c (- (* y y3) (* t y2)))))
                   (if (or (<= k 7.8e+71) (not (<= k 1.75e+143)))
                     t_5
                     (*
                      y5
                      (- (* y0 (- (* j y3) (* k y2))) (* i t_1))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (b * y0) - (i * y1);
	double t_5 = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * t_4));
	double tmp;
	if (k <= -2.6e+147) {
		tmp = t_5;
	} else if (k <= -1.25e+113) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)));
	} else if (k <= -1.6e-134) {
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * ((z * y3) - (x * y2)))));
	} else if (k <= 4.1e-236) {
		tmp = z * ((k * t_4) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (k <= 2.8e-122) {
		tmp = y2 * (((x * t_2) + (k * t_3)) + (t * ((a * y5) - (c * y4))));
	} else if (k <= 2.8e-103) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (k <= 5e-80) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 4.6e-29) {
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))));
	} else if ((k <= 7.8e+71) || !(k <= 1.75e+143)) {
		tmp = t_5;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = (c * y0) - (a * y1)
    t_3 = (y1 * y4) - (y0 * y5)
    t_4 = (b * y0) - (i * y1)
    t_5 = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * t_4))
    if (k <= (-2.6d+147)) then
        tmp = t_5
    else if (k <= (-1.25d+113)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)))
    else if (k <= (-1.6d-134)) then
        tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * ((z * y3) - (x * y2)))))
    else if (k <= 4.1d-236) then
        tmp = z * ((k * t_4) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    else if (k <= 2.8d-122) then
        tmp = y2 * (((x * t_2) + (k * t_3)) + (t * ((a * y5) - (c * y4))))
    else if (k <= 2.8d-103) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (k <= 5d-80) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (k <= 4.6d-29) then
        tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))))
    else if ((k <= 7.8d+71) .or. (.not. (k <= 1.75d+143))) then
        tmp = t_5
    else
        tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (b * y0) - (i * y1);
	double t_5 = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * t_4));
	double tmp;
	if (k <= -2.6e+147) {
		tmp = t_5;
	} else if (k <= -1.25e+113) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)));
	} else if (k <= -1.6e-134) {
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * ((z * y3) - (x * y2)))));
	} else if (k <= 4.1e-236) {
		tmp = z * ((k * t_4) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (k <= 2.8e-122) {
		tmp = y2 * (((x * t_2) + (k * t_3)) + (t * ((a * y5) - (c * y4))));
	} else if (k <= 2.8e-103) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (k <= 5e-80) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 4.6e-29) {
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))));
	} else if ((k <= 7.8e+71) || !(k <= 1.75e+143)) {
		tmp = t_5;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = (c * y0) - (a * y1)
	t_3 = (y1 * y4) - (y0 * y5)
	t_4 = (b * y0) - (i * y1)
	t_5 = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * t_4))
	tmp = 0
	if k <= -2.6e+147:
		tmp = t_5
	elif k <= -1.25e+113:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)))
	elif k <= -1.6e-134:
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * ((z * y3) - (x * y2)))))
	elif k <= 4.1e-236:
		tmp = z * ((k * t_4) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	elif k <= 2.8e-122:
		tmp = y2 * (((x * t_2) + (k * t_3)) + (t * ((a * y5) - (c * y4))))
	elif k <= 2.8e-103:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif k <= 5e-80:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif k <= 4.6e-29:
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))))
	elif (k <= 7.8e+71) or not (k <= 1.75e+143):
		tmp = t_5
	else:
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(Float64(b * y0) - Float64(i * y1))
	t_5 = Float64(k * Float64(Float64(Float64(y2 * t_3) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * t_4)))
	tmp = 0.0
	if (k <= -2.6e+147)
		tmp = t_5;
	elseif (k <= -1.25e+113)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(z * t_2))));
	elseif (k <= -1.6e-134)
		tmp = Float64(y1 * Float64(Float64(Float64(x * Float64(i * j)) - Float64(j * Float64(y3 * y4))) + Float64(Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))));
	elseif (k <= 4.1e-236)
		tmp = Float64(z * Float64(Float64(k * t_4) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (k <= 2.8e-122)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * t_3)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (k <= 2.8e-103)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (k <= 5e-80)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (k <= 4.6e-29)
		tmp = Float64(y4 * Float64(Float64(b * t_1) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif ((k <= 7.8e+71) || !(k <= 1.75e+143))
		tmp = t_5;
	else
		tmp = Float64(y5 * Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(i * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = (c * y0) - (a * y1);
	t_3 = (y1 * y4) - (y0 * y5);
	t_4 = (b * y0) - (i * y1);
	t_5 = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * t_4));
	tmp = 0.0;
	if (k <= -2.6e+147)
		tmp = t_5;
	elseif (k <= -1.25e+113)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)));
	elseif (k <= -1.6e-134)
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * ((z * y3) - (x * y2)))));
	elseif (k <= 4.1e-236)
		tmp = z * ((k * t_4) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	elseif (k <= 2.8e-122)
		tmp = y2 * (((x * t_2) + (k * t_3)) + (t * ((a * y5) - (c * y4))));
	elseif (k <= 2.8e-103)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (k <= 5e-80)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (k <= 4.6e-29)
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))));
	elseif ((k <= 7.8e+71) || ~((k <= 1.75e+143)))
		tmp = t_5;
	else
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(k * N[(N[(N[(y2 * t$95$3), $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[k, -2.6e+147], t$95$5, If[LessEqual[k, -1.25e+113], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.6e-134], N[(y1 * N[(N[(N[(x * N[(i * j), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.1e-236], N[(z * N[(N[(k * t$95$4), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.8e-122], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.8e-103], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5e-80], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.6e-29], N[(y4 * N[(N[(b * t$95$1), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 7.8e+71], N[Not[LessEqual[k, 1.75e+143]], $MachinePrecision]], t$95$5, N[(y5 * N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if k < -2.5999999999999999e147 or 4.59999999999999982e-29 < k < 7.8000000000000002e71 or 1.75000000000000004e143 < k

   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. Taylor expanded in k around inf 68.7%

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

      1. sub-neg 68.7%

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

      2. +-commutative 68.7%

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

      3. mul-1-neg 68.7%

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

      4. unsub-neg 68.7%

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

      5. *-commutative 68.7%

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

      6. mul-1-neg 68.7%

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

      7. remove-double-neg 68.7%

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

   4. Simplified 68.7%

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

   if -2.5999999999999999e147 < k < -1.25e113

   1. Initial program 30.0%

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

   2. Taylor expanded in y3 around -inf 100.0%

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

   if -1.25e113 < k < -1.6000000000000001e-134

   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. Taylor expanded in y1 around -inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. *-commutative 53.7%

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

      3. distribute-rgt-neg-in 53.7%

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

   4. Simplified 53.7%

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

   5. Taylor expanded in k around 0 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

      4. *-commutative 60.7%

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

      5. *-commutative 60.7%

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

      6. *-commutative 60.7%

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

      7. +-commutative 60.7%

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

      8. mul-1-neg 60.7%

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

      9. unsub-neg 60.7%

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

      10. *-commutative 60.7%

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

      11. +-commutative 60.7%

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

      12. mul-1-neg 60.7%

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

   7. Simplified 63.0%

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

   if -1.6000000000000001e-134 < k < 4.1000000000000003e-236

   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. Taylor expanded in z around -inf 62.1%

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

   3. Taylor expanded in z around inf 59.4%

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

   if 4.1000000000000003e-236 < k < 2.7999999999999999e-122

   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. Taylor expanded in y2 around inf 39.4%

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

   if 2.7999999999999999e-122 < k < 2.80000000000000023e-103

   1. Initial program 66.7%

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

   2. Taylor expanded in j around inf 34.8%

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

      1. +-commutative 34.8%

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

      2. mul-1-neg 34.8%

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

      3. unsub-neg 34.8%

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

      4. *-commutative 34.8%

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

   4. Simplified 34.8%

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

   5. Taylor expanded in y4 around inf 67.3%

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

   if 2.80000000000000023e-103 < k < 5e-80

   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. Taylor expanded in y4 around inf 71.4%

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

      1. *-commutative 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in a around inf 85.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 85.7%

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

      2. *-commutative 85.7%

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

   7. Simplified 85.7%

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

   if 5e-80 < k < 4.59999999999999982e-29

   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. Taylor expanded in y4 around inf 64.0%

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

   3. Taylor expanded in y1 around 0 64.6%

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

      1. *-commutative 64.6%

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

      2. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   if 7.8000000000000002e71 < k < 1.75000000000000004e143

   1. Initial program 30.8%

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

   2. Taylor expanded in i around -inf 40.1%

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

   3. Taylor expanded in y5 around -inf 63.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.6 \cdot 10^{+147}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -1.25 \cdot 10^{+113}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-134}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot \left(i \cdot j\right) - j \cdot \left(y3 \cdot y4\right)\right) + \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;k \leq 4.1 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-122}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{-29}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+71} \lor \neg \left(k \leq 1.75 \cdot 10^{+143}\right):\\ \;\;\;\;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{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]

Alternative 7: 39.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := k \cdot \left(\left(y2 \cdot t_1 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_3 := t \cdot j - y \cdot k\\ \mathbf{if}\;k \leq -2.7 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -1.26 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -3.2 \cdot 10^{-304}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 1.62 \cdot 10^{-130}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot t_1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 3 \cdot 10^{-29}:\\ \;\;\;\;y4 \cdot \left(b \cdot t_3 + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+71} \lor \neg \left(k \leq 4.1 \cdot 10^{+143}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2
         (*
          k
          (+
           (+ (* y2 t_1) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1))))))
        (t_3 (- (* t j) (* y k))))
   (if (<= k -2.7e+132)
     t_2
     (if (<= k -1.26e-241)
       (* y1 (+ (* i (- (* x j) (* z k))) (* a (- (* z y3) (* x y2)))))
       (if (<= k -3.2e-304)
         (* (* z t) (- (* c i) (* a b)))
         (if (<= k 1.62e-130)
           (*
            y2
            (+
             (+ (* x (- (* c y0) (* a y1))) (* k t_1))
             (* t (- (* a y5) (* c y4)))))
           (if (<= k 6.2e-103)
             (* a (* z (- (* y1 y3) (* t b))))
             (if (<= k 9e-97)
               (* a (* y5 (- (* t y2) (* y y3))))
               (if (<= k 3e-29)
                 (* y4 (+ (* b t_3) (* c (- (* y y3) (* t y2)))))
                 (if (or (<= k 7.5e+71) (not (<= k 4.1e+143)))
                   t_2
                   (* y5 (- (* y0 (- (* j y3) (* k y2))) (* i 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 = (y1 * y4) - (y0 * y5);
	double t_2 = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_3 = (t * j) - (y * k);
	double tmp;
	if (k <= -2.7e+132) {
		tmp = t_2;
	} else if (k <= -1.26e-241) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (k <= -3.2e-304) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 1.62e-130) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (k <= 6.2e-103) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 9e-97) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 3e-29) {
		tmp = y4 * ((b * t_3) + (c * ((y * y3) - (t * y2))));
	} else if ((k <= 7.5e+71) || !(k <= 4.1e+143)) {
		tmp = t_2;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * 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 = (y1 * y4) - (y0 * y5)
    t_2 = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    t_3 = (t * j) - (y * k)
    if (k <= (-2.7d+132)) then
        tmp = t_2
    else if (k <= (-1.26d-241)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
    else if (k <= (-3.2d-304)) then
        tmp = (z * t) * ((c * i) - (a * b))
    else if (k <= 1.62d-130) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * ((a * y5) - (c * y4))))
    else if (k <= 6.2d-103) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (k <= 9d-97) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (k <= 3d-29) then
        tmp = y4 * ((b * t_3) + (c * ((y * y3) - (t * y2))))
    else if ((k <= 7.5d+71) .or. (.not. (k <= 4.1d+143))) then
        tmp = t_2
    else
        tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * 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 = (y1 * y4) - (y0 * y5);
	double t_2 = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_3 = (t * j) - (y * k);
	double tmp;
	if (k <= -2.7e+132) {
		tmp = t_2;
	} else if (k <= -1.26e-241) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (k <= -3.2e-304) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 1.62e-130) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (k <= 6.2e-103) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 9e-97) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 3e-29) {
		tmp = y4 * ((b * t_3) + (c * ((y * y3) - (t * y2))));
	} else if ((k <= 7.5e+71) || !(k <= 4.1e+143)) {
		tmp = t_2;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * 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 = (y1 * y4) - (y0 * y5)
	t_2 = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	t_3 = (t * j) - (y * k)
	tmp = 0
	if k <= -2.7e+132:
		tmp = t_2
	elif k <= -1.26e-241:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
	elif k <= -3.2e-304:
		tmp = (z * t) * ((c * i) - (a * b))
	elif k <= 1.62e-130:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * ((a * y5) - (c * y4))))
	elif k <= 6.2e-103:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif k <= 9e-97:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif k <= 3e-29:
		tmp = y4 * ((b * t_3) + (c * ((y * y3) - (t * y2))))
	elif (k <= 7.5e+71) or not (k <= 4.1e+143):
		tmp = t_2
	else:
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * 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(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(k * Float64(Float64(Float64(y2 * t_1) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	tmp = 0.0
	if (k <= -2.7e+132)
		tmp = t_2;
	elseif (k <= -1.26e-241)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (k <= -3.2e-304)
		tmp = Float64(Float64(z * t) * Float64(Float64(c * i) - Float64(a * b)));
	elseif (k <= 1.62e-130)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * t_1)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (k <= 6.2e-103)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (k <= 9e-97)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (k <= 3e-29)
		tmp = Float64(y4 * Float64(Float64(b * t_3) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif ((k <= 7.5e+71) || !(k <= 4.1e+143))
		tmp = t_2;
	else
		tmp = Float64(y5 * Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(i * 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 = (y1 * y4) - (y0 * y5);
	t_2 = k * (((y2 * t_1) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	t_3 = (t * j) - (y * k);
	tmp = 0.0;
	if (k <= -2.7e+132)
		tmp = t_2;
	elseif (k <= -1.26e-241)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	elseif (k <= -3.2e-304)
		tmp = (z * t) * ((c * i) - (a * b));
	elseif (k <= 1.62e-130)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * ((a * y5) - (c * y4))));
	elseif (k <= 6.2e-103)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (k <= 9e-97)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (k <= 3e-29)
		tmp = y4 * ((b * t_3) + (c * ((y * y3) - (t * y2))));
	elseif ((k <= 7.5e+71) || ~((k <= 4.1e+143)))
		tmp = t_2;
	else
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * 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[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(N[(N[(y2 * t$95$1), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.7e+132], t$95$2, If[LessEqual[k, -1.26e-241], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.2e-304], N[(N[(z * t), $MachinePrecision] * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.62e-130], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.2e-103], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9e-97], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3e-29], N[(y4 * N[(N[(b * t$95$3), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 7.5e+71], N[Not[LessEqual[k, 4.1e+143]], $MachinePrecision]], t$95$2, N[(y5 * N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -2.7e132 or 3.0000000000000003e-29 < k < 7.50000000000000007e71 or 4.1000000000000004e143 < k

   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. Taylor expanded in k around inf 68.9%

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

      1. sub-neg 68.9%

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

      2. +-commutative 68.9%

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

      3. mul-1-neg 68.9%

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

      4. unsub-neg 68.9%

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

      5. *-commutative 68.9%

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

      6. mul-1-neg 68.9%

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

      7. remove-double-neg 68.9%

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

   4. Simplified 68.9%

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

   if -2.7e132 < k < -1.26e-241

   1. Initial program 24.0%

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

   2. Taylor expanded in y1 around -inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. *-commutative 51.3%

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

      3. distribute-rgt-neg-in 51.3%

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

   4. Simplified 51.3%

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

   5. Taylor expanded in y4 around 0 56.5%

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

   if -1.26e-241 < k < -3.19999999999999999e-304

   1. Initial program 46.2%

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

   2. Taylor expanded in z around -inf 69.5%

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

   3. Taylor expanded in t around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. associate-*r* 77.4%

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

      3. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   if -3.19999999999999999e-304 < k < 1.62e-130

   1. Initial program 38.2%

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

   2. Taylor expanded in y2 around inf 42.7%

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

   if 1.62e-130 < k < 6.2000000000000003e-103

   1. Initial program 50.0%

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

   2. Taylor expanded in z around -inf 30.4%

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

   3. Taylor expanded in a around -inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

      4. *-commutative 60.7%

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

      5. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   if 6.2000000000000003e-103 < k < 9.0000000000000002e-97

   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. Taylor expanded in y4 around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 9.0000000000000002e-97 < k < 3.0000000000000003e-29

   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. Taylor expanded in y4 around inf 64.8%

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

   3. Taylor expanded in y1 around 0 65.2%

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

      1. *-commutative 65.2%

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

      2. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   if 7.50000000000000007e71 < k < 4.1000000000000004e143

   1. Initial program 30.8%

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

   2. Taylor expanded in i around -inf 40.1%

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

   3. Taylor expanded in y5 around -inf 63.1%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.7 \cdot 10^{+132}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -1.26 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -3.2 \cdot 10^{-304}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 1.62 \cdot 10^{-130}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 3 \cdot 10^{-29}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+71} \lor \neg \left(k \leq 4.1 \cdot 10^{+143}\right):\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]

Alternative 8: 40.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y3 - x \cdot y2\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := t \cdot j - y \cdot k\\ t_4 := i \cdot t_3\\ t_5 := y1 \cdot y4 - y0 \cdot y5\\ t_6 := k \cdot \left(\left(y2 \cdot t_5 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_7 := k \cdot y2 - j \cdot y3\\ \mathbf{if}\;k \leq -3.3 \cdot 10^{+146}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;k \leq -4.5 \cdot 10^{+113}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot t_2\right)\right)\\ \mathbf{elif}\;k \leq -6.2 \cdot 10^{-249}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot \left(i \cdot j\right) - j \cdot \left(y3 \cdot y4\right)\right) + \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right) + a \cdot t_1\right)\right)\\ \mathbf{elif}\;k \leq 2.75 \cdot 10^{-158}:\\ \;\;\;\;t_7 \cdot t_5 + y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - c \cdot t_1\right)\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-135}:\\ \;\;\;\;y2 \cdot \left(x \cdot t_2\right)\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{-95}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(t_4 + y0 \cdot t_7\right)\right)\\ \mathbf{elif}\;k \leq 2.25 \cdot 10^{-29}:\\ \;\;\;\;y4 \cdot \left(b \cdot t_3 + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+71} \lor \neg \left(k \leq 2.3 \cdot 10^{+146}\right):\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - t_4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z y3) (* x y2)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* t j) (* y k)))
        (t_4 (* i t_3))
        (t_5 (- (* y1 y4) (* y0 y5)))
        (t_6
         (*
          k
          (+
           (+ (* y2 t_5) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1))))))
        (t_7 (- (* k y2) (* j y3))))
   (if (<= k -3.3e+146)
     t_6
     (if (<= k -4.5e+113)
       (*
        y3
        (+
         (* y (- (* c y4) (* a y5)))
         (- (* j (- (* y0 y5) (* y1 y4))) (* z t_2))))
       (if (<= k -6.2e-249)
         (*
          y1
          (+
           (- (* x (* i j)) (* j (* y3 y4)))
           (+ (* k (- (* y2 y4) (* z i))) (* a t_1))))
         (if (<= k 2.75e-158)
           (+ (* t_7 t_5) (* y0 (- (* b (- (* z k) (* x j))) (* c t_1))))
           (if (<= k 3.9e-135)
             (* y2 (* x t_2))
             (if (<= k 1.2e-95)
               (* y5 (- (* a (- (* t y2) (* y y3))) (+ t_4 (* y0 t_7))))
               (if (<= k 2.25e-29)
                 (* y4 (+ (* b t_3) (* c (- (* y y3) (* t y2)))))
                 (if (or (<= k 7.8e+71) (not (<= k 2.3e+146)))
                   t_6
                   (* y5 (- (* y0 (- (* j y3) (* k y2))) 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 = (z * y3) - (x * y2);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (t * j) - (y * k);
	double t_4 = i * t_3;
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_7 = (k * y2) - (j * y3);
	double tmp;
	if (k <= -3.3e+146) {
		tmp = t_6;
	} else if (k <= -4.5e+113) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)));
	} else if (k <= -6.2e-249) {
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)));
	} else if (k <= 2.75e-158) {
		tmp = (t_7 * t_5) + (y0 * ((b * ((z * k) - (x * j))) - (c * t_1)));
	} else if (k <= 3.9e-135) {
		tmp = y2 * (x * t_2);
	} else if (k <= 1.2e-95) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (t_4 + (y0 * t_7)));
	} else if (k <= 2.25e-29) {
		tmp = y4 * ((b * t_3) + (c * ((y * y3) - (t * y2))));
	} else if ((k <= 7.8e+71) || !(k <= 2.3e+146)) {
		tmp = t_6;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - t_4);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (z * y3) - (x * y2)
    t_2 = (c * y0) - (a * y1)
    t_3 = (t * j) - (y * k)
    t_4 = i * t_3
    t_5 = (y1 * y4) - (y0 * y5)
    t_6 = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    t_7 = (k * y2) - (j * y3)
    if (k <= (-3.3d+146)) then
        tmp = t_6
    else if (k <= (-4.5d+113)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)))
    else if (k <= (-6.2d-249)) then
        tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)))
    else if (k <= 2.75d-158) then
        tmp = (t_7 * t_5) + (y0 * ((b * ((z * k) - (x * j))) - (c * t_1)))
    else if (k <= 3.9d-135) then
        tmp = y2 * (x * t_2)
    else if (k <= 1.2d-95) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) - (t_4 + (y0 * t_7)))
    else if (k <= 2.25d-29) then
        tmp = y4 * ((b * t_3) + (c * ((y * y3) - (t * y2))))
    else if ((k <= 7.8d+71) .or. (.not. (k <= 2.3d+146))) then
        tmp = t_6
    else
        tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - 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 = (z * y3) - (x * y2);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (t * j) - (y * k);
	double t_4 = i * t_3;
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_7 = (k * y2) - (j * y3);
	double tmp;
	if (k <= -3.3e+146) {
		tmp = t_6;
	} else if (k <= -4.5e+113) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)));
	} else if (k <= -6.2e-249) {
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)));
	} else if (k <= 2.75e-158) {
		tmp = (t_7 * t_5) + (y0 * ((b * ((z * k) - (x * j))) - (c * t_1)));
	} else if (k <= 3.9e-135) {
		tmp = y2 * (x * t_2);
	} else if (k <= 1.2e-95) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (t_4 + (y0 * t_7)));
	} else if (k <= 2.25e-29) {
		tmp = y4 * ((b * t_3) + (c * ((y * y3) - (t * y2))));
	} else if ((k <= 7.8e+71) || !(k <= 2.3e+146)) {
		tmp = t_6;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - 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 = (z * y3) - (x * y2)
	t_2 = (c * y0) - (a * y1)
	t_3 = (t * j) - (y * k)
	t_4 = i * t_3
	t_5 = (y1 * y4) - (y0 * y5)
	t_6 = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	t_7 = (k * y2) - (j * y3)
	tmp = 0
	if k <= -3.3e+146:
		tmp = t_6
	elif k <= -4.5e+113:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)))
	elif k <= -6.2e-249:
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)))
	elif k <= 2.75e-158:
		tmp = (t_7 * t_5) + (y0 * ((b * ((z * k) - (x * j))) - (c * t_1)))
	elif k <= 3.9e-135:
		tmp = y2 * (x * t_2)
	elif k <= 1.2e-95:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (t_4 + (y0 * t_7)))
	elif k <= 2.25e-29:
		tmp = y4 * ((b * t_3) + (c * ((y * y3) - (t * y2))))
	elif (k <= 7.8e+71) or not (k <= 2.3e+146):
		tmp = t_6
	else:
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - 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(z * y3) - Float64(x * y2))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	t_4 = Float64(i * t_3)
	t_5 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_6 = Float64(k * Float64(Float64(Float64(y2 * t_5) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_7 = Float64(Float64(k * y2) - Float64(j * y3))
	tmp = 0.0
	if (k <= -3.3e+146)
		tmp = t_6;
	elseif (k <= -4.5e+113)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(z * t_2))));
	elseif (k <= -6.2e-249)
		tmp = Float64(y1 * Float64(Float64(Float64(x * Float64(i * j)) - Float64(j * Float64(y3 * y4))) + Float64(Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))) + Float64(a * t_1))));
	elseif (k <= 2.75e-158)
		tmp = Float64(Float64(t_7 * t_5) + Float64(y0 * Float64(Float64(b * Float64(Float64(z * k) - Float64(x * j))) - Float64(c * t_1))));
	elseif (k <= 3.9e-135)
		tmp = Float64(y2 * Float64(x * t_2));
	elseif (k <= 1.2e-95)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(t_4 + Float64(y0 * t_7))));
	elseif (k <= 2.25e-29)
		tmp = Float64(y4 * Float64(Float64(b * t_3) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif ((k <= 7.8e+71) || !(k <= 2.3e+146))
		tmp = t_6;
	else
		tmp = Float64(y5 * Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - 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 = (z * y3) - (x * y2);
	t_2 = (c * y0) - (a * y1);
	t_3 = (t * j) - (y * k);
	t_4 = i * t_3;
	t_5 = (y1 * y4) - (y0 * y5);
	t_6 = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	t_7 = (k * y2) - (j * y3);
	tmp = 0.0;
	if (k <= -3.3e+146)
		tmp = t_6;
	elseif (k <= -4.5e+113)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * t_2)));
	elseif (k <= -6.2e-249)
		tmp = y1 * (((x * (i * j)) - (j * (y3 * y4))) + ((k * ((y2 * y4) - (z * i))) + (a * t_1)));
	elseif (k <= 2.75e-158)
		tmp = (t_7 * t_5) + (y0 * ((b * ((z * k) - (x * j))) - (c * t_1)));
	elseif (k <= 3.9e-135)
		tmp = y2 * (x * t_2);
	elseif (k <= 1.2e-95)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (t_4 + (y0 * t_7)));
	elseif (k <= 2.25e-29)
		tmp = y4 * ((b * t_3) + (c * ((y * y3) - (t * y2))));
	elseif ((k <= 7.8e+71) || ~((k <= 2.3e+146)))
		tmp = t_6;
	else
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - 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[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(i * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = 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 * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.3e+146], t$95$6, If[LessEqual[k, -4.5e+113], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -6.2e-249], N[(y1 * N[(N[(N[(x * N[(i * j), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.75e-158], N[(N[(t$95$7 * t$95$5), $MachinePrecision] + N[(y0 * N[(N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.9e-135], N[(y2 * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.2e-95], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$4 + N[(y0 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.25e-29], N[(y4 * N[(N[(b * t$95$3), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 7.8e+71], N[Not[LessEqual[k, 2.3e+146]], $MachinePrecision]], t$95$6, N[(y5 * N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -3.30000000000000016e146 or 2.2499999999999999e-29 < k < 7.8000000000000002e71 or 2.3e146 < k

   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. Taylor expanded in k around inf 68.7%

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

      1. sub-neg 68.7%

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

      2. +-commutative 68.7%

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

      3. mul-1-neg 68.7%

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

      4. unsub-neg 68.7%

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

      5. *-commutative 68.7%

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

      6. mul-1-neg 68.7%

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

      7. remove-double-neg 68.7%

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

   4. Simplified 68.7%

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

   if -3.30000000000000016e146 < k < -4.5000000000000001e113

   1. Initial program 30.0%

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

   2. Taylor expanded in y3 around -inf 100.0%

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

   if -4.5000000000000001e113 < k < -6.19999999999999971e-249

   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. Taylor expanded in y1 around -inf 52.9%

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

      1. mul-1-neg 52.9%

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

      2. *-commutative 52.9%

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

      3. distribute-rgt-neg-in 52.9%

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

   4. Simplified 52.9%

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

   5. Taylor expanded in k around 0 59.6%

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

      1. +-commutative 59.6%

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

      2. mul-1-neg 59.6%

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

      3. unsub-neg 59.6%

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

      4. *-commutative 59.6%

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

      5. *-commutative 59.6%

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

      6. *-commutative 59.6%

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

      7. +-commutative 59.6%

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

      8. mul-1-neg 59.6%

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

      9. unsub-neg 59.6%

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

      10. *-commutative 59.6%

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

      11. +-commutative 59.6%

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

      12. mul-1-neg 59.6%

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

   7. Simplified 59.6%

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

   if -6.19999999999999971e-249 < k < 2.75000000000000013e-158

   1. Initial program 39.6%

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

   2. Taylor expanded in y0 around inf 55.6%

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

      1. *-commutative 55.6%

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

      2. *-commutative 55.6%

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

      3. *-commutative 55.6%

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

   4. Simplified 55.6%

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

   if 2.75000000000000013e-158 < k < 3.90000000000000022e-135

   1. Initial program 42.9%

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

   2. Taylor expanded in y2 around inf 44.1%

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

   3. Taylor expanded in x around inf 72.2%

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

   if 3.90000000000000022e-135 < k < 1.2e-95

   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. Taylor expanded in y5 around -inf 64.9%

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

   if 1.2e-95 < k < 2.2499999999999999e-29

   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. Taylor expanded in y4 around inf 64.8%

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

   3. Taylor expanded in y1 around 0 65.2%

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

      1. *-commutative 65.2%

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

      2. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   if 7.8000000000000002e71 < k < 2.3e146

   1. Initial program 30.8%

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

   2. Taylor expanded in i around -inf 40.1%

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

   3. Taylor expanded in y5 around -inf 63.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.3 \cdot 10^{+146}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -4.5 \cdot 10^{+113}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;k \leq -6.2 \cdot 10^{-249}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot \left(i \cdot j\right) - j \cdot \left(y3 \cdot y4\right)\right) + \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.75 \cdot 10^{-158}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-135}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{-95}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.25 \cdot 10^{-29}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+71} \lor \neg \left(k \leq 2.3 \cdot 10^{+146}\right):\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]

Alternative 9: 40.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := i \cdot t_1\\ t_3 := b \cdot y0 - i \cdot y1\\ t_4 := k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot t_3\right)\\ \mathbf{if}\;k \leq -3.7 \cdot 10^{+146}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq -5.8 \cdot 10^{+125}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;k \leq -2.2 \cdot 10^{-229}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-136}:\\ \;\;\;\;z \cdot \left(k \cdot t_3 + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-97}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(t_2 + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-29}:\\ \;\;\;\;y4 \cdot \left(b \cdot t_1 + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+71} \lor \neg \left(k \leq 1.75 \cdot 10^{+143}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (* i t_1))
        (t_3 (- (* b y0) (* i y1)))
        (t_4
         (*
          k
          (+
           (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* i y5) (* b y4))))
           (* z t_3)))))
   (if (<= k -3.7e+146)
     t_4
     (if (<= k -5.8e+125)
       (*
        y3
        (+
         (* y (- (* c y4) (* a y5)))
         (- (* j (- (* y0 y5) (* y1 y4))) (* z (- (* c y0) (* a y1))))))
       (if (<= k -2.2e-229)
         (* y1 (+ (* i (- (* x j) (* z k))) (* a (- (* z y3) (* x y2)))))
         (if (<= k 4.8e-136)
           (*
            z
            (+
             (* k t_3)
             (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0))))))
           (if (<= k 9.5e-97)
             (*
              y5
              (-
               (* a (- (* t y2) (* y y3)))
               (+ t_2 (* y0 (- (* k y2) (* j y3))))))
             (if (<= k 2.9e-29)
               (* y4 (+ (* b t_1) (* c (- (* y y3) (* t y2)))))
               (if (or (<= k 7.8e+71) (not (<= k 1.75e+143)))
                 t_4
                 (* y5 (- (* y0 (- (* j y3) (* k y2))) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = i * t_1;
	double t_3 = (b * y0) - (i * y1);
	double t_4 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_3));
	double tmp;
	if (k <= -3.7e+146) {
		tmp = t_4;
	} else if (k <= -5.8e+125) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * ((c * y0) - (a * y1)))));
	} else if (k <= -2.2e-229) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (k <= 4.8e-136) {
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (k <= 9.5e-97) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (t_2 + (y0 * ((k * y2) - (j * y3)))));
	} else if (k <= 2.9e-29) {
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))));
	} else if ((k <= 7.8e+71) || !(k <= 1.75e+143)) {
		tmp = t_4;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - 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) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = i * t_1
    t_3 = (b * y0) - (i * y1)
    t_4 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_3))
    if (k <= (-3.7d+146)) then
        tmp = t_4
    else if (k <= (-5.8d+125)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * ((c * y0) - (a * y1)))))
    else if (k <= (-2.2d-229)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
    else if (k <= 4.8d-136) then
        tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    else if (k <= 9.5d-97) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) - (t_2 + (y0 * ((k * y2) - (j * y3)))))
    else if (k <= 2.9d-29) then
        tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))))
    else if ((k <= 7.8d+71) .or. (.not. (k <= 1.75d+143))) then
        tmp = t_4
    else
        tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = i * t_1;
	double t_3 = (b * y0) - (i * y1);
	double t_4 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_3));
	double tmp;
	if (k <= -3.7e+146) {
		tmp = t_4;
	} else if (k <= -5.8e+125) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * ((c * y0) - (a * y1)))));
	} else if (k <= -2.2e-229) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (k <= 4.8e-136) {
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	} else if (k <= 9.5e-97) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (t_2 + (y0 * ((k * y2) - (j * y3)))));
	} else if (k <= 2.9e-29) {
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))));
	} else if ((k <= 7.8e+71) || !(k <= 1.75e+143)) {
		tmp = t_4;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = i * t_1
	t_3 = (b * y0) - (i * y1)
	t_4 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_3))
	tmp = 0
	if k <= -3.7e+146:
		tmp = t_4
	elif k <= -5.8e+125:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * ((c * y0) - (a * y1)))))
	elif k <= -2.2e-229:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
	elif k <= 4.8e-136:
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	elif k <= 9.5e-97:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (t_2 + (y0 * ((k * y2) - (j * y3)))))
	elif k <= 2.9e-29:
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))))
	elif (k <= 7.8e+71) or not (k <= 1.75e+143):
		tmp = t_4
	else:
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(i * t_1)
	t_3 = Float64(Float64(b * y0) - Float64(i * y1))
	t_4 = 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)))
	tmp = 0.0
	if (k <= -3.7e+146)
		tmp = t_4;
	elseif (k <= -5.8e+125)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (k <= -2.2e-229)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (k <= 4.8e-136)
		tmp = Float64(z * Float64(Float64(k * t_3) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (k <= 9.5e-97)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(t_2 + Float64(y0 * Float64(Float64(k * y2) - Float64(j * y3))))));
	elseif (k <= 2.9e-29)
		tmp = Float64(y4 * Float64(Float64(b * t_1) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif ((k <= 7.8e+71) || !(k <= 1.75e+143))
		tmp = t_4;
	else
		tmp = Float64(y5 * Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = i * t_1;
	t_3 = (b * y0) - (i * y1);
	t_4 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * t_3));
	tmp = 0.0;
	if (k <= -3.7e+146)
		tmp = t_4;
	elseif (k <= -5.8e+125)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) - (z * ((c * y0) - (a * y1)))));
	elseif (k <= -2.2e-229)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	elseif (k <= 4.8e-136)
		tmp = z * ((k * t_3) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	elseif (k <= 9.5e-97)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) - (t_2 + (y0 * ((k * y2) - (j * y3)))));
	elseif (k <= 2.9e-29)
		tmp = y4 * ((b * t_1) + (c * ((y * y3) - (t * y2))));
	elseif ((k <= 7.8e+71) || ~((k <= 1.75e+143)))
		tmp = t_4;
	else
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = 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[k, -3.7e+146], t$95$4, If[LessEqual[k, -5.8e+125], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.2e-229], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.8e-136], N[(z * N[(N[(k * t$95$3), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9.5e-97], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$2 + N[(y0 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.9e-29], N[(y4 * N[(N[(b * t$95$1), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 7.8e+71], N[Not[LessEqual[k, 1.75e+143]], $MachinePrecision]], t$95$4, N[(y5 * N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -3.70000000000000004e146 or 2.90000000000000024e-29 < k < 7.8000000000000002e71 or 1.75000000000000004e143 < k

   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. Taylor expanded in k around inf 68.7%

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

      1. sub-neg 68.7%

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

      2. +-commutative 68.7%

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

      3. mul-1-neg 68.7%

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

      4. unsub-neg 68.7%

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

      5. *-commutative 68.7%

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

      6. mul-1-neg 68.7%

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

      7. remove-double-neg 68.7%

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

   4. Simplified 68.7%

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

   if -3.70000000000000004e146 < k < -5.79999999999999986e125

   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. Taylor expanded in y3 around -inf 100.0%

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

   if -5.79999999999999986e125 < k < -2.1999999999999999e-229

   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. Taylor expanded in y1 around -inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. *-commutative 54.6%

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

      3. distribute-rgt-neg-in 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in y4 around 0 60.5%

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

   if -2.1999999999999999e-229 < k < 4.7999999999999997e-136

   1. Initial program 39.7%

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

   2. Taylor expanded in z around -inf 54.0%

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

   3. Taylor expanded in z around inf 47.1%

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

   if 4.7999999999999997e-136 < k < 9.5000000000000001e-97

   1. Initial program 53.3%

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

   2. Taylor expanded in y5 around -inf 60.8%

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

   if 9.5000000000000001e-97 < k < 2.90000000000000024e-29

   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. Taylor expanded in y4 around inf 64.8%

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

   3. Taylor expanded in y1 around 0 65.2%

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

      1. *-commutative 65.2%

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

      2. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   if 7.8000000000000002e71 < k < 1.75000000000000004e143

   1. Initial program 30.8%

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

   2. Taylor expanded in i around -inf 40.1%

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

   3. Taylor expanded in y5 around -inf 63.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.7 \cdot 10^{+146}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -5.8 \cdot 10^{+125}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;k \leq -2.2 \cdot 10^{-229}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-136}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-97}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-29}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+71} \lor \neg \left(k \leq 1.75 \cdot 10^{+143}\right):\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]

Alternative 10: 34.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot k - c \cdot y3\\ t_2 := y0 \cdot \left(z \cdot t_1 - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ t_3 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{if}\;k \leq -4 \cdot 10^{+184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -1.4 \cdot 10^{+159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -1.02 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -1.5 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -2.5 \cdot 10^{-308}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{-180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 10^{+144}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{+179}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+260}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b k) (* c y3)))
        (t_2 (* y0 (- (* z t_1) (* y5 (- (* k y2) (* j y3))))))
        (t_3
         (*
          y2
          (-
           (+ (* k (- (* y1 y4) (* y0 y5))) (* c (* x y0)))
           (* c (* t y4))))))
   (if (<= k -4e+184)
     t_2
     (if (<= k -1.4e+159)
       t_3
       (if (<= k -1.02e+123)
         t_2
         (if (<= k -1.5e-241)
           (* y1 (+ (* i (- (* x j) (* z k))) (* a (- (* z y3) (* x y2)))))
           (if (<= k -2.5e-308)
             (* (* z t) (- (* c i) (* a b)))
             (if (<= k 1.05e-180)
               t_3
               (if (<= k 1e+144)
                 (*
                  j
                  (+
                   (+
                    (* t (- (* b y4) (* i y5)))
                    (* y3 (- (* y0 y5) (* y1 y4))))
                   (* x (- (* i y1) (* b y0)))))
                 (if (<= k 9e+179)
                   (* y1 (* k (- (* y2 y4) (* z i))))
                   (if (<= k 1.35e+260)
                     (* (* z y0) t_1)
                     (* i (* z (- (* t c) (* k 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 * k) - (c * y3);
	double t_2 = y0 * ((z * t_1) - (y5 * ((k * y2) - (j * y3))));
	double t_3 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)));
	double tmp;
	if (k <= -4e+184) {
		tmp = t_2;
	} else if (k <= -1.4e+159) {
		tmp = t_3;
	} else if (k <= -1.02e+123) {
		tmp = t_2;
	} else if (k <= -1.5e-241) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (k <= -2.5e-308) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 1.05e-180) {
		tmp = t_3;
	} else if (k <= 1e+144) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (k <= 9e+179) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (k <= 1.35e+260) {
		tmp = (z * y0) * t_1;
	} else {
		tmp = i * (z * ((t * c) - (k * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * k) - (c * y3)
    t_2 = y0 * ((z * t_1) - (y5 * ((k * y2) - (j * y3))))
    t_3 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)))
    if (k <= (-4d+184)) then
        tmp = t_2
    else if (k <= (-1.4d+159)) then
        tmp = t_3
    else if (k <= (-1.02d+123)) then
        tmp = t_2
    else if (k <= (-1.5d-241)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
    else if (k <= (-2.5d-308)) then
        tmp = (z * t) * ((c * i) - (a * b))
    else if (k <= 1.05d-180) then
        tmp = t_3
    else if (k <= 1d+144) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else if (k <= 9d+179) then
        tmp = y1 * (k * ((y2 * y4) - (z * i)))
    else if (k <= 1.35d+260) then
        tmp = (z * y0) * t_1
    else
        tmp = i * (z * ((t * c) - (k * 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 * k) - (c * y3);
	double t_2 = y0 * ((z * t_1) - (y5 * ((k * y2) - (j * y3))));
	double t_3 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)));
	double tmp;
	if (k <= -4e+184) {
		tmp = t_2;
	} else if (k <= -1.4e+159) {
		tmp = t_3;
	} else if (k <= -1.02e+123) {
		tmp = t_2;
	} else if (k <= -1.5e-241) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (k <= -2.5e-308) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 1.05e-180) {
		tmp = t_3;
	} else if (k <= 1e+144) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (k <= 9e+179) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (k <= 1.35e+260) {
		tmp = (z * y0) * t_1;
	} else {
		tmp = i * (z * ((t * c) - (k * 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 * k) - (c * y3)
	t_2 = y0 * ((z * t_1) - (y5 * ((k * y2) - (j * y3))))
	t_3 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)))
	tmp = 0
	if k <= -4e+184:
		tmp = t_2
	elif k <= -1.4e+159:
		tmp = t_3
	elif k <= -1.02e+123:
		tmp = t_2
	elif k <= -1.5e-241:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
	elif k <= -2.5e-308:
		tmp = (z * t) * ((c * i) - (a * b))
	elif k <= 1.05e-180:
		tmp = t_3
	elif k <= 1e+144:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	elif k <= 9e+179:
		tmp = y1 * (k * ((y2 * y4) - (z * i)))
	elif k <= 1.35e+260:
		tmp = (z * y0) * t_1
	else:
		tmp = i * (z * ((t * c) - (k * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * k) - Float64(c * y3))
	t_2 = Float64(y0 * Float64(Float64(z * t_1) - Float64(y5 * Float64(Float64(k * y2) - Float64(j * y3)))))
	t_3 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(c * Float64(x * y0))) - Float64(c * Float64(t * y4))))
	tmp = 0.0
	if (k <= -4e+184)
		tmp = t_2;
	elseif (k <= -1.4e+159)
		tmp = t_3;
	elseif (k <= -1.02e+123)
		tmp = t_2;
	elseif (k <= -1.5e-241)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (k <= -2.5e-308)
		tmp = Float64(Float64(z * t) * Float64(Float64(c * i) - Float64(a * b)));
	elseif (k <= 1.05e-180)
		tmp = t_3;
	elseif (k <= 1e+144)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (k <= 9e+179)
		tmp = Float64(y1 * Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (k <= 1.35e+260)
		tmp = Float64(Float64(z * y0) * t_1);
	else
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * 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 * k) - (c * y3);
	t_2 = y0 * ((z * t_1) - (y5 * ((k * y2) - (j * y3))));
	t_3 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)));
	tmp = 0.0;
	if (k <= -4e+184)
		tmp = t_2;
	elseif (k <= -1.4e+159)
		tmp = t_3;
	elseif (k <= -1.02e+123)
		tmp = t_2;
	elseif (k <= -1.5e-241)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	elseif (k <= -2.5e-308)
		tmp = (z * t) * ((c * i) - (a * b));
	elseif (k <= 1.05e-180)
		tmp = t_3;
	elseif (k <= 1e+144)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	elseif (k <= 9e+179)
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	elseif (k <= 1.35e+260)
		tmp = (z * y0) * t_1;
	else
		tmp = i * (z * ((t * c) - (k * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(N[(z * t$95$1), $MachinePrecision] - N[(y5 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -4e+184], t$95$2, If[LessEqual[k, -1.4e+159], t$95$3, If[LessEqual[k, -1.02e+123], t$95$2, If[LessEqual[k, -1.5e-241], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.5e-308], N[(N[(z * t), $MachinePrecision] * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.05e-180], t$95$3, If[LessEqual[k, 1e+144], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9e+179], N[(y1 * N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.35e+260], N[(N[(z * y0), $MachinePrecision] * t$95$1), $MachinePrecision], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -4.00000000000000007e184 or -1.4000000000000001e159 < k < -1.02e123

   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. Taylor expanded in z around -inf 54.3%

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

   3. Taylor expanded in y0 around inf 63.4%

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

   if -4.00000000000000007e184 < k < -1.4000000000000001e159 or -2.49999999999999977e-308 < k < 1.0499999999999999e-180

   1. Initial program 32.5%

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

   2. Taylor expanded in y2 around inf 58.0%

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

   3. Taylor expanded in a around 0 57.8%

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

   if -1.02e123 < k < -1.5e-241

   1. Initial program 25.6%

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

   2. Taylor expanded in y1 around -inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. *-commutative 54.5%

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

      3. distribute-rgt-neg-in 54.5%

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

   4. Simplified 54.5%

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

   5. Taylor expanded in y4 around 0 60.1%

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

   if -1.5e-241 < k < -2.49999999999999977e-308

   1. Initial program 46.2%

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

   2. Taylor expanded in z around -inf 69.5%

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

   3. Taylor expanded in t around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. associate-*r* 77.4%

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

      3. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   if 1.0499999999999999e-180 < k < 1.00000000000000002e144

   1. Initial program 39.0%

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

   2. Taylor expanded in j around inf 47.4%

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

      1. +-commutative 47.4%

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

      2. mul-1-neg 47.4%

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

      3. unsub-neg 47.4%

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

      4. *-commutative 47.4%

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

   4. Simplified 47.4%

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

   if 1.00000000000000002e144 < k < 9.0000000000000005e179

   1. Initial program 17.1%

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

   2. Taylor expanded in y1 around -inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. *-commutative 44.8%

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

      3. distribute-rgt-neg-in 44.8%

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

   4. Simplified 44.8%

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

   5. Taylor expanded in k around -inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. *-commutative 56.2%

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

   7. Simplified 56.2%

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

   if 9.0000000000000005e179 < k < 1.3499999999999999e260

   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. Taylor expanded in z around -inf 31.7%

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

   3. Taylor expanded in z around inf 56.9%

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

   4. Taylor expanded in y0 around inf 63.3%

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

      1. associate-*r* 63.2%

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

      2. *-commutative 63.2%

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

      3. *-commutative 63.2%

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

   6. Simplified 63.2%

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

   if 1.3499999999999999e260 < k

   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. Taylor expanded in z around -inf 33.3%

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

   3. Taylor expanded in i around -inf 67.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -4 \cdot 10^{+184}:\\ \;\;\;\;y0 \cdot \left(z \cdot \left(b \cdot k - c \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -1.4 \cdot 10^{+159}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.02 \cdot 10^{+123}:\\ \;\;\;\;y0 \cdot \left(z \cdot \left(b \cdot k - c \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -1.5 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -2.5 \cdot 10^{-308}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{-180}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 10^{+144}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{+179}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+260}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \end{array} \]

Alternative 11: 41.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{if}\;k \leq -5.2 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -4.7 \cdot 10^{-243}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3.5 \cdot 10^{-29}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+71} \lor \neg \left(k \leq 1.75 \cdot 10^{+143}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          k
          (+
           (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1)))))))
   (if (<= k -5.2e+131)
     t_1
     (if (<= k -4.7e-243)
       (* y1 (+ (* i (- (* x j) (* z k))) (* a (- (* z y3) (* x y2)))))
       (if (<= k 3.5e-29)
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0)))))
         (if (or (<= k 7.5e+71) (not (<= k 1.75e+143)))
           t_1
           (*
            y5
            (- (* y0 (- (* j y3) (* k y2))) (* i (- (* t j) (* y k)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double tmp;
	if (k <= -5.2e+131) {
		tmp = t_1;
	} else if (k <= -4.7e-243) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (k <= 3.5e-29) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if ((k <= 7.5e+71) || !(k <= 1.75e+143)) {
		tmp = t_1;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * ((t * j) - (y * k))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    if (k <= (-5.2d+131)) then
        tmp = t_1
    else if (k <= (-4.7d-243)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
    else if (k <= 3.5d-29) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else if ((k <= 7.5d+71) .or. (.not. (k <= 1.75d+143))) then
        tmp = t_1
    else
        tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * ((t * j) - (y * k))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double tmp;
	if (k <= -5.2e+131) {
		tmp = t_1;
	} else if (k <= -4.7e-243) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (k <= 3.5e-29) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if ((k <= 7.5e+71) || !(k <= 1.75e+143)) {
		tmp = t_1;
	} else {
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * ((t * j) - (y * k))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	tmp = 0
	if k <= -5.2e+131:
		tmp = t_1
	elif k <= -4.7e-243:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
	elif k <= 3.5e-29:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	elif (k <= 7.5e+71) or not (k <= 1.75e+143):
		tmp = t_1
	else:
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * ((t * j) - (y * k))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	tmp = 0.0
	if (k <= -5.2e+131)
		tmp = t_1;
	elseif (k <= -4.7e-243)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (k <= 3.5e-29)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif ((k <= 7.5e+71) || !(k <= 1.75e+143))
		tmp = t_1;
	else
		tmp = Float64(y5 * Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(i * Float64(Float64(t * j) - Float64(y * k)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	tmp = 0.0;
	if (k <= -5.2e+131)
		tmp = t_1;
	elseif (k <= -4.7e-243)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	elseif (k <= 3.5e-29)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	elseif ((k <= 7.5e+71) || ~((k <= 1.75e+143)))
		tmp = t_1;
	else
		tmp = y5 * ((y0 * ((j * y3) - (k * y2))) - (i * ((t * j) - (y * k))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -5.2e+131], t$95$1, If[LessEqual[k, -4.7e-243], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.5e-29], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 7.5e+71], N[Not[LessEqual[k, 1.75e+143]], $MachinePrecision]], t$95$1, N[(y5 * N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -5.2e131 or 3.4999999999999997e-29 < k < 7.50000000000000007e71 or 1.75000000000000004e143 < k

   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. Taylor expanded in k around inf 68.9%

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

      1. sub-neg 68.9%

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

      2. +-commutative 68.9%

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

      3. mul-1-neg 68.9%

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

      4. unsub-neg 68.9%

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

      5. *-commutative 68.9%

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

      6. mul-1-neg 68.9%

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

      7. remove-double-neg 68.9%

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

   4. Simplified 68.9%

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

   if -5.2e131 < k < -4.7000000000000004e-243

   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. Taylor expanded in y1 around -inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. *-commutative 50.5%

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

      3. distribute-rgt-neg-in 50.5%

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

   4. Simplified 50.5%

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

   5. Taylor expanded in y4 around 0 55.6%

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

   if -4.7000000000000004e-243 < k < 3.4999999999999997e-29

   1. Initial program 39.5%

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

   2. Taylor expanded in j around inf 44.7%

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

      1. +-commutative 44.7%

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

      2. mul-1-neg 44.7%

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

      3. unsub-neg 44.7%

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

      4. *-commutative 44.7%

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

   4. Simplified 44.7%

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

   if 7.50000000000000007e71 < k < 1.75000000000000004e143

   1. Initial program 30.8%

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

   2. Taylor expanded in i around -inf 40.1%

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

   3. Taylor expanded in y5 around -inf 63.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.2 \cdot 10^{+131}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -4.7 \cdot 10^{-243}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3.5 \cdot 10^{-29}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+71} \lor \neg \left(k \leq 1.75 \cdot 10^{+143}\right):\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]

Alternative 12: 34.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+78}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+32}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-33}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-43}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(-y2 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-53}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-185}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-182}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+40}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(k \cdot y0 - t \cdot a\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+79}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+117}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* y4 (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3)))))))
   (if (<= z -3e+78)
     (* a (* z (- (* y1 y3) (* t b))))
     (if (<= z -4.2e+32)
       (* (* j y0) (- (* y3 y5) (* x b)))
       (if (<= z -5.8e-33)
         (* (* z t) (- (* c i) (* a b)))
         (if (<= z -1.28e-43)
           (* k (* y0 (- (* y2 y5))))
           (if (<= z -3.45e-53)
             (* i (* y1 (- (* x j) (* z k))))
             (if (<= z -2.9e-185)
               (* y2 (* x (- (* c y0) (* a y1))))
               (if (<= z 3.2e-198)
                 t_1
                 (if (<= z 1e-182)
                   (* y1 (* y2 (- (* k y4) (* x a))))
                   (if (<= z 1.45e-17)
                     t_1
                     (if (<= z 5.8e+40)
                       (* (* z b) (- (* k y0) (* t a)))
                       (if (<= z 6.5e+79)
                         (* y1 (* z (- (* a y3) (* i k))))
                         (if (<= z 8.6e+117)
                           (* c (* y2 (- (* x y0) (* t y4))))
                           (* i (* z (- (* t c) (* k 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 = y4 * ((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3))));
	double tmp;
	if (z <= -3e+78) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (z <= -4.2e+32) {
		tmp = (j * y0) * ((y3 * y5) - (x * b));
	} else if (z <= -5.8e-33) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (z <= -1.28e-43) {
		tmp = k * (y0 * -(y2 * y5));
	} else if (z <= -3.45e-53) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (z <= -2.9e-185) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (z <= 3.2e-198) {
		tmp = t_1;
	} else if (z <= 1e-182) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (z <= 1.45e-17) {
		tmp = t_1;
	} else if (z <= 5.8e+40) {
		tmp = (z * b) * ((k * y0) - (t * a));
	} else if (z <= 6.5e+79) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (z <= 8.6e+117) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = i * (z * ((t * c) - (k * 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 = y4 * ((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3))))
    if (z <= (-3d+78)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (z <= (-4.2d+32)) then
        tmp = (j * y0) * ((y3 * y5) - (x * b))
    else if (z <= (-5.8d-33)) then
        tmp = (z * t) * ((c * i) - (a * b))
    else if (z <= (-1.28d-43)) then
        tmp = k * (y0 * -(y2 * y5))
    else if (z <= (-3.45d-53)) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (z <= (-2.9d-185)) then
        tmp = y2 * (x * ((c * y0) - (a * y1)))
    else if (z <= 3.2d-198) then
        tmp = t_1
    else if (z <= 1d-182) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (z <= 1.45d-17) then
        tmp = t_1
    else if (z <= 5.8d+40) then
        tmp = (z * b) * ((k * y0) - (t * a))
    else if (z <= 6.5d+79) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (z <= 8.6d+117) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else
        tmp = i * (z * ((t * c) - (k * 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 = y4 * ((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3))));
	double tmp;
	if (z <= -3e+78) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (z <= -4.2e+32) {
		tmp = (j * y0) * ((y3 * y5) - (x * b));
	} else if (z <= -5.8e-33) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (z <= -1.28e-43) {
		tmp = k * (y0 * -(y2 * y5));
	} else if (z <= -3.45e-53) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (z <= -2.9e-185) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (z <= 3.2e-198) {
		tmp = t_1;
	} else if (z <= 1e-182) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (z <= 1.45e-17) {
		tmp = t_1;
	} else if (z <= 5.8e+40) {
		tmp = (z * b) * ((k * y0) - (t * a));
	} else if (z <= 6.5e+79) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (z <= 8.6e+117) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = i * (z * ((t * c) - (k * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * ((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3))))
	tmp = 0
	if z <= -3e+78:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif z <= -4.2e+32:
		tmp = (j * y0) * ((y3 * y5) - (x * b))
	elif z <= -5.8e-33:
		tmp = (z * t) * ((c * i) - (a * b))
	elif z <= -1.28e-43:
		tmp = k * (y0 * -(y2 * y5))
	elif z <= -3.45e-53:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif z <= -2.9e-185:
		tmp = y2 * (x * ((c * y0) - (a * y1)))
	elif z <= 3.2e-198:
		tmp = t_1
	elif z <= 1e-182:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif z <= 1.45e-17:
		tmp = t_1
	elif z <= 5.8e+40:
		tmp = (z * b) * ((k * y0) - (t * a))
	elif z <= 6.5e+79:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif z <= 8.6e+117:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	else:
		tmp = i * (z * ((t * c) - (k * 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(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))))
	tmp = 0.0
	if (z <= -3e+78)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (z <= -4.2e+32)
		tmp = Float64(Float64(j * y0) * Float64(Float64(y3 * y5) - Float64(x * b)));
	elseif (z <= -5.8e-33)
		tmp = Float64(Float64(z * t) * Float64(Float64(c * i) - Float64(a * b)));
	elseif (z <= -1.28e-43)
		tmp = Float64(k * Float64(y0 * Float64(-Float64(y2 * y5))));
	elseif (z <= -3.45e-53)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (z <= -2.9e-185)
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (z <= 3.2e-198)
		tmp = t_1;
	elseif (z <= 1e-182)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (z <= 1.45e-17)
		tmp = t_1;
	elseif (z <= 5.8e+40)
		tmp = Float64(Float64(z * b) * Float64(Float64(k * y0) - Float64(t * a)));
	elseif (z <= 6.5e+79)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (z <= 8.6e+117)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	else
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * 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 = y4 * ((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3))));
	tmp = 0.0;
	if (z <= -3e+78)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (z <= -4.2e+32)
		tmp = (j * y0) * ((y3 * y5) - (x * b));
	elseif (z <= -5.8e-33)
		tmp = (z * t) * ((c * i) - (a * b));
	elseif (z <= -1.28e-43)
		tmp = k * (y0 * -(y2 * y5));
	elseif (z <= -3.45e-53)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (z <= -2.9e-185)
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	elseif (z <= 3.2e-198)
		tmp = t_1;
	elseif (z <= 1e-182)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (z <= 1.45e-17)
		tmp = t_1;
	elseif (z <= 5.8e+40)
		tmp = (z * b) * ((k * y0) - (t * a));
	elseif (z <= 6.5e+79)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (z <= 8.6e+117)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	else
		tmp = i * (z * ((t * c) - (k * 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[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+78], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e+32], N[(N[(j * y0), $MachinePrecision] * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-33], N[(N[(z * t), $MachinePrecision] * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.28e-43], N[(k * N[(y0 * (-N[(y2 * y5), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.45e-53], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-185], N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-198], t$95$1, If[LessEqual[z, 1e-182], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-17], t$95$1, If[LessEqual[z, 5.8e+40], N[(N[(z * b), $MachinePrecision] * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+79], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e+117], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if z < -2.99999999999999982e78

   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. Taylor expanded in z around -inf 55.7%

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

   3. Taylor expanded in a around -inf 53.7%

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

      1. +-commutative 53.7%

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

      2. mul-1-neg 53.7%

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

      3. unsub-neg 53.7%

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

      4. *-commutative 53.7%

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

      5. *-commutative 53.7%

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

   5. Simplified 53.7%

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

   if -2.99999999999999982e78 < z < -4.2000000000000001e32

   1. Initial program 9.1%

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

   2. Taylor expanded in j around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

   4. Simplified 64.1%

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

   5. Taylor expanded in y0 around -inf 64.5%

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

      1. associate-*r* 73.1%

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

      2. +-commutative 73.1%

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

      3. mul-1-neg 73.1%

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

      4. unsub-neg 73.1%

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

   7. Simplified 73.1%

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

   if -4.2000000000000001e32 < z < -5.80000000000000005e-33

   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. Taylor expanded in z around -inf 56.4%

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

   3. Taylor expanded in t around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. associate-*r* 57.5%

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

      3. *-commutative 57.5%

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

   5. Simplified 57.5%

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

   if -5.80000000000000005e-33 < z < -1.27999999999999998e-43

   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. Taylor expanded in z around -inf 0.0%

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

   3. Taylor expanded in y2 around inf 100.0%

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

   4. Taylor expanded in y1 around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

   6. Simplified 100.0%

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

   if -1.27999999999999998e-43 < z < -3.45000000000000019e-53

   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. Taylor expanded in y1 around -inf 28.7%

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

      1. mul-1-neg 28.7%

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

      2. *-commutative 28.7%

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

      3. distribute-rgt-neg-in 28.7%

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

   4. Simplified 28.7%

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

   5. Taylor expanded in i around -inf 78.1%

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

   if -3.45000000000000019e-53 < z < -2.89999999999999995e-185

   1. Initial program 39.7%

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

   2. Taylor expanded in y2 around inf 52.1%

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

   3. Taylor expanded in x around inf 46.3%

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

   if -2.89999999999999995e-185 < z < 3.19999999999999994e-198 or 1e-182 < z < 1.4500000000000001e-17

   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. Taylor expanded in y4 around inf 50.6%

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

   3. Taylor expanded in c around 0 53.6%

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

   if 3.19999999999999994e-198 < z < 1e-182

   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. Taylor expanded in y1 around -inf 43.2%

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

      1. mul-1-neg 43.2%

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

      2. *-commutative 43.2%

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

      3. distribute-rgt-neg-in 43.2%

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

   4. Simplified 43.2%

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

   5. Taylor expanded in y2 around inf 80.7%

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

   if 1.4500000000000001e-17 < z < 5.80000000000000035e40

   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. Taylor expanded in z around -inf 27.8%

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

   3. Taylor expanded in b around inf 46.6%

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

      1. mul-1-neg 46.6%

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

      2. associate-*r* 46.6%

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

      3. *-commutative 46.6%

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

   5. Simplified 46.6%

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

   if 5.80000000000000035e40 < z < 6.49999999999999954e79

   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. Taylor expanded in y1 around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around -inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 6.49999999999999954e79 < z < 8.59999999999999996e117

   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. Taylor expanded in y2 around inf 47.0%

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

   3. Taylor expanded in c around inf 61.0%

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

   if 8.59999999999999996e117 < z

   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. Taylor expanded in z around -inf 41.3%

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

   3. Taylor expanded in i around -inf 62.1%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
3. Recombined 12 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+78}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+32}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-33}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-43}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(-y2 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-53}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-185}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-198}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 10^{-182}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-17}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+40}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(k \cdot y0 - t \cdot a\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+79}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+117}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \end{array} \]

Alternative 13: 33.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot j - z \cdot k\\ t_2 := b \cdot k - c \cdot y3\\ t_3 := y0 \cdot \left(z \cdot t_2 - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ t_4 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{if}\;k \leq -3.8 \cdot 10^{+186}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -1.25 \cdot 10^{+159}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq -1.58 \cdot 10^{+122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -5.4 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot t_1 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.7 \cdot 10^{-305}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 2.05 \cdot 10^{-158}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{-95}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+148}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{+179}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+213}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot t_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x j) (* z k)))
        (t_2 (- (* b k) (* c y3)))
        (t_3 (* y0 (- (* z t_2) (* y5 (- (* k y2) (* j y3))))))
        (t_4
         (*
          y2
          (-
           (+ (* k (- (* y1 y4) (* y0 y5))) (* c (* x y0)))
           (* c (* t y4))))))
   (if (<= k -3.8e+186)
     t_3
     (if (<= k -1.25e+159)
       t_4
       (if (<= k -1.58e+122)
         t_3
         (if (<= k -5.4e-241)
           (* y1 (+ (* i t_1) (* a (- (* z y3) (* x y2)))))
           (if (<= k -1.7e-305)
             (* (* z t) (- (* c i) (* a b)))
             (if (<= k 2.05e-158)
               t_4
               (if (<= k 6e-103)
                 (* a (* z (- (* y1 y3) (* t b))))
                 (if (<= k 1.1e-95)
                   (* a (* y5 (- (* t y2) (* y y3))))
                   (if (<= k 1.35e+148)
                     (*
                      y4
                      (+
                       (* b (- (* t j) (* y k)))
                       (* c (- (* y y3) (* t y2)))))
                     (if (<= k 1.22e+179)
                       (* y1 (* k (- (* y2 y4) (* z i))))
                       (if (<= k 4.5e+213)
                         (* (* z y0) t_2)
                         (* i (* 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 = (x * j) - (z * k);
	double t_2 = (b * k) - (c * y3);
	double t_3 = y0 * ((z * t_2) - (y5 * ((k * y2) - (j * y3))));
	double t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)));
	double tmp;
	if (k <= -3.8e+186) {
		tmp = t_3;
	} else if (k <= -1.25e+159) {
		tmp = t_4;
	} else if (k <= -1.58e+122) {
		tmp = t_3;
	} else if (k <= -5.4e-241) {
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))));
	} else if (k <= -1.7e-305) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 2.05e-158) {
		tmp = t_4;
	} else if (k <= 6e-103) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 1.1e-95) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 1.35e+148) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 1.22e+179) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (k <= 4.5e+213) {
		tmp = (z * y0) * t_2;
	} else {
		tmp = i * (y1 * 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 = (x * j) - (z * k)
    t_2 = (b * k) - (c * y3)
    t_3 = y0 * ((z * t_2) - (y5 * ((k * y2) - (j * y3))))
    t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)))
    if (k <= (-3.8d+186)) then
        tmp = t_3
    else if (k <= (-1.25d+159)) then
        tmp = t_4
    else if (k <= (-1.58d+122)) then
        tmp = t_3
    else if (k <= (-5.4d-241)) then
        tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))))
    else if (k <= (-1.7d-305)) then
        tmp = (z * t) * ((c * i) - (a * b))
    else if (k <= 2.05d-158) then
        tmp = t_4
    else if (k <= 6d-103) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (k <= 1.1d-95) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (k <= 1.35d+148) then
        tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))))
    else if (k <= 1.22d+179) then
        tmp = y1 * (k * ((y2 * y4) - (z * i)))
    else if (k <= 4.5d+213) then
        tmp = (z * y0) * t_2
    else
        tmp = i * (y1 * 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 = (x * j) - (z * k);
	double t_2 = (b * k) - (c * y3);
	double t_3 = y0 * ((z * t_2) - (y5 * ((k * y2) - (j * y3))));
	double t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)));
	double tmp;
	if (k <= -3.8e+186) {
		tmp = t_3;
	} else if (k <= -1.25e+159) {
		tmp = t_4;
	} else if (k <= -1.58e+122) {
		tmp = t_3;
	} else if (k <= -5.4e-241) {
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))));
	} else if (k <= -1.7e-305) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 2.05e-158) {
		tmp = t_4;
	} else if (k <= 6e-103) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 1.1e-95) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 1.35e+148) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 1.22e+179) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (k <= 4.5e+213) {
		tmp = (z * y0) * t_2;
	} else {
		tmp = i * (y1 * 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 = (x * j) - (z * k)
	t_2 = (b * k) - (c * y3)
	t_3 = y0 * ((z * t_2) - (y5 * ((k * y2) - (j * y3))))
	t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)))
	tmp = 0
	if k <= -3.8e+186:
		tmp = t_3
	elif k <= -1.25e+159:
		tmp = t_4
	elif k <= -1.58e+122:
		tmp = t_3
	elif k <= -5.4e-241:
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))))
	elif k <= -1.7e-305:
		tmp = (z * t) * ((c * i) - (a * b))
	elif k <= 2.05e-158:
		tmp = t_4
	elif k <= 6e-103:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif k <= 1.1e-95:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif k <= 1.35e+148:
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))))
	elif k <= 1.22e+179:
		tmp = y1 * (k * ((y2 * y4) - (z * i)))
	elif k <= 4.5e+213:
		tmp = (z * y0) * t_2
	else:
		tmp = i * (y1 * 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(x * j) - Float64(z * k))
	t_2 = Float64(Float64(b * k) - Float64(c * y3))
	t_3 = Float64(y0 * Float64(Float64(z * t_2) - Float64(y5 * Float64(Float64(k * y2) - Float64(j * y3)))))
	t_4 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(c * Float64(x * y0))) - Float64(c * Float64(t * y4))))
	tmp = 0.0
	if (k <= -3.8e+186)
		tmp = t_3;
	elseif (k <= -1.25e+159)
		tmp = t_4;
	elseif (k <= -1.58e+122)
		tmp = t_3;
	elseif (k <= -5.4e-241)
		tmp = Float64(y1 * Float64(Float64(i * t_1) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (k <= -1.7e-305)
		tmp = Float64(Float64(z * t) * Float64(Float64(c * i) - Float64(a * b)));
	elseif (k <= 2.05e-158)
		tmp = t_4;
	elseif (k <= 6e-103)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (k <= 1.1e-95)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (k <= 1.35e+148)
		tmp = Float64(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (k <= 1.22e+179)
		tmp = Float64(y1 * Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (k <= 4.5e+213)
		tmp = Float64(Float64(z * y0) * t_2);
	else
		tmp = Float64(i * Float64(y1 * 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 = (x * j) - (z * k);
	t_2 = (b * k) - (c * y3);
	t_3 = y0 * ((z * t_2) - (y5 * ((k * y2) - (j * y3))));
	t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)));
	tmp = 0.0;
	if (k <= -3.8e+186)
		tmp = t_3;
	elseif (k <= -1.25e+159)
		tmp = t_4;
	elseif (k <= -1.58e+122)
		tmp = t_3;
	elseif (k <= -5.4e-241)
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))));
	elseif (k <= -1.7e-305)
		tmp = (z * t) * ((c * i) - (a * b));
	elseif (k <= 2.05e-158)
		tmp = t_4;
	elseif (k <= 6e-103)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (k <= 1.1e-95)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (k <= 1.35e+148)
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))));
	elseif (k <= 1.22e+179)
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	elseif (k <= 4.5e+213)
		tmp = (z * y0) * t_2;
	else
		tmp = i * (y1 * 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[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y0 * N[(N[(z * t$95$2), $MachinePrecision] - N[(y5 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.8e+186], t$95$3, If[LessEqual[k, -1.25e+159], t$95$4, If[LessEqual[k, -1.58e+122], t$95$3, If[LessEqual[k, -5.4e-241], N[(y1 * N[(N[(i * t$95$1), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.7e-305], N[(N[(z * t), $MachinePrecision] * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.05e-158], t$95$4, If[LessEqual[k, 6e-103], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.1e-95], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.35e+148], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.22e+179], N[(y1 * N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.5e+213], N[(N[(z * y0), $MachinePrecision] * t$95$2), $MachinePrecision], N[(i * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if k < -3.7999999999999998e186 or -1.25000000000000001e159 < k < -1.58e122

   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. Taylor expanded in z around -inf 54.3%

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

   3. Taylor expanded in y0 around inf 63.4%

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

   if -3.7999999999999998e186 < k < -1.25000000000000001e159 or -1.7e-305 < k < 2.05000000000000002e-158

   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. Taylor expanded in y2 around inf 54.4%

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

   3. Taylor expanded in a around 0 54.2%

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

   if -1.58e122 < k < -5.3999999999999998e-241

   1. Initial program 25.6%

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

   2. Taylor expanded in y1 around -inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. *-commutative 54.5%

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

      3. distribute-rgt-neg-in 54.5%

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

   4. Simplified 54.5%

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

   5. Taylor expanded in y4 around 0 60.1%

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

   if -5.3999999999999998e-241 < k < -1.7e-305

   1. Initial program 46.2%

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

   2. Taylor expanded in z around -inf 69.5%

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

   3. Taylor expanded in t around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. associate-*r* 77.4%

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

      3. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   if 2.05000000000000002e-158 < k < 6e-103

   1. Initial program 47.1%

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

   2. Taylor expanded in z around -inf 35.8%

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

   3. Taylor expanded in a around -inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

      5. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   if 6e-103 < k < 1.0999999999999999e-95

   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. Taylor expanded in y4 around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 1.0999999999999999e-95 < k < 1.35000000000000009e148

   1. Initial program 32.8%

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

   2. Taylor expanded in y4 around inf 50.8%

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

   3. Taylor expanded in y1 around 0 53.0%

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

      1. *-commutative 53.0%

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

      2. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   if 1.35000000000000009e148 < k < 1.22e179

   1. Initial program 17.1%

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

   2. Taylor expanded in y1 around -inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. *-commutative 44.8%

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

      3. distribute-rgt-neg-in 44.8%

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

   4. Simplified 44.8%

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

   5. Taylor expanded in k around -inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. *-commutative 56.2%

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

   7. Simplified 56.2%

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

   if 1.22e179 < k < 4.5000000000000002e213

   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. Taylor expanded in z around -inf 43.9%

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

   3. Taylor expanded in z around inf 72.5%

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

   4. Taylor expanded in y0 around inf 71.7%

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

      1. associate-*r* 71.7%

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

      2. *-commutative 71.7%

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

      3. *-commutative 71.7%

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

   6. Simplified 71.7%

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

   if 4.5000000000000002e213 < 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. Taylor expanded in y1 around -inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. distribute-rgt-neg-in 50.1%

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

   4. Simplified 50.1%

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

   5. Taylor expanded in i around -inf 63.7%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.8 \cdot 10^{+186}:\\ \;\;\;\;y0 \cdot \left(z \cdot \left(b \cdot k - c \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -1.25 \cdot 10^{+159}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.58 \cdot 10^{+122}:\\ \;\;\;\;y0 \cdot \left(z \cdot \left(b \cdot k - c \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -5.4 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.7 \cdot 10^{-305}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 2.05 \cdot 10^{-158}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{-95}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+148}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{+179}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+213}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]

Alternative 14: 33.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot j - z \cdot k\\ t_2 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;k \leq -2.25 \cdot 10^{+127}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -3.2 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot t_1 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.32 \cdot 10^{-306}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 2.05 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{-152}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 2.15 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 8.6 \cdot 10^{+148}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{+177}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{+209}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x j) (* z k))) (t_2 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= k -2.25e+127)
     (* y2 (* y0 (- (* x c) (* k y5))))
     (if (<= k -3.2e-241)
       (* y1 (+ (* i t_1) (* a (- (* z y3) (* x y2)))))
       (if (<= k 1.32e-306)
         (* (* z t) (- (* c i) (* a b)))
         (if (<= k 2.05e-197)
           t_2
           (if (<= k 6.2e-152)
             (* y2 (* x (- (* c y0) (* a y1))))
             (if (<= k 2.15e-103)
               (* a (* z (- (* y1 y3) (* t b))))
               (if (<= k 1e-97)
                 t_2
                 (if (<= k 8.6e+148)
                   (*
                    y4
                    (+ (* b (- (* t j) (* y k))) (* c (- (* y y3) (* t y2)))))
                   (if (<= k 8.5e+177)
                     (* y1 (* k (- (* y2 y4) (* z i))))
                     (if (<= k 1.55e+209)
                       (* (* z y0) (- (* b k) (* c y3)))
                       (* i (* 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 = (x * j) - (z * k);
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (k <= -2.25e+127) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else if (k <= -3.2e-241) {
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))));
	} else if (k <= 1.32e-306) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 2.05e-197) {
		tmp = t_2;
	} else if (k <= 6.2e-152) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (k <= 2.15e-103) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 1e-97) {
		tmp = t_2;
	} else if (k <= 8.6e+148) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 8.5e+177) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (k <= 1.55e+209) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else {
		tmp = i * (y1 * 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 = (x * j) - (z * k)
    t_2 = a * (y5 * ((t * y2) - (y * y3)))
    if (k <= (-2.25d+127)) then
        tmp = y2 * (y0 * ((x * c) - (k * y5)))
    else if (k <= (-3.2d-241)) then
        tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))))
    else if (k <= 1.32d-306) then
        tmp = (z * t) * ((c * i) - (a * b))
    else if (k <= 2.05d-197) then
        tmp = t_2
    else if (k <= 6.2d-152) then
        tmp = y2 * (x * ((c * y0) - (a * y1)))
    else if (k <= 2.15d-103) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (k <= 1d-97) then
        tmp = t_2
    else if (k <= 8.6d+148) then
        tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))))
    else if (k <= 8.5d+177) then
        tmp = y1 * (k * ((y2 * y4) - (z * i)))
    else if (k <= 1.55d+209) then
        tmp = (z * y0) * ((b * k) - (c * y3))
    else
        tmp = i * (y1 * 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 = (x * j) - (z * k);
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (k <= -2.25e+127) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else if (k <= -3.2e-241) {
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))));
	} else if (k <= 1.32e-306) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 2.05e-197) {
		tmp = t_2;
	} else if (k <= 6.2e-152) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (k <= 2.15e-103) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 1e-97) {
		tmp = t_2;
	} else if (k <= 8.6e+148) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 8.5e+177) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (k <= 1.55e+209) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else {
		tmp = i * (y1 * 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 = (x * j) - (z * k)
	t_2 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if k <= -2.25e+127:
		tmp = y2 * (y0 * ((x * c) - (k * y5)))
	elif k <= -3.2e-241:
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))))
	elif k <= 1.32e-306:
		tmp = (z * t) * ((c * i) - (a * b))
	elif k <= 2.05e-197:
		tmp = t_2
	elif k <= 6.2e-152:
		tmp = y2 * (x * ((c * y0) - (a * y1)))
	elif k <= 2.15e-103:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif k <= 1e-97:
		tmp = t_2
	elif k <= 8.6e+148:
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))))
	elif k <= 8.5e+177:
		tmp = y1 * (k * ((y2 * y4) - (z * i)))
	elif k <= 1.55e+209:
		tmp = (z * y0) * ((b * k) - (c * y3))
	else:
		tmp = i * (y1 * 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(x * j) - Float64(z * k))
	t_2 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (k <= -2.25e+127)
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (k <= -3.2e-241)
		tmp = Float64(y1 * Float64(Float64(i * t_1) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (k <= 1.32e-306)
		tmp = Float64(Float64(z * t) * Float64(Float64(c * i) - Float64(a * b)));
	elseif (k <= 2.05e-197)
		tmp = t_2;
	elseif (k <= 6.2e-152)
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (k <= 2.15e-103)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (k <= 1e-97)
		tmp = t_2;
	elseif (k <= 8.6e+148)
		tmp = Float64(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (k <= 8.5e+177)
		tmp = Float64(y1 * Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (k <= 1.55e+209)
		tmp = Float64(Float64(z * y0) * Float64(Float64(b * k) - Float64(c * y3)));
	else
		tmp = Float64(i * Float64(y1 * 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 = (x * j) - (z * k);
	t_2 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (k <= -2.25e+127)
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	elseif (k <= -3.2e-241)
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))));
	elseif (k <= 1.32e-306)
		tmp = (z * t) * ((c * i) - (a * b));
	elseif (k <= 2.05e-197)
		tmp = t_2;
	elseif (k <= 6.2e-152)
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	elseif (k <= 2.15e-103)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (k <= 1e-97)
		tmp = t_2;
	elseif (k <= 8.6e+148)
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))));
	elseif (k <= 8.5e+177)
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	elseif (k <= 1.55e+209)
		tmp = (z * y0) * ((b * k) - (c * y3));
	else
		tmp = i * (y1 * 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[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.25e+127], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.2e-241], N[(y1 * N[(N[(i * t$95$1), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.32e-306], N[(N[(z * t), $MachinePrecision] * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.05e-197], t$95$2, If[LessEqual[k, 6.2e-152], N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.15e-103], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1e-97], t$95$2, If[LessEqual[k, 8.6e+148], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.5e+177], N[(y1 * N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.55e+209], N[(N[(z * y0), $MachinePrecision] * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if k < -2.25000000000000017e127

   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. Taylor expanded in y2 around inf 42.3%

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

   3. Taylor expanded in y0 around inf 43.2%

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

      1. *-commutative 43.2%

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

      2. associate-*l* 51.7%

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

      3. *-commutative 51.7%

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

      4. +-commutative 51.7%

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

      5. mul-1-neg 51.7%

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

      6. unsub-neg 51.7%

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

      7. *-commutative 51.7%

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

      8. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   if -2.25000000000000017e127 < k < -3.2e-241

   1. Initial program 25.6%

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

   2. Taylor expanded in y1 around -inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. *-commutative 54.5%

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

      3. distribute-rgt-neg-in 54.5%

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

   4. Simplified 54.5%

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

   5. Taylor expanded in y4 around 0 60.1%

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

   if -3.2e-241 < k < 1.32e-306

   1. Initial program 50.0%

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

   2. Taylor expanded in z around -inf 71.7%

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

   3. Taylor expanded in t around inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. associate-*r* 72.0%

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

      3. *-commutative 72.0%

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

   5. Simplified 72.0%

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

   if 1.32e-306 < k < 2.05e-197 or 2.15000000000000011e-103 < k < 1.00000000000000004e-97

   1. Initial program 35.5%

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

   2. Taylor expanded in y4 around inf 55.3%

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

      1. *-commutative 55.3%

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

   4. Simplified 55.3%

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

   5. Taylor expanded in a around inf 56.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 56.0%

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

      2. *-commutative 56.0%

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

   7. Simplified 56.0%

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

   if 2.05e-197 < k < 6.1999999999999997e-152

   1. Initial program 49.8%

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

   2. Taylor expanded in y2 around inf 38.4%

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

   3. Taylor expanded in x around inf 51.6%

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

   if 6.1999999999999997e-152 < k < 2.15000000000000011e-103

   1. Initial program 50.0%

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

   2. Taylor expanded in z around -inf 36.3%

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

   3. Taylor expanded in a around -inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

      4. *-commutative 57.9%

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

      5. *-commutative 57.9%

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

   5. Simplified 57.9%

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

   if 1.00000000000000004e-97 < k < 8.6000000000000003e148

   1. Initial program 32.8%

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

   2. Taylor expanded in y4 around inf 50.8%

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

   3. Taylor expanded in y1 around 0 53.0%

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

      1. *-commutative 53.0%

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

      2. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   if 8.6000000000000003e148 < k < 8.5000000000000006e177

   1. Initial program 17.1%

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

   2. Taylor expanded in y1 around -inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. *-commutative 44.8%

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

      3. distribute-rgt-neg-in 44.8%

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

   4. Simplified 44.8%

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

   5. Taylor expanded in k around -inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. *-commutative 56.2%

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

   7. Simplified 56.2%

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

   if 8.5000000000000006e177 < k < 1.55e209

   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. Taylor expanded in z around -inf 43.9%

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

   3. Taylor expanded in z around inf 72.5%

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

   4. Taylor expanded in y0 around inf 71.7%

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

      1. associate-*r* 71.7%

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

      2. *-commutative 71.7%

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

      3. *-commutative 71.7%

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

   6. Simplified 71.7%

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

   if 1.55e209 < 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. Taylor expanded in y1 around -inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. distribute-rgt-neg-in 50.1%

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

   4. Simplified 50.1%

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

   5. Taylor expanded in i around -inf 63.7%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.25 \cdot 10^{+127}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -3.2 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.32 \cdot 10^{-306}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 2.05 \cdot 10^{-197}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{-152}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 2.15 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 10^{-97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 8.6 \cdot 10^{+148}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{+177}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{+209}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]

Alternative 15: 33.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot j - z \cdot k\\ \mathbf{if}\;k \leq -2.06 \cdot 10^{+123}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2.95 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot t_1 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -5 \cdot 10^{-309}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{-158}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{+143}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{+179}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{+213}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x j) (* z k))))
   (if (<= k -2.06e+123)
     (* y2 (* y0 (- (* x c) (* k y5))))
     (if (<= k -2.95e-241)
       (* y1 (+ (* i t_1) (* a (- (* z y3) (* x y2)))))
       (if (<= k -5e-309)
         (* (* z t) (- (* c i) (* a b)))
         (if (<= k 1.7e-158)
           (*
            y2
            (-
             (+ (* k (- (* y1 y4) (* y0 y5))) (* c (* x y0)))
             (* c (* t y4))))
           (if (<= k 3.4e-103)
             (* a (* z (- (* y1 y3) (* t b))))
             (if (<= k 3.2e-97)
               (* a (* y5 (- (* t y2) (* y y3))))
               (if (<= k 1.8e+143)
                 (*
                  y4
                  (+ (* b (- (* t j) (* y k))) (* c (- (* y y3) (* t y2)))))
                 (if (<= k 4.8e+179)
                   (* y1 (* k (- (* y2 y4) (* z i))))
                   (if (<= k 1.22e+213)
                     (* (* z y0) (- (* b k) (* c y3)))
                     (* i (* 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 = (x * j) - (z * k);
	double tmp;
	if (k <= -2.06e+123) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else if (k <= -2.95e-241) {
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))));
	} else if (k <= -5e-309) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 1.7e-158) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)));
	} else if (k <= 3.4e-103) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 3.2e-97) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 1.8e+143) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 4.8e+179) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (k <= 1.22e+213) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else {
		tmp = i * (y1 * 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 = (x * j) - (z * k)
    if (k <= (-2.06d+123)) then
        tmp = y2 * (y0 * ((x * c) - (k * y5)))
    else if (k <= (-2.95d-241)) then
        tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))))
    else if (k <= (-5d-309)) then
        tmp = (z * t) * ((c * i) - (a * b))
    else if (k <= 1.7d-158) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)))
    else if (k <= 3.4d-103) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (k <= 3.2d-97) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (k <= 1.8d+143) then
        tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))))
    else if (k <= 4.8d+179) then
        tmp = y1 * (k * ((y2 * y4) - (z * i)))
    else if (k <= 1.22d+213) then
        tmp = (z * y0) * ((b * k) - (c * y3))
    else
        tmp = i * (y1 * 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 = (x * j) - (z * k);
	double tmp;
	if (k <= -2.06e+123) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else if (k <= -2.95e-241) {
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))));
	} else if (k <= -5e-309) {
		tmp = (z * t) * ((c * i) - (a * b));
	} else if (k <= 1.7e-158) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)));
	} else if (k <= 3.4e-103) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (k <= 3.2e-97) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= 1.8e+143) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))));
	} else if (k <= 4.8e+179) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (k <= 1.22e+213) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else {
		tmp = i * (y1 * 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 = (x * j) - (z * k)
	tmp = 0
	if k <= -2.06e+123:
		tmp = y2 * (y0 * ((x * c) - (k * y5)))
	elif k <= -2.95e-241:
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))))
	elif k <= -5e-309:
		tmp = (z * t) * ((c * i) - (a * b))
	elif k <= 1.7e-158:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)))
	elif k <= 3.4e-103:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif k <= 3.2e-97:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif k <= 1.8e+143:
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))))
	elif k <= 4.8e+179:
		tmp = y1 * (k * ((y2 * y4) - (z * i)))
	elif k <= 1.22e+213:
		tmp = (z * y0) * ((b * k) - (c * y3))
	else:
		tmp = i * (y1 * 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(x * j) - Float64(z * k))
	tmp = 0.0
	if (k <= -2.06e+123)
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (k <= -2.95e-241)
		tmp = Float64(y1 * Float64(Float64(i * t_1) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (k <= -5e-309)
		tmp = Float64(Float64(z * t) * Float64(Float64(c * i) - Float64(a * b)));
	elseif (k <= 1.7e-158)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(c * Float64(x * y0))) - Float64(c * Float64(t * y4))));
	elseif (k <= 3.4e-103)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (k <= 3.2e-97)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (k <= 1.8e+143)
		tmp = Float64(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (k <= 4.8e+179)
		tmp = Float64(y1 * Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (k <= 1.22e+213)
		tmp = Float64(Float64(z * y0) * Float64(Float64(b * k) - Float64(c * y3)));
	else
		tmp = Float64(i * Float64(y1 * 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 = (x * j) - (z * k);
	tmp = 0.0;
	if (k <= -2.06e+123)
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	elseif (k <= -2.95e-241)
		tmp = y1 * ((i * t_1) + (a * ((z * y3) - (x * y2))));
	elseif (k <= -5e-309)
		tmp = (z * t) * ((c * i) - (a * b));
	elseif (k <= 1.7e-158)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (c * (x * y0))) - (c * (t * y4)));
	elseif (k <= 3.4e-103)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (k <= 3.2e-97)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (k <= 1.8e+143)
		tmp = y4 * ((b * ((t * j) - (y * k))) + (c * ((y * y3) - (t * y2))));
	elseif (k <= 4.8e+179)
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	elseif (k <= 1.22e+213)
		tmp = (z * y0) * ((b * k) - (c * y3));
	else
		tmp = i * (y1 * 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[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.06e+123], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.95e-241], N[(y1 * N[(N[(i * t$95$1), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -5e-309], N[(N[(z * t), $MachinePrecision] * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.7e-158], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.4e-103], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.2e-97], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.8e+143], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.8e+179], N[(y1 * N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.22e+213], N[(N[(z * y0), $MachinePrecision] * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if k < -2.0599999999999999e123

   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. Taylor expanded in y2 around inf 42.3%

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

   3. Taylor expanded in y0 around inf 43.2%

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

      1. *-commutative 43.2%

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

      2. associate-*l* 51.7%

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

      3. *-commutative 51.7%

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

      4. +-commutative 51.7%

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

      5. mul-1-neg 51.7%

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

      6. unsub-neg 51.7%

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

      7. *-commutative 51.7%

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

      8. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   if -2.0599999999999999e123 < k < -2.9499999999999999e-241

   1. Initial program 25.6%

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

   2. Taylor expanded in y1 around -inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. *-commutative 54.5%

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

      3. distribute-rgt-neg-in 54.5%

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

   4. Simplified 54.5%

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

   5. Taylor expanded in y4 around 0 60.1%

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

   if -2.9499999999999999e-241 < k < -4.9999999999999995e-309

   1. Initial program 46.2%

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

   2. Taylor expanded in z around -inf 69.5%

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

   3. Taylor expanded in t around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. associate-*r* 77.4%

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

      3. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   if -4.9999999999999995e-309 < k < 1.7e-158

   1. Initial program 36.7%

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

   2. Taylor expanded in y2 around inf 42.3%

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

   3. Taylor expanded in a around 0 42.1%

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

   if 1.7e-158 < k < 3.40000000000000003e-103

   1. Initial program 47.1%

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

   2. Taylor expanded in z around -inf 35.8%

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

   3. Taylor expanded in a around -inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

      5. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   if 3.40000000000000003e-103 < k < 3.1999999999999998e-97

   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. Taylor expanded in y4 around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 3.1999999999999998e-97 < k < 1.8e143

   1. Initial program 32.8%

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

   2. Taylor expanded in y4 around inf 50.8%

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

   3. Taylor expanded in y1 around 0 53.0%

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

      1. *-commutative 53.0%

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

      2. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   if 1.8e143 < k < 4.80000000000000025e179

   1. Initial program 17.1%

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

   2. Taylor expanded in y1 around -inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. *-commutative 44.8%

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

      3. distribute-rgt-neg-in 44.8%

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

   4. Simplified 44.8%

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

   5. Taylor expanded in k around -inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. *-commutative 56.2%

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

   7. Simplified 56.2%

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

   if 4.80000000000000025e179 < k < 1.2199999999999999e213

   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. Taylor expanded in z around -inf 43.9%

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

   3. Taylor expanded in z around inf 72.5%

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

   4. Taylor expanded in y0 around inf 71.7%

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

      1. associate-*r* 71.7%

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

      2. *-commutative 71.7%

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

      3. *-commutative 71.7%

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

   6. Simplified 71.7%

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

   if 1.2199999999999999e213 < 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. Taylor expanded in y1 around -inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. distribute-rgt-neg-in 50.1%

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

   4. Simplified 50.1%

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

   5. Taylor expanded in i around -inf 63.7%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.06 \cdot 10^{+123}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2.95 \cdot 10^{-241}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -5 \cdot 10^{-309}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(c \cdot i - a \cdot b\right)\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{-158}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{+143}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{+179}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{+213}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]

Alternative 16: 31.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ t_2 := c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{if}\;y2 \leq -4 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -2.85 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -2.22 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 1.36 \cdot 10^{-213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 3.8 \cdot 10^{+77}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 1.55 \cdot 10^{+240}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4)))))
        (t_2 (* c (* z (- (* t i) (* y0 y3))))))
   (if (<= y2 -4e+139)
     t_1
     (if (<= y2 -2.85e+93)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= y2 -2.22e-26)
         t_1
         (if (<= y2 -3.4e-140)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= y2 1.36e-213)
             t_2
             (if (<= y2 3.8e+77)
               (* i (* y1 (- (* x j) (* z k))))
               (if (<= y2 2.4e+142)
                 t_2
                 (if (<= y2 1.55e+240) (* y1 (* y4 (* k y2))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double t_2 = c * (z * ((t * i) - (y0 * y3)));
	double tmp;
	if (y2 <= -4e+139) {
		tmp = t_1;
	} else if (y2 <= -2.85e+93) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -2.22e-26) {
		tmp = t_1;
	} else if (y2 <= -3.4e-140) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 1.36e-213) {
		tmp = t_2;
	} else if (y2 <= 3.8e+77) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y2 <= 2.4e+142) {
		tmp = t_2;
	} else if (y2 <= 1.55e+240) {
		tmp = y1 * (y4 * (k * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (y2 * ((x * y0) - (t * y4)))
    t_2 = c * (z * ((t * i) - (y0 * y3)))
    if (y2 <= (-4d+139)) then
        tmp = t_1
    else if (y2 <= (-2.85d+93)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y2 <= (-2.22d-26)) then
        tmp = t_1
    else if (y2 <= (-3.4d-140)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y2 <= 1.36d-213) then
        tmp = t_2
    else if (y2 <= 3.8d+77) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y2 <= 2.4d+142) then
        tmp = t_2
    else if (y2 <= 1.55d+240) then
        tmp = y1 * (y4 * (k * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double t_2 = c * (z * ((t * i) - (y0 * y3)));
	double tmp;
	if (y2 <= -4e+139) {
		tmp = t_1;
	} else if (y2 <= -2.85e+93) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -2.22e-26) {
		tmp = t_1;
	} else if (y2 <= -3.4e-140) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 1.36e-213) {
		tmp = t_2;
	} else if (y2 <= 3.8e+77) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y2 <= 2.4e+142) {
		tmp = t_2;
	} else if (y2 <= 1.55e+240) {
		tmp = y1 * (y4 * (k * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y2 * ((x * y0) - (t * y4)))
	t_2 = c * (z * ((t * i) - (y0 * y3)))
	tmp = 0
	if y2 <= -4e+139:
		tmp = t_1
	elif y2 <= -2.85e+93:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y2 <= -2.22e-26:
		tmp = t_1
	elif y2 <= -3.4e-140:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y2 <= 1.36e-213:
		tmp = t_2
	elif y2 <= 3.8e+77:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y2 <= 2.4e+142:
		tmp = t_2
	elif y2 <= 1.55e+240:
		tmp = y1 * (y4 * (k * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	t_2 = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))))
	tmp = 0.0
	if (y2 <= -4e+139)
		tmp = t_1;
	elseif (y2 <= -2.85e+93)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y2 <= -2.22e-26)
		tmp = t_1;
	elseif (y2 <= -3.4e-140)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y2 <= 1.36e-213)
		tmp = t_2;
	elseif (y2 <= 3.8e+77)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y2 <= 2.4e+142)
		tmp = t_2;
	elseif (y2 <= 1.55e+240)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * ((x * y0) - (t * y4)));
	t_2 = c * (z * ((t * i) - (y0 * y3)));
	tmp = 0.0;
	if (y2 <= -4e+139)
		tmp = t_1;
	elseif (y2 <= -2.85e+93)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y2 <= -2.22e-26)
		tmp = t_1;
	elseif (y2 <= -3.4e-140)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y2 <= 1.36e-213)
		tmp = t_2;
	elseif (y2 <= 3.8e+77)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y2 <= 2.4e+142)
		tmp = t_2;
	elseif (y2 <= 1.55e+240)
		tmp = y1 * (y4 * (k * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -4e+139], t$95$1, If[LessEqual[y2, -2.85e+93], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.22e-26], t$95$1, If[LessEqual[y2, -3.4e-140], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.36e-213], t$95$2, If[LessEqual[y2, 3.8e+77], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.4e+142], t$95$2, If[LessEqual[y2, 1.55e+240], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -4.00000000000000013e139 or -2.8500000000000001e93 < y2 < -2.22e-26 or 1.55e240 < y2

   1. Initial program 24.2%

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

   2. Taylor expanded in y2 around inf 55.9%

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

   3. Taylor expanded in c around inf 52.0%

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

   if -4.00000000000000013e139 < y2 < -2.8500000000000001e93

   1. Initial program 11.1%

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

   2. Taylor expanded in z around -inf 44.4%

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

   3. Taylor expanded in a around -inf 66.7%

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

      1. +-commutative 66.7%

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

      2. mul-1-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -2.22e-26 < y2 < -3.40000000000000008e-140

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 24.1%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 24.1%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 24.1%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 47.2%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -3.40000000000000008e-140 < y2 < 1.36e-213 or 3.8000000000000001e77 < y2 < 2.3999999999999999e142

   1. Initial program 42.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 55.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in c around -inf 52.4%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.4%

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      2. mul-1-neg 52.4%

         \[\leadsto c \cdot \left(z \cdot \left(i \cdot t + \color{blue}{\left(-y0 \cdot y3\right)}\right)\right) \]

      3. sub-neg 52.4%

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t - y0 \cdot y3\right)}\right) \]

      4. *-commutative 52.4%

         \[\leadsto c \cdot \left(z \cdot \left(\color{blue}{t \cdot i} - y0 \cdot y3\right)\right) \]

      5. *-commutative 52.4%

         \[\leadsto c \cdot \left(z \cdot \left(t \cdot i - \color{blue}{y3 \cdot y0}\right)\right) \]

   5. Simplified 52.4%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(t \cdot i - y3 \cdot y0\right)\right)} \]

   if 1.36e-213 < y2 < 3.8000000000000001e77

   1. Initial program 33.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 41.8%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 41.8%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 41.8%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in i around -inf 37.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 2.3999999999999999e142 < y2 < 1.55e240

   1. Initial program 21.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 42.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 52.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 42.8%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 58.0%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   6. Simplified 58.0%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.85 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -2.22 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 1.36 \cdot 10^{-213}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 3.8 \cdot 10^{+77}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{+142}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.55 \cdot 10^{+240}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

Alternative 17: 30.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-196}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-36}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-16}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* z (- (* y1 y3) (* t b))))))
   (if (<= z -2.8e-20)
     t_1
     (if (<= z 1.2e-196)
       (* b (* y4 (- (* t j) (* y k))))
       (if (<= z 4.5e-41)
         (* a (* y5 (- (* t y2) (* y y3))))
         (if (<= z 9.5e-36)
           (* c (* y (* y3 y4)))
           (if (<= z 2.4e-16)
             (* y1 (* y4 (* k y2)))
             (if (<= z 1.14e+111) t_1 (* c (* (* z t) 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 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (z <= -2.8e-20) {
		tmp = t_1;
	} else if (z <= 1.2e-196) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (z <= 4.5e-41) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (z <= 9.5e-36) {
		tmp = c * (y * (y3 * y4));
	} else if (z <= 2.4e-16) {
		tmp = y1 * (y4 * (k * y2));
	} else if (z <= 1.14e+111) {
		tmp = t_1;
	} else {
		tmp = c * ((z * t) * 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) :: tmp
    t_1 = a * (z * ((y1 * y3) - (t * b)))
    if (z <= (-2.8d-20)) then
        tmp = t_1
    else if (z <= 1.2d-196) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (z <= 4.5d-41) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (z <= 9.5d-36) then
        tmp = c * (y * (y3 * y4))
    else if (z <= 2.4d-16) then
        tmp = y1 * (y4 * (k * y2))
    else if (z <= 1.14d+111) then
        tmp = t_1
    else
        tmp = c * ((z * t) * 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 = a * (z * ((y1 * y3) - (t * b)));
	double tmp;
	if (z <= -2.8e-20) {
		tmp = t_1;
	} else if (z <= 1.2e-196) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (z <= 4.5e-41) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (z <= 9.5e-36) {
		tmp = c * (y * (y3 * y4));
	} else if (z <= 2.4e-16) {
		tmp = y1 * (y4 * (k * y2));
	} else if (z <= 1.14e+111) {
		tmp = t_1;
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (z * ((y1 * y3) - (t * b)))
	tmp = 0
	if z <= -2.8e-20:
		tmp = t_1
	elif z <= 1.2e-196:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif z <= 4.5e-41:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif z <= 9.5e-36:
		tmp = c * (y * (y3 * y4))
	elif z <= 2.4e-16:
		tmp = y1 * (y4 * (k * y2))
	elif z <= 1.14e+111:
		tmp = t_1
	else:
		tmp = c * ((z * t) * 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(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))))
	tmp = 0.0
	if (z <= -2.8e-20)
		tmp = t_1;
	elseif (z <= 1.2e-196)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (z <= 4.5e-41)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (z <= 9.5e-36)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (z <= 2.4e-16)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (z <= 1.14e+111)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 = a * (z * ((y1 * y3) - (t * b)));
	tmp = 0.0;
	if (z <= -2.8e-20)
		tmp = t_1;
	elseif (z <= 1.2e-196)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (z <= 4.5e-41)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (z <= 9.5e-36)
		tmp = c * (y * (y3 * y4));
	elseif (z <= 2.4e-16)
		tmp = y1 * (y4 * (k * y2));
	elseif (z <= 1.14e+111)
		tmp = t_1;
	else
		tmp = c * ((z * t) * 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[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-20], t$95$1, If[LessEqual[z, 1.2e-196], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-41], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-36], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-16], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.14e+111], t$95$1, N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.8000000000000003e-20 or 2.40000000000000005e-16 < z < 1.14e111

   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. Taylor expanded in z around -inf 51.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around -inf 44.9%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.9%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 44.9%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 44.9%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 44.9%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 44.9%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -2.8000000000000003e-20 < z < 1.2000000000000001e-196

   1. Initial program 32.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 36.7%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 36.7%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 39.1%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 1.2000000000000001e-196 < z < 4.5e-41

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 50.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 50.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 40.3%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 40.3%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if 4.5e-41 < z < 9.5000000000000003e-36

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 4.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 4.3%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 4.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in c around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 100.0%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      4. *-commutative 100.0%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 100.0%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if 9.5000000000000003e-36 < z < 2.40000000000000005e-16

   1. Initial program 66.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 83.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 67.0%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 51.1%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 67.3%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   6. Simplified 67.3%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   if 1.14e111 < z

   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. Taylor expanded in z around -inf 38.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in z around inf 40.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in c around inf 41.3%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(z \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 39.0%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(c \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]

      2. *-commutative 39.0%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(z \cdot c\right)} \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]

      3. +-commutative 39.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)}\right) \]

      4. mul-1-neg 39.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \]

      5. unsub-neg 39.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \]

      6. *-commutative 39.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \]

      7. *-commutative 39.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \]

   6. Simplified 39.0%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \]

   7. Taylor expanded in y3 around 0 43.3%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 43.3%

         \[\leadsto -1 \cdot \color{blue}{\left(-c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]

   9. Simplified 43.3%

      \[\leadsto -1 \cdot \color{blue}{\left(-c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-196}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-36}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-16}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+111}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]

Alternative 18: 30.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-197}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{+28}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(-y2 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= z -3.4e-20)
     (* a (* z (- (* y1 y3) (* t b))))
     (if (<= z 8e-197)
       (* b (* y4 (- (* t j) (* y k))))
       (if (<= z 5.8e-86)
         (* a (* y5 (- (* t y2) (* y y3))))
         (if (<= z 1.75e-32)
           t_1
           (if (<= z 1e+28)
             (* k (* y0 (- (* y2 y5))))
             (if (<= z 1.7e+112) t_1 (* c (* (* z t) 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 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (z <= -3.4e-20) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (z <= 8e-197) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (z <= 5.8e-86) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (z <= 1.75e-32) {
		tmp = t_1;
	} else if (z <= 1e+28) {
		tmp = k * (y0 * -(y2 * y5));
	} else if (z <= 1.7e+112) {
		tmp = t_1;
	} else {
		tmp = c * ((z * t) * 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) :: tmp
    t_1 = c * (y2 * ((x * y0) - (t * y4)))
    if (z <= (-3.4d-20)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (z <= 8d-197) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (z <= 5.8d-86) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (z <= 1.75d-32) then
        tmp = t_1
    else if (z <= 1d+28) then
        tmp = k * (y0 * -(y2 * y5))
    else if (z <= 1.7d+112) then
        tmp = t_1
    else
        tmp = c * ((z * t) * 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 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (z <= -3.4e-20) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (z <= 8e-197) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (z <= 5.8e-86) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (z <= 1.75e-32) {
		tmp = t_1;
	} else if (z <= 1e+28) {
		tmp = k * (y0 * -(y2 * y5));
	} else if (z <= 1.7e+112) {
		tmp = t_1;
	} else {
		tmp = c * ((z * t) * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if z <= -3.4e-20:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif z <= 8e-197:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif z <= 5.8e-86:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif z <= 1.75e-32:
		tmp = t_1
	elif z <= 1e+28:
		tmp = k * (y0 * -(y2 * y5))
	elif z <= 1.7e+112:
		tmp = t_1
	else:
		tmp = c * ((z * t) * 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(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (z <= -3.4e-20)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (z <= 8e-197)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (z <= 5.8e-86)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (z <= 1.75e-32)
		tmp = t_1;
	elseif (z <= 1e+28)
		tmp = Float64(k * Float64(y0 * Float64(-Float64(y2 * y5))));
	elseif (z <= 1.7e+112)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(z * t) * 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 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (z <= -3.4e-20)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (z <= 8e-197)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (z <= 5.8e-86)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (z <= 1.75e-32)
		tmp = t_1;
	elseif (z <= 1e+28)
		tmp = k * (y0 * -(y2 * y5));
	elseif (z <= 1.7e+112)
		tmp = t_1;
	else
		tmp = c * ((z * t) * 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[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-20], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-197], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-86], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-32], t$95$1, If[LessEqual[z, 1e+28], N[(k * N[(y0 * (-N[(y2 * y5), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+112], t$95$1, N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.3999999999999997e-20

   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. Taylor expanded in z around -inf 54.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around -inf 46.9%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.9%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 46.9%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 46.9%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 46.9%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 46.9%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 46.9%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -3.3999999999999997e-20 < z < 7.9999999999999999e-197

   1. Initial program 32.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 36.7%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 36.7%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 39.1%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 7.9999999999999999e-197 < z < 5.7999999999999998e-86

   1. Initial program 39.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 48.2%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 48.2%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 40.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.1%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 40.1%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 40.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if 5.7999999999999998e-86 < z < 1.7499999999999999e-32 or 9.99999999999999958e27 < z < 1.69999999999999997e112

   1. Initial program 46.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 46.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 54.6%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if 1.7499999999999999e-32 < z < 9.99999999999999958e27

   1. Initial program 38.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 46.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y2 around inf 47.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y1 around 0 47.5%

      \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.5%

         \[\leadsto k \cdot \color{blue}{\left(-y0 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. distribute-rgt-neg-in 47.5%

         \[\leadsto k \cdot \color{blue}{\left(y0 \cdot \left(-y2 \cdot y5\right)\right)} \]

   6. Simplified 47.5%

      \[\leadsto k \cdot \color{blue}{\left(y0 \cdot \left(-y2 \cdot y5\right)\right)} \]

   if 1.69999999999999997e112 < z

   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. Taylor expanded in z around -inf 38.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in z around inf 40.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in c around inf 41.3%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(z \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 39.0%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(c \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]

      2. *-commutative 39.0%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(z \cdot c\right)} \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]

      3. +-commutative 39.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)}\right) \]

      4. mul-1-neg 39.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \]

      5. unsub-neg 39.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \]

      6. *-commutative 39.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \]

      7. *-commutative 39.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \]

   6. Simplified 39.0%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \]

   7. Taylor expanded in y3 around 0 43.3%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 43.3%

         \[\leadsto -1 \cdot \color{blue}{\left(-c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]

   9. Simplified 43.3%

      \[\leadsto -1 \cdot \color{blue}{\left(-c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-197}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-32}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 10^{+28}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(-y2 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+112}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \end{array} \]

Alternative 19: 32.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -1.1 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -3.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -6.4 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -6.5 \cdot 10^{-54}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -5 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{+137}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= y2 -1.1e+139)
     t_1
     (if (<= y2 -3.2e+93)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= y2 -6.4e+22)
         t_1
         (if (<= y2 -6.5e-54)
           (* y1 (* z (- (* a y3) (* i k))))
           (if (<= y2 -5e-113)
             (* j (* y4 (- (* t b) (* y1 y3))))
             (if (<= y2 2.7e+137)
               (* i (* z (- (* t c) (* k y1))))
               (* k (* y2 (- (* y1 y4) (* y0 y5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -1.1e+139) {
		tmp = t_1;
	} else if (y2 <= -3.2e+93) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -6.4e+22) {
		tmp = t_1;
	} else if (y2 <= -6.5e-54) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y2 <= -5e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 2.7e+137) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y2 * ((x * y0) - (t * y4)))
    if (y2 <= (-1.1d+139)) then
        tmp = t_1
    else if (y2 <= (-3.2d+93)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y2 <= (-6.4d+22)) then
        tmp = t_1
    else if (y2 <= (-6.5d-54)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (y2 <= (-5d-113)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y2 <= 2.7d+137) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -1.1e+139) {
		tmp = t_1;
	} else if (y2 <= -3.2e+93) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -6.4e+22) {
		tmp = t_1;
	} else if (y2 <= -6.5e-54) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y2 <= -5e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 2.7e+137) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if y2 <= -1.1e+139:
		tmp = t_1
	elif y2 <= -3.2e+93:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y2 <= -6.4e+22:
		tmp = t_1
	elif y2 <= -6.5e-54:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif y2 <= -5e-113:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y2 <= 2.7e+137:
		tmp = i * (z * ((t * c) - (k * y1)))
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (y2 <= -1.1e+139)
		tmp = t_1;
	elseif (y2 <= -3.2e+93)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y2 <= -6.4e+22)
		tmp = t_1;
	elseif (y2 <= -6.5e-54)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y2 <= -5e-113)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y2 <= 2.7e+137)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (y2 <= -1.1e+139)
		tmp = t_1;
	elseif (y2 <= -3.2e+93)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y2 <= -6.4e+22)
		tmp = t_1;
	elseif (y2 <= -6.5e-54)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (y2 <= -5e-113)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y2 <= 2.7e+137)
		tmp = i * (z * ((t * c) - (k * y1)));
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.1e+139], t$95$1, If[LessEqual[y2, -3.2e+93], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6.4e+22], t$95$1, If[LessEqual[y2, -6.5e-54], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5e-113], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.7e+137], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -1.1e139 or -3.2000000000000001e93 < y2 < -6.4e22

   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. Taylor expanded in y2 around inf 56.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 56.7%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if -1.1e139 < y2 < -3.2000000000000001e93

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 44.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around -inf 66.7%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -6.4e22 < y2 < -6.49999999999999991e-54

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 53.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 53.2%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 53.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 53.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in z around -inf 54.2%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto y1 \cdot \left(z \cdot \left(\color{blue}{y3 \cdot a} - i \cdot k\right)\right) \]

      2. *-commutative 54.2%

         \[\leadsto y1 \cdot \left(z \cdot \left(y3 \cdot a - \color{blue}{k \cdot i}\right)\right) \]

   7. Simplified 54.2%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(y3 \cdot a - k \cdot i\right)\right)} \]

   if -6.49999999999999991e-54 < y2 < -4.9999999999999997e-113

   1. Initial program 11.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 41.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 41.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 41.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 41.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 41.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 41.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y4 around inf 71.0%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   if -4.9999999999999997e-113 < y2 < 2.70000000000000017e137

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 44.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in i around -inf 43.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if 2.70000000000000017e137 < y2

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y2 around inf 49.1%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.1 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -6.4 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -6.5 \cdot 10^{-54}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -5 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{+137}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]

Alternative 20: 32.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -3.6 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{+82}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -8.2 \cdot 10^{-54}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -6.2 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -3.6e+138)
   (* c (* y2 (- (* x y0) (* t y4))))
   (if (<= y2 -2.6e+82)
     (* a (* z (- (* y1 y3) (* t b))))
     (if (<= y2 -5.8e+20)
       (* y2 (* x (- (* c y0) (* a y1))))
       (if (<= y2 -8.2e-54)
         (* y1 (* z (- (* a y3) (* i k))))
         (if (<= y2 -6.2e-113)
           (* j (* y4 (- (* t b) (* y1 y3))))
           (if (<= y2 4.8e+141)
             (* i (* z (- (* t c) (* k y1))))
             (* k (* y2 (- (* y1 y4) (* y0 y5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -3.6e+138) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -2.6e+82) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -5.8e+20) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (y2 <= -8.2e-54) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y2 <= -6.2e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 4.8e+141) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-3.6d+138)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y2 <= (-2.6d+82)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y2 <= (-5.8d+20)) then
        tmp = y2 * (x * ((c * y0) - (a * y1)))
    else if (y2 <= (-8.2d-54)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (y2 <= (-6.2d-113)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y2 <= 4.8d+141) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -3.6e+138) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -2.6e+82) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -5.8e+20) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (y2 <= -8.2e-54) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y2 <= -6.2e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 4.8e+141) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -3.6e+138:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y2 <= -2.6e+82:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y2 <= -5.8e+20:
		tmp = y2 * (x * ((c * y0) - (a * y1)))
	elif y2 <= -8.2e-54:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif y2 <= -6.2e-113:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y2 <= 4.8e+141:
		tmp = i * (z * ((t * c) - (k * y1)))
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -3.6e+138)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y2 <= -2.6e+82)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y2 <= -5.8e+20)
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y2 <= -8.2e-54)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y2 <= -6.2e-113)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y2 <= 4.8e+141)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -3.6e+138)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y2 <= -2.6e+82)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y2 <= -5.8e+20)
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	elseif (y2 <= -8.2e-54)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (y2 <= -6.2e-113)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y2 <= 4.8e+141)
		tmp = i * (z * ((t * c) - (k * y1)));
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -3.6e+138], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.6e+82], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.8e+20], N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8.2e-54], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6.2e-113], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.8e+141], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -3.6000000000000001e138

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 53.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 54.2%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if -3.6000000000000001e138 < y2 < -2.5999999999999998e82

   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. Taylor expanded in z around -inf 50.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around -inf 66.7%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -2.5999999999999998e82 < y2 < -5.8e20

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 64.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in x around inf 64.6%

      \[\leadsto y2 \cdot \color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   if -5.8e20 < y2 < -8.2000000000000001e-54

   1. Initial program 15.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 49.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 49.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 49.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 49.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 49.9%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in z around -inf 57.9%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 57.9%

         \[\leadsto y1 \cdot \left(z \cdot \left(\color{blue}{y3 \cdot a} - i \cdot k\right)\right) \]

      2. *-commutative 57.9%

         \[\leadsto y1 \cdot \left(z \cdot \left(y3 \cdot a - \color{blue}{k \cdot i}\right)\right) \]

   7. Simplified 57.9%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(y3 \cdot a - k \cdot i\right)\right)} \]

   if -8.2000000000000001e-54 < y2 < -6.20000000000000024e-113

   1. Initial program 11.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 41.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 41.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 41.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 41.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 41.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 41.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y4 around inf 71.0%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   if -6.20000000000000024e-113 < y2 < 4.79999999999999995e141

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 44.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in i around -inf 43.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if 4.79999999999999995e141 < y2

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y2 around inf 49.1%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.6 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{+82}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -8.2 \cdot 10^{-54}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq -6.2 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]

Alternative 21: 32.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -4.9 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.1 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -370000000000:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -1.8 \cdot 10^{-55}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq -6 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+138}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -4.9e+138)
   (* c (* y2 (- (* x y0) (* t y4))))
   (if (<= y2 -3.1e+83)
     (* a (* z (- (* y1 y3) (* t b))))
     (if (<= y2 -370000000000.0)
       (* y2 (* x (- (* c y0) (* a y1))))
       (if (<= y2 -1.8e-55)
         (* y1 (* k (- (* y2 y4) (* z i))))
         (if (<= y2 -6e-113)
           (* j (* y4 (- (* t b) (* y1 y3))))
           (if (<= y2 9.5e+138)
             (* i (* z (- (* t c) (* k y1))))
             (* k (* y2 (- (* y1 y4) (* y0 y5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -4.9e+138) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -3.1e+83) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -370000000000.0) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (y2 <= -1.8e-55) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (y2 <= -6e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 9.5e+138) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-4.9d+138)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y2 <= (-3.1d+83)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y2 <= (-370000000000.0d0)) then
        tmp = y2 * (x * ((c * y0) - (a * y1)))
    else if (y2 <= (-1.8d-55)) then
        tmp = y1 * (k * ((y2 * y4) - (z * i)))
    else if (y2 <= (-6d-113)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y2 <= 9.5d+138) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -4.9e+138) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -3.1e+83) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -370000000000.0) {
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	} else if (y2 <= -1.8e-55) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (y2 <= -6e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 9.5e+138) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -4.9e+138:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y2 <= -3.1e+83:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y2 <= -370000000000.0:
		tmp = y2 * (x * ((c * y0) - (a * y1)))
	elif y2 <= -1.8e-55:
		tmp = y1 * (k * ((y2 * y4) - (z * i)))
	elif y2 <= -6e-113:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y2 <= 9.5e+138:
		tmp = i * (z * ((t * c) - (k * y1)))
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -4.9e+138)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y2 <= -3.1e+83)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y2 <= -370000000000.0)
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y2 <= -1.8e-55)
		tmp = Float64(y1 * Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (y2 <= -6e-113)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y2 <= 9.5e+138)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -4.9e+138)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y2 <= -3.1e+83)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y2 <= -370000000000.0)
		tmp = y2 * (x * ((c * y0) - (a * y1)));
	elseif (y2 <= -1.8e-55)
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	elseif (y2 <= -6e-113)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y2 <= 9.5e+138)
		tmp = i * (z * ((t * c) - (k * y1)));
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -4.9e+138], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.1e+83], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -370000000000.0], N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.8e-55], N[(y1 * N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6e-113], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.5e+138], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -4.89999999999999983e138

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 53.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 54.2%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if -4.89999999999999983e138 < y2 < -3.09999999999999992e83

   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. Taylor expanded in z around -inf 50.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around -inf 66.7%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -3.09999999999999992e83 < y2 < -3.7e11

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 54.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in x around inf 62.4%

      \[\leadsto y2 \cdot \color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   if -3.7e11 < y2 < -1.8e-55

   1. Initial program 15.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 49.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 49.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 49.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 49.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 49.9%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in k around -inf 65.0%

      \[\leadsto \color{blue}{\left(k \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \cdot \left(-y1\right) \]
   6. Step-by-step derivation

      1. +-commutative 65.0%

         \[\leadsto \left(k \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \cdot \left(-y1\right) \]

      2. mul-1-neg 65.0%

         \[\leadsto \left(k \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \cdot \left(-y1\right) \]

      3. unsub-neg 65.0%

         \[\leadsto \left(k \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \cdot \left(-y1\right) \]

      4. *-commutative 65.0%

         \[\leadsto \left(k \cdot \left(\color{blue}{z \cdot i} - y2 \cdot y4\right)\right) \cdot \left(-y1\right) \]

   7. Simplified 65.0%

      \[\leadsto \color{blue}{\left(k \cdot \left(z \cdot i - y2 \cdot y4\right)\right)} \cdot \left(-y1\right) \]

   if -1.8e-55 < y2 < -6.0000000000000002e-113

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 47.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 47.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 47.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 47.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 47.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y4 around inf 73.9%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   if -6.0000000000000002e-113 < y2 < 9.49999999999999998e138

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 44.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in i around -inf 43.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if 9.49999999999999998e138 < y2

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y2 around inf 49.1%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4.9 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.1 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -370000000000:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -1.8 \cdot 10^{-55}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq -6 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+138}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]

Alternative 22: 30.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -3.6 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -3.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.66 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -1.46 \cdot 10^{-139}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 3.8 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= y2 -3.6e+138)
     t_1
     (if (<= y2 -3.2e+93)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= y2 -1.66e-25)
         t_1
         (if (<= y2 -1.46e-139)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= y2 3.8e+140)
             (* c (* z (- (* t i) (* y0 y3))))
             (* y1 (* y4 (* k y2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -3.6e+138) {
		tmp = t_1;
	} else if (y2 <= -3.2e+93) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -1.66e-25) {
		tmp = t_1;
	} else if (y2 <= -1.46e-139) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 3.8e+140) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y2 * ((x * y0) - (t * y4)))
    if (y2 <= (-3.6d+138)) then
        tmp = t_1
    else if (y2 <= (-3.2d+93)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y2 <= (-1.66d-25)) then
        tmp = t_1
    else if (y2 <= (-1.46d-139)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y2 <= 3.8d+140) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else
        tmp = y1 * (y4 * (k * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -3.6e+138) {
		tmp = t_1;
	} else if (y2 <= -3.2e+93) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -1.66e-25) {
		tmp = t_1;
	} else if (y2 <= -1.46e-139) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 3.8e+140) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if y2 <= -3.6e+138:
		tmp = t_1
	elif y2 <= -3.2e+93:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y2 <= -1.66e-25:
		tmp = t_1
	elif y2 <= -1.46e-139:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y2 <= 3.8e+140:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	else:
		tmp = y1 * (y4 * (k * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (y2 <= -3.6e+138)
		tmp = t_1;
	elseif (y2 <= -3.2e+93)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y2 <= -1.66e-25)
		tmp = t_1;
	elseif (y2 <= -1.46e-139)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y2 <= 3.8e+140)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (y2 <= -3.6e+138)
		tmp = t_1;
	elseif (y2 <= -3.2e+93)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y2 <= -1.66e-25)
		tmp = t_1;
	elseif (y2 <= -1.46e-139)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y2 <= 3.8e+140)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	else
		tmp = y1 * (y4 * (k * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -3.6e+138], t$95$1, If[LessEqual[y2, -3.2e+93], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.66e-25], t$95$1, If[LessEqual[y2, -1.46e-139], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.8e+140], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -3.6000000000000001e138 or -3.2000000000000001e93 < y2 < -1.6599999999999999e-25

   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. Taylor expanded in y2 around inf 51.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 50.5%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if -3.6000000000000001e138 < y2 < -3.2000000000000001e93

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 44.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around -inf 66.7%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -1.6599999999999999e-25 < y2 < -1.46000000000000005e-139

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 24.1%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 24.1%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 24.1%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 47.2%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -1.46000000000000005e-139 < y2 < 3.8000000000000001e140

   1. Initial program 37.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 44.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in c around -inf 38.1%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.1%

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      2. mul-1-neg 38.1%

         \[\leadsto c \cdot \left(z \cdot \left(i \cdot t + \color{blue}{\left(-y0 \cdot y3\right)}\right)\right) \]

      3. sub-neg 38.1%

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t - y0 \cdot y3\right)}\right) \]

      4. *-commutative 38.1%

         \[\leadsto c \cdot \left(z \cdot \left(\color{blue}{t \cdot i} - y0 \cdot y3\right)\right) \]

      5. *-commutative 38.1%

         \[\leadsto c \cdot \left(z \cdot \left(t \cdot i - \color{blue}{y3 \cdot y0}\right)\right) \]

   5. Simplified 38.1%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(t \cdot i - y3 \cdot y0\right)\right)} \]

   if 3.8000000000000001e140 < y2

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 42.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 27.1%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 45.7%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   6. Simplified 45.7%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.6 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.66 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.46 \cdot 10^{-139}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 3.8 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]

Alternative 23: 30.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -4.8 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -3.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.25 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -6.5 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{+141}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= y2 -4.8e+138)
     t_1
     (if (<= y2 -3.2e+93)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= y2 -1.25e-23)
         t_1
         (if (<= y2 -6.5e-146)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= y2 4.2e+141)
             (* i (* z (- (* t c) (* k y1))))
             (* y1 (* y4 (* k y2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -4.8e+138) {
		tmp = t_1;
	} else if (y2 <= -3.2e+93) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -1.25e-23) {
		tmp = t_1;
	} else if (y2 <= -6.5e-146) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 4.2e+141) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y2 * ((x * y0) - (t * y4)))
    if (y2 <= (-4.8d+138)) then
        tmp = t_1
    else if (y2 <= (-3.2d+93)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y2 <= (-1.25d-23)) then
        tmp = t_1
    else if (y2 <= (-6.5d-146)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y2 <= 4.2d+141) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else
        tmp = y1 * (y4 * (k * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -4.8e+138) {
		tmp = t_1;
	} else if (y2 <= -3.2e+93) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -1.25e-23) {
		tmp = t_1;
	} else if (y2 <= -6.5e-146) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 4.2e+141) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if y2 <= -4.8e+138:
		tmp = t_1
	elif y2 <= -3.2e+93:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y2 <= -1.25e-23:
		tmp = t_1
	elif y2 <= -6.5e-146:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y2 <= 4.2e+141:
		tmp = i * (z * ((t * c) - (k * y1)))
	else:
		tmp = y1 * (y4 * (k * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (y2 <= -4.8e+138)
		tmp = t_1;
	elseif (y2 <= -3.2e+93)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y2 <= -1.25e-23)
		tmp = t_1;
	elseif (y2 <= -6.5e-146)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y2 <= 4.2e+141)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (y2 <= -4.8e+138)
		tmp = t_1;
	elseif (y2 <= -3.2e+93)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y2 <= -1.25e-23)
		tmp = t_1;
	elseif (y2 <= -6.5e-146)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y2 <= 4.2e+141)
		tmp = i * (z * ((t * c) - (k * y1)));
	else
		tmp = y1 * (y4 * (k * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -4.8e+138], t$95$1, If[LessEqual[y2, -3.2e+93], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.25e-23], t$95$1, If[LessEqual[y2, -6.5e-146], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.2e+141], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -4.8000000000000002e138 or -3.2000000000000001e93 < y2 < -1.2500000000000001e-23

   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. Taylor expanded in y2 around inf 51.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 50.5%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if -4.8000000000000002e138 < y2 < -3.2000000000000001e93

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 44.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around -inf 66.7%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 66.7%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 66.7%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -1.2500000000000001e-23 < y2 < -6.4999999999999999e-146

   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. Taylor expanded in y4 around inf 22.7%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 22.7%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 22.7%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 44.0%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -6.4999999999999999e-146 < y2 < 4.1999999999999997e141

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 44.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in i around -inf 43.4%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if 4.1999999999999997e141 < y2

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 42.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 27.1%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 45.7%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   6. Simplified 45.7%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4.8 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.25 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -6.5 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{+141}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]

Alternative 24: 30.9% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{if}\;y2 \leq -2.15 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.7 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -4.1 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -5.8 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* z (- (* t c) (* k y1))))))
   (if (<= y2 -2.15e+139)
     (* c (* y2 (- (* x y0) (* t y4))))
     (if (<= y2 -3.7e+71)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= y2 -4.1e-35)
         t_1
         (if (<= y2 -5.8e-113)
           (* j (* y4 (- (* t b) (* y1 y3))))
           (if (<= y2 5e+146) t_1 (* y1 (* y4 (* k y2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (z * ((t * c) - (k * y1)));
	double tmp;
	if (y2 <= -2.15e+139) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -3.7e+71) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -4.1e-35) {
		tmp = t_1;
	} else if (y2 <= -5.8e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 5e+146) {
		tmp = t_1;
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (z * ((t * c) - (k * y1)))
    if (y2 <= (-2.15d+139)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y2 <= (-3.7d+71)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y2 <= (-4.1d-35)) then
        tmp = t_1
    else if (y2 <= (-5.8d-113)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y2 <= 5d+146) then
        tmp = t_1
    else
        tmp = y1 * (y4 * (k * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (z * ((t * c) - (k * y1)));
	double tmp;
	if (y2 <= -2.15e+139) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -3.7e+71) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -4.1e-35) {
		tmp = t_1;
	} else if (y2 <= -5.8e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 5e+146) {
		tmp = t_1;
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (z * ((t * c) - (k * y1)))
	tmp = 0
	if y2 <= -2.15e+139:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y2 <= -3.7e+71:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y2 <= -4.1e-35:
		tmp = t_1
	elif y2 <= -5.8e-113:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y2 <= 5e+146:
		tmp = t_1
	else:
		tmp = y1 * (y4 * (k * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))))
	tmp = 0.0
	if (y2 <= -2.15e+139)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y2 <= -3.7e+71)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y2 <= -4.1e-35)
		tmp = t_1;
	elseif (y2 <= -5.8e-113)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y2 <= 5e+146)
		tmp = t_1;
	else
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (z * ((t * c) - (k * y1)));
	tmp = 0.0;
	if (y2 <= -2.15e+139)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y2 <= -3.7e+71)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y2 <= -4.1e-35)
		tmp = t_1;
	elseif (y2 <= -5.8e-113)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y2 <= 5e+146)
		tmp = t_1;
	else
		tmp = y1 * (y4 * (k * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.15e+139], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.7e+71], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4.1e-35], t$95$1, If[LessEqual[y2, -5.8e-113], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5e+146], t$95$1, N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -2.1499999999999999e139

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 53.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 54.2%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if -2.1499999999999999e139 < y2 < -3.7e71

   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. Taylor expanded in z around -inf 57.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around -inf 64.8%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 64.8%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 64.8%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 64.8%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 64.8%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 64.8%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 64.8%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -3.7e71 < y2 < -4.10000000000000026e-35 or -5.80000000000000008e-113 < y2 < 4.9999999999999999e146

   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. Taylor expanded in z around -inf 44.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in i around -inf 42.9%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if -4.10000000000000026e-35 < y2 < -5.80000000000000008e-113

   1. Initial program 19.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 38.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 38.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 38.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 38.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 38.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 38.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y4 around inf 62.7%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   if 4.9999999999999999e146 < y2

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 42.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 27.1%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 45.7%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   6. Simplified 45.7%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.15 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.7 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -4.1 \cdot 10^{-35}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -5.8 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+146}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]

Alternative 25: 32.5% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{if}\;y2 \leq -3.5 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.7 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.14 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -6 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* z (- (* t c) (* k y1))))))
   (if (<= y2 -3.5e+139)
     (* c (* y2 (- (* x y0) (* t y4))))
     (if (<= y2 -1.7e+72)
       (* a (* z (- (* y1 y3) (* t b))))
       (if (<= y2 -1.14e-35)
         t_1
         (if (<= y2 -6e-113)
           (* j (* y4 (- (* t b) (* y1 y3))))
           (if (<= y2 5e+138) t_1 (* k (* y2 (- (* y1 y4) (* y0 y5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (z * ((t * c) - (k * y1)));
	double tmp;
	if (y2 <= -3.5e+139) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -1.7e+72) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -1.14e-35) {
		tmp = t_1;
	} else if (y2 <= -6e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 5e+138) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (z * ((t * c) - (k * y1)))
    if (y2 <= (-3.5d+139)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y2 <= (-1.7d+72)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (y2 <= (-1.14d-35)) then
        tmp = t_1
    else if (y2 <= (-6d-113)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y2 <= 5d+138) then
        tmp = t_1
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (z * ((t * c) - (k * y1)));
	double tmp;
	if (y2 <= -3.5e+139) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -1.7e+72) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (y2 <= -1.14e-35) {
		tmp = t_1;
	} else if (y2 <= -6e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 5e+138) {
		tmp = t_1;
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (z * ((t * c) - (k * y1)))
	tmp = 0
	if y2 <= -3.5e+139:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y2 <= -1.7e+72:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif y2 <= -1.14e-35:
		tmp = t_1
	elif y2 <= -6e-113:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y2 <= 5e+138:
		tmp = t_1
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))))
	tmp = 0.0
	if (y2 <= -3.5e+139)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y2 <= -1.7e+72)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y2 <= -1.14e-35)
		tmp = t_1;
	elseif (y2 <= -6e-113)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y2 <= 5e+138)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (z * ((t * c) - (k * y1)));
	tmp = 0.0;
	if (y2 <= -3.5e+139)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y2 <= -1.7e+72)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (y2 <= -1.14e-35)
		tmp = t_1;
	elseif (y2 <= -6e-113)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y2 <= 5e+138)
		tmp = t_1;
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -3.5e+139], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.7e+72], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.14e-35], t$95$1, If[LessEqual[y2, -6e-113], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5e+138], t$95$1, N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -3.49999999999999978e139

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 53.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 54.2%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if -3.49999999999999978e139 < y2 < -1.6999999999999999e72

   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. Taylor expanded in z around -inf 57.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around -inf 64.8%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 64.8%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 64.8%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 64.8%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 64.8%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 64.8%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 64.8%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -1.6999999999999999e72 < y2 < -1.14e-35 or -6.0000000000000002e-113 < y2 < 5.00000000000000016e138

   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. Taylor expanded in z around -inf 44.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in i around -inf 42.9%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if -1.14e-35 < y2 < -6.0000000000000002e-113

   1. Initial program 19.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 38.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 38.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 38.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 38.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 38.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 38.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y4 around inf 62.7%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   if 5.00000000000000016e138 < y2

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y2 around inf 49.1%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.5 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.7 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.14 \cdot 10^{-35}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -6 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+138}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]

Alternative 26: 32.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -2.8 \cdot 10^{+93}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -4 \cdot 10^{-37}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq -6.2 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{+139}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -2.8e+93)
   (* y1 (* y2 (- (* k y4) (* x a))))
   (if (<= y2 -6.8e+40)
     (* c (* y2 (- (* x y0) (* t y4))))
     (if (<= y2 -4e-37)
       (* y1 (* k (- (* y2 y4) (* z i))))
       (if (<= y2 -6.2e-113)
         (* j (* y4 (- (* t b) (* y1 y3))))
         (if (<= y2 1.1e+139)
           (* i (* z (- (* t c) (* k y1))))
           (* k (* y2 (- (* y1 y4) (* y0 y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -2.8e+93) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y2 <= -6.8e+40) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -4e-37) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (y2 <= -6.2e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 1.1e+139) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-2.8d+93)) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (y2 <= (-6.8d+40)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y2 <= (-4d-37)) then
        tmp = y1 * (k * ((y2 * y4) - (z * i)))
    else if (y2 <= (-6.2d-113)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y2 <= 1.1d+139) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -2.8e+93) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y2 <= -6.8e+40) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -4e-37) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (y2 <= -6.2e-113) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y2 <= 1.1e+139) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -2.8e+93:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif y2 <= -6.8e+40:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y2 <= -4e-37:
		tmp = y1 * (k * ((y2 * y4) - (z * i)))
	elif y2 <= -6.2e-113:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y2 <= 1.1e+139:
		tmp = i * (z * ((t * c) - (k * y1)))
	else:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -2.8e+93)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y2 <= -6.8e+40)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y2 <= -4e-37)
		tmp = Float64(y1 * Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (y2 <= -6.2e-113)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y2 <= 1.1e+139)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	else
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -2.8e+93)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (y2 <= -6.8e+40)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y2 <= -4e-37)
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	elseif (y2 <= -6.2e-113)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y2 <= 1.1e+139)
		tmp = i * (z * ((t * c) - (k * y1)));
	else
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -2.8e+93], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6.8e+40], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4e-37], N[(y1 * N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6.2e-113], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.1e+139], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -2.79999999999999989e93

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 39.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 39.2%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 39.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 39.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y2 around inf 54.8%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]

   if -2.79999999999999989e93 < y2 < -6.79999999999999977e40

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 60.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 71.1%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if -6.79999999999999977e40 < y2 < -4.00000000000000027e-37

   1. Initial program 13.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 40.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 40.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 40.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 40.0%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in k around -inf 54.3%

      \[\leadsto \color{blue}{\left(k \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \cdot \left(-y1\right) \]
   6. Step-by-step derivation

      1. +-commutative 54.3%

         \[\leadsto \left(k \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \cdot \left(-y1\right) \]

      2. mul-1-neg 54.3%

         \[\leadsto \left(k \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \cdot \left(-y1\right) \]

      3. unsub-neg 54.3%

         \[\leadsto \left(k \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \cdot \left(-y1\right) \]

      4. *-commutative 54.3%

         \[\leadsto \left(k \cdot \left(\color{blue}{z \cdot i} - y2 \cdot y4\right)\right) \cdot \left(-y1\right) \]

   7. Simplified 54.3%

      \[\leadsto \color{blue}{\left(k \cdot \left(z \cdot i - y2 \cdot y4\right)\right)} \cdot \left(-y1\right) \]

   if -4.00000000000000027e-37 < y2 < -6.20000000000000024e-113

   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. Taylor expanded in j around inf 40.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 40.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 40.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 40.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 40.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 40.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y4 around inf 65.6%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   if -6.20000000000000024e-113 < y2 < 1.1e139

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 44.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in i around -inf 43.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if 1.1e139 < y2

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y2 around inf 49.1%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.8 \cdot 10^{+93}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -4 \cdot 10^{-37}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq -6.2 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{+139}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \end{array} \]

Alternative 27: 28.9% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-208}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= z -1.15e-34)
     (* a (* z (- (* y1 y3) (* t b))))
     (if (<= z -2.75e-298)
       t_1
       (if (<= z 2.5e-208)
         (* y1 (* y4 (* j (- y3))))
         (if (<= z 1.45e+183) t_1 (* (* t i) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (z <= -1.15e-34) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (z <= -2.75e-298) {
		tmp = t_1;
	} else if (z <= 2.5e-208) {
		tmp = y1 * (y4 * (j * -y3));
	} else if (z <= 1.45e+183) {
		tmp = t_1;
	} else {
		tmp = (t * i) * (z * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    if (z <= (-1.15d-34)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (z <= (-2.75d-298)) then
        tmp = t_1
    else if (z <= 2.5d-208) then
        tmp = y1 * (y4 * (j * -y3))
    else if (z <= 1.45d+183) then
        tmp = t_1
    else
        tmp = (t * i) * (z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (z <= -1.15e-34) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (z <= -2.75e-298) {
		tmp = t_1;
	} else if (z <= 2.5e-208) {
		tmp = y1 * (y4 * (j * -y3));
	} else if (z <= 1.45e+183) {
		tmp = t_1;
	} else {
		tmp = (t * i) * (z * c);
	}
	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 * ((t * y2) - (y * y3)))
	tmp = 0
	if z <= -1.15e-34:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif z <= -2.75e-298:
		tmp = t_1
	elif z <= 2.5e-208:
		tmp = y1 * (y4 * (j * -y3))
	elif z <= 1.45e+183:
		tmp = t_1
	else:
		tmp = (t * i) * (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (z <= -1.15e-34)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (z <= -2.75e-298)
		tmp = t_1;
	elseif (z <= 2.5e-208)
		tmp = Float64(y1 * Float64(y4 * Float64(j * Float64(-y3))));
	elseif (z <= 1.45e+183)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * i) * Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (z <= -1.15e-34)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (z <= -2.75e-298)
		tmp = t_1;
	elseif (z <= 2.5e-208)
		tmp = y1 * (y4 * (j * -y3));
	elseif (z <= 1.45e+183)
		tmp = t_1;
	else
		tmp = (t * i) * (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e-34], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.75e-298], t$95$1, If[LessEqual[z, 2.5e-208], N[(y1 * N[(y4 * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+183], t$95$1, N[(N[(t * i), $MachinePrecision] * N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.15000000000000006e-34

   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. Taylor expanded in z around -inf 53.7%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around -inf 46.5%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.5%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. mul-1-neg 46.5%

         \[\leadsto a \cdot \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-b \cdot t\right)}\right)\right) \]

      3. unsub-neg 46.5%

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(y1 \cdot y3 - b \cdot t\right)}\right) \]

      4. *-commutative 46.5%

         \[\leadsto a \cdot \left(z \cdot \left(\color{blue}{y3 \cdot y1} - b \cdot t\right)\right) \]

      5. *-commutative 46.5%

         \[\leadsto a \cdot \left(z \cdot \left(y3 \cdot y1 - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 46.5%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \]

   if -1.15000000000000006e-34 < z < -2.7499999999999998e-298 or 2.49999999999999981e-208 < z < 1.45e183

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 38.7%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 38.7%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 38.7%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 33.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.8%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 33.8%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 33.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if -2.7499999999999998e-298 < z < 2.49999999999999981e-208

   1. Initial program 23.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 46.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 41.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around 0 38.2%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 38.2%

         \[\leadsto \color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

      2. neg-mul-1 38.2%

         \[\leadsto \color{blue}{\left(-j\right)} \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right) \]

      3. *-commutative 38.2%

         \[\leadsto \left(-j\right) \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot y1\right)} \]

      4. associate-*r* 38.3%

         \[\leadsto \color{blue}{\left(\left(-j\right) \cdot \left(y3 \cdot y4\right)\right) \cdot y1} \]

      5. associate-*r* 42.0%

         \[\leadsto \color{blue}{\left(\left(\left(-j\right) \cdot y3\right) \cdot y4\right)} \cdot y1 \]

      6. *-commutative 42.0%

         \[\leadsto \left(\color{blue}{\left(y3 \cdot \left(-j\right)\right)} \cdot y4\right) \cdot y1 \]

   6. Simplified 42.0%

      \[\leadsto \color{blue}{\left(\left(y3 \cdot \left(-j\right)\right) \cdot y4\right) \cdot y1} \]

   if 1.45e183 < z

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 40.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in z around inf 44.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in c around inf 44.4%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(z \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 44.5%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(c \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]

      2. *-commutative 44.5%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(z \cdot c\right)} \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]

      3. +-commutative 44.5%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)}\right) \]

      4. mul-1-neg 44.5%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \]

      5. unsub-neg 44.5%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \]

      6. *-commutative 44.5%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \]

      7. *-commutative 44.5%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \]

   6. Simplified 44.5%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \]

   7. Taylor expanded in y3 around 0 44.3%

      \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot t\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 44.3%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(-i \cdot t\right)}\right) \]

      2. *-commutative 44.3%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(-\color{blue}{t \cdot i}\right)\right) \]

      3. distribute-rgt-neg-in 44.3%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(t \cdot \left(-i\right)\right)}\right) \]

   9. Simplified 44.3%

      \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(t \cdot \left(-i\right)\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-208}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+183}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 28: 21.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ t_2 := c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{if}\;y2 \leq -8 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{-213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 3500:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+80}:\\ \;\;\;\;\left(y \cdot \left(-a\right)\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* y4 (* k y2)))) (t_2 (* c (* (* z t) i))))
   (if (<= y2 -8e-163)
     t_1
     (if (<= y2 1.1e-213)
       t_2
       (if (<= y2 3500.0)
         (* y1 (* j (* y3 (- y4))))
         (if (<= y2 9.5e+80)
           (* (* y (- a)) (* y3 y5))
           (if (<= y2 4.2e+140) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (y4 * (k * y2));
	double t_2 = c * ((z * t) * i);
	double tmp;
	if (y2 <= -8e-163) {
		tmp = t_1;
	} else if (y2 <= 1.1e-213) {
		tmp = t_2;
	} else if (y2 <= 3500.0) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 9.5e+80) {
		tmp = (y * -a) * (y3 * y5);
	} else if (y2 <= 4.2e+140) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y1 * (y4 * (k * y2))
    t_2 = c * ((z * t) * i)
    if (y2 <= (-8d-163)) then
        tmp = t_1
    else if (y2 <= 1.1d-213) then
        tmp = t_2
    else if (y2 <= 3500.0d0) then
        tmp = y1 * (j * (y3 * -y4))
    else if (y2 <= 9.5d+80) then
        tmp = (y * -a) * (y3 * y5)
    else if (y2 <= 4.2d+140) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (y4 * (k * y2));
	double t_2 = c * ((z * t) * i);
	double tmp;
	if (y2 <= -8e-163) {
		tmp = t_1;
	} else if (y2 <= 1.1e-213) {
		tmp = t_2;
	} else if (y2 <= 3500.0) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 9.5e+80) {
		tmp = (y * -a) * (y3 * y5);
	} else if (y2 <= 4.2e+140) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (y4 * (k * y2))
	t_2 = c * ((z * t) * i)
	tmp = 0
	if y2 <= -8e-163:
		tmp = t_1
	elif y2 <= 1.1e-213:
		tmp = t_2
	elif y2 <= 3500.0:
		tmp = y1 * (j * (y3 * -y4))
	elif y2 <= 9.5e+80:
		tmp = (y * -a) * (y3 * y5)
	elif y2 <= 4.2e+140:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(y4 * Float64(k * y2)))
	t_2 = Float64(c * Float64(Float64(z * t) * i))
	tmp = 0.0
	if (y2 <= -8e-163)
		tmp = t_1;
	elseif (y2 <= 1.1e-213)
		tmp = t_2;
	elseif (y2 <= 3500.0)
		tmp = Float64(y1 * Float64(j * Float64(y3 * Float64(-y4))));
	elseif (y2 <= 9.5e+80)
		tmp = Float64(Float64(y * Float64(-a)) * Float64(y3 * y5));
	elseif (y2 <= 4.2e+140)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (y4 * (k * y2));
	t_2 = c * ((z * t) * i);
	tmp = 0.0;
	if (y2 <= -8e-163)
		tmp = t_1;
	elseif (y2 <= 1.1e-213)
		tmp = t_2;
	elseif (y2 <= 3500.0)
		tmp = y1 * (j * (y3 * -y4));
	elseif (y2 <= 9.5e+80)
		tmp = (y * -a) * (y3 * y5);
	elseif (y2 <= 4.2e+140)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -8e-163], t$95$1, If[LessEqual[y2, 1.1e-213], t$95$2, If[LessEqual[y2, 3500.0], N[(y1 * N[(j * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.5e+80], N[(N[(y * (-a)), $MachinePrecision] * N[(y3 * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.2e+140], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -7.99999999999999939e-163 or 4.2000000000000004e140 < y2

   1. Initial program 23.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 44.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 37.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 26.2%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 32.4%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   6. Simplified 32.4%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   if -7.99999999999999939e-163 < y2 < 1.10000000000000005e-213 or 9.499999999999999e80 < y2 < 4.2000000000000004e140

   1. Initial program 44.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 54.7%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in z around inf 56.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in c around inf 51.6%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(z \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 48.3%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(c \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]

      2. *-commutative 48.3%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(z \cdot c\right)} \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]

      3. +-commutative 48.3%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)}\right) \]

      4. mul-1-neg 48.3%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \]

      5. unsub-neg 48.3%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \]

      6. *-commutative 48.3%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \]

      7. *-commutative 48.3%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \]

   6. Simplified 48.3%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \]

   7. Taylor expanded in y3 around 0 45.1%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 45.1%

         \[\leadsto -1 \cdot \color{blue}{\left(-c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]

   9. Simplified 45.1%

      \[\leadsto -1 \cdot \color{blue}{\left(-c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]

   if 1.10000000000000005e-213 < y2 < 3500

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 34.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 30.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around 0 33.1%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]

   if 3500 < y2 < 9.499999999999999e80

   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. Taylor expanded in y4 around inf 37.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 37.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 25.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 25.5%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 25.5%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 25.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 25.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 25.7%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

      2. associate-*r* 25.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot a\right) \cdot y\right) \cdot \left(y3 \cdot y5\right)} \]

      3. neg-mul-1 25.7%

         \[\leadsto \left(\color{blue}{\left(-a\right)} \cdot y\right) \cdot \left(y3 \cdot y5\right) \]

   10. Simplified 25.7%

       \[\leadsto \color{blue}{\left(\left(-a\right) \cdot y\right) \cdot \left(y3 \cdot y5\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -8 \cdot 10^{-163}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{-213}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y2 \leq 3500:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+80}:\\ \;\;\;\;\left(y \cdot \left(-a\right)\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]

Alternative 29: 21.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -5.5 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 10^{-212}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y2 \leq 2700:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{+82}:\\ \;\;\;\;\left(y \cdot \left(-a\right)\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{elif}\;y2 \leq 10^{+137}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* y4 (* k y2)))))
   (if (<= y2 -5.5e-162)
     t_1
     (if (<= y2 1e-212)
       (* (* t i) (* z c))
       (if (<= y2 2700.0)
         (* y1 (* j (* y3 (- y4))))
         (if (<= y2 1.1e+82)
           (* (* y (- a)) (* y3 y5))
           (if (<= y2 1e+137) (* c (* (* z t) i)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (y4 * (k * y2));
	double tmp;
	if (y2 <= -5.5e-162) {
		tmp = t_1;
	} else if (y2 <= 1e-212) {
		tmp = (t * i) * (z * c);
	} else if (y2 <= 2700.0) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 1.1e+82) {
		tmp = (y * -a) * (y3 * y5);
	} else if (y2 <= 1e+137) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y1 * (y4 * (k * y2))
    if (y2 <= (-5.5d-162)) then
        tmp = t_1
    else if (y2 <= 1d-212) then
        tmp = (t * i) * (z * c)
    else if (y2 <= 2700.0d0) then
        tmp = y1 * (j * (y3 * -y4))
    else if (y2 <= 1.1d+82) then
        tmp = (y * -a) * (y3 * y5)
    else if (y2 <= 1d+137) then
        tmp = c * ((z * t) * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (y4 * (k * y2));
	double tmp;
	if (y2 <= -5.5e-162) {
		tmp = t_1;
	} else if (y2 <= 1e-212) {
		tmp = (t * i) * (z * c);
	} else if (y2 <= 2700.0) {
		tmp = y1 * (j * (y3 * -y4));
	} else if (y2 <= 1.1e+82) {
		tmp = (y * -a) * (y3 * y5);
	} else if (y2 <= 1e+137) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (y4 * (k * y2))
	tmp = 0
	if y2 <= -5.5e-162:
		tmp = t_1
	elif y2 <= 1e-212:
		tmp = (t * i) * (z * c)
	elif y2 <= 2700.0:
		tmp = y1 * (j * (y3 * -y4))
	elif y2 <= 1.1e+82:
		tmp = (y * -a) * (y3 * y5)
	elif y2 <= 1e+137:
		tmp = c * ((z * t) * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(y4 * Float64(k * y2)))
	tmp = 0.0
	if (y2 <= -5.5e-162)
		tmp = t_1;
	elseif (y2 <= 1e-212)
		tmp = Float64(Float64(t * i) * Float64(z * c));
	elseif (y2 <= 2700.0)
		tmp = Float64(y1 * Float64(j * Float64(y3 * Float64(-y4))));
	elseif (y2 <= 1.1e+82)
		tmp = Float64(Float64(y * Float64(-a)) * Float64(y3 * y5));
	elseif (y2 <= 1e+137)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (y4 * (k * y2));
	tmp = 0.0;
	if (y2 <= -5.5e-162)
		tmp = t_1;
	elseif (y2 <= 1e-212)
		tmp = (t * i) * (z * c);
	elseif (y2 <= 2700.0)
		tmp = y1 * (j * (y3 * -y4));
	elseif (y2 <= 1.1e+82)
		tmp = (y * -a) * (y3 * y5);
	elseif (y2 <= 1e+137)
		tmp = c * ((z * t) * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -5.5e-162], t$95$1, If[LessEqual[y2, 1e-212], N[(N[(t * i), $MachinePrecision] * N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2700.0], N[(y1 * N[(j * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.1e+82], N[(N[(y * (-a)), $MachinePrecision] * N[(y3 * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1e+137], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -5.50000000000000006e-162 or 1e137 < y2

   1. Initial program 23.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 44.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 37.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 26.2%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 32.4%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   6. Simplified 32.4%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   if -5.50000000000000006e-162 < y2 < 9.99999999999999954e-213

   1. Initial program 45.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 52.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in z around inf 57.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in c around inf 48.7%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(z \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 46.8%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(c \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]

      2. *-commutative 46.8%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(z \cdot c\right)} \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]

      3. +-commutative 46.8%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)}\right) \]

      4. mul-1-neg 46.8%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \]

      5. unsub-neg 46.8%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \]

      6. *-commutative 46.8%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \]

      7. *-commutative 46.8%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \]

   6. Simplified 46.8%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \]

   7. Taylor expanded in y3 around 0 42.6%

      \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot t\right)\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg 42.6%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(-i \cdot t\right)}\right) \]

      2. *-commutative 42.6%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(-\color{blue}{t \cdot i}\right)\right) \]

      3. distribute-rgt-neg-in 42.6%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(t \cdot \left(-i\right)\right)}\right) \]

   9. Simplified 42.6%

      \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(t \cdot \left(-i\right)\right)}\right) \]

   if 9.99999999999999954e-213 < y2 < 2700

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 34.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 30.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around 0 33.1%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]

   if 2700 < y2 < 1.1000000000000001e82

   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. Taylor expanded in y4 around inf 37.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 37.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 25.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 25.5%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 25.5%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 25.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 25.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 25.7%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

      2. associate-*r* 25.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot a\right) \cdot y\right) \cdot \left(y3 \cdot y5\right)} \]

      3. neg-mul-1 25.7%

         \[\leadsto \left(\color{blue}{\left(-a\right)} \cdot y\right) \cdot \left(y3 \cdot y5\right) \]

   10. Simplified 25.7%

       \[\leadsto \color{blue}{\left(\left(-a\right) \cdot y\right) \cdot \left(y3 \cdot y5\right)} \]

   if 1.1000000000000001e82 < y2 < 1e137

   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. Taylor expanded in z around -inf 64.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in z around inf 55.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   4. Taylor expanded in c around inf 64.1%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(z \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 55.0%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(c \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]

      2. *-commutative 55.0%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(z \cdot c\right)} \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right) \]

      3. +-commutative 55.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)}\right) \]

      4. mul-1-neg 55.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \]

      5. unsub-neg 55.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \]

      6. *-commutative 55.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \]

      7. *-commutative 55.0%

         \[\leadsto -1 \cdot \left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \]

   6. Simplified 55.0%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(z \cdot c\right) \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \]

   7. Taylor expanded in y3 around 0 73.2%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 73.2%

         \[\leadsto -1 \cdot \color{blue}{\left(-c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]

   9. Simplified 73.2%

      \[\leadsto -1 \cdot \color{blue}{\left(-c \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.5 \cdot 10^{-162}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 10^{-212}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y2 \leq 2700:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{+82}:\\ \;\;\;\;\left(y \cdot \left(-a\right)\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{elif}\;y2 \leq 10^{+137}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]

Alternative 30: 21.8% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -3.35 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 3.9 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.85 \cdot 10^{+166} \lor \neg \left(y2 \leq 1.6 \cdot 10^{+223}\right):\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* y4 (* k y2)))))
   (if (<= y2 -3.35e-56)
     t_1
     (if (<= y2 3.9e-17)
       (* j (* y1 (* y3 (- y4))))
       (if (or (<= y2 2.85e+166) (not (<= y2 1.6e+223)))
         (* a (* y5 (* t y2)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (y4 * (k * y2));
	double tmp;
	if (y2 <= -3.35e-56) {
		tmp = t_1;
	} else if (y2 <= 3.9e-17) {
		tmp = j * (y1 * (y3 * -y4));
	} else if ((y2 <= 2.85e+166) || !(y2 <= 1.6e+223)) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y1 * (y4 * (k * y2))
    if (y2 <= (-3.35d-56)) then
        tmp = t_1
    else if (y2 <= 3.9d-17) then
        tmp = j * (y1 * (y3 * -y4))
    else if ((y2 <= 2.85d+166) .or. (.not. (y2 <= 1.6d+223))) then
        tmp = a * (y5 * (t * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (y4 * (k * y2));
	double tmp;
	if (y2 <= -3.35e-56) {
		tmp = t_1;
	} else if (y2 <= 3.9e-17) {
		tmp = j * (y1 * (y3 * -y4));
	} else if ((y2 <= 2.85e+166) || !(y2 <= 1.6e+223)) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (y4 * (k * y2))
	tmp = 0
	if y2 <= -3.35e-56:
		tmp = t_1
	elif y2 <= 3.9e-17:
		tmp = j * (y1 * (y3 * -y4))
	elif (y2 <= 2.85e+166) or not (y2 <= 1.6e+223):
		tmp = a * (y5 * (t * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(y4 * Float64(k * y2)))
	tmp = 0.0
	if (y2 <= -3.35e-56)
		tmp = t_1;
	elseif (y2 <= 3.9e-17)
		tmp = Float64(j * Float64(y1 * Float64(y3 * Float64(-y4))));
	elseif ((y2 <= 2.85e+166) || !(y2 <= 1.6e+223))
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (y4 * (k * y2));
	tmp = 0.0;
	if (y2 <= -3.35e-56)
		tmp = t_1;
	elseif (y2 <= 3.9e-17)
		tmp = j * (y1 * (y3 * -y4));
	elseif ((y2 <= 2.85e+166) || ~((y2 <= 1.6e+223)))
		tmp = a * (y5 * (t * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -3.35e-56], t$95$1, If[LessEqual[y2, 3.9e-17], N[(j * N[(y1 * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y2, 2.85e+166], N[Not[LessEqual[y2, 1.6e+223]], $MachinePrecision]], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -3.3499999999999998e-56 or 2.84999999999999989e166 < y2 < 1.6000000000000001e223

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 47.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 39.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 33.0%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 37.5%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   6. Simplified 37.5%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   if -3.3499999999999998e-56 < y2 < 3.89999999999999989e-17

   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. Taylor expanded in z around -inf 44.7%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 23.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around 0 25.5%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 25.5%

         \[\leadsto \color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

      2. neg-mul-1 25.5%

         \[\leadsto \color{blue}{\left(-j\right)} \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right) \]

   6. Simplified 25.5%

      \[\leadsto \color{blue}{\left(-j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

   if 3.89999999999999989e-17 < y2 < 2.84999999999999989e166 or 1.6000000000000001e223 < y2

   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. Taylor expanded in y4 around inf 38.8%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 38.8%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 38.8%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 38.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 38.9%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 38.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around inf 35.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.35 \cdot 10^{-56}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 3.9 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.85 \cdot 10^{+166} \lor \neg \left(y2 \leq 1.6 \cdot 10^{+223}\right):\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]

Alternative 31: 21.8% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -1.86 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 5.8 \cdot 10^{-12}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.9 \cdot 10^{+165} \lor \neg \left(y2 \leq 8.8 \cdot 10^{+222}\right):\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* y4 (* k y2)))))
   (if (<= y2 -1.86e-56)
     t_1
     (if (<= y2 5.8e-12)
       (* y1 (* j (* y3 (- y4))))
       (if (or (<= y2 6.9e+165) (not (<= y2 8.8e+222)))
         (* a (* y5 (* t y2)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (y4 * (k * y2));
	double tmp;
	if (y2 <= -1.86e-56) {
		tmp = t_1;
	} else if (y2 <= 5.8e-12) {
		tmp = y1 * (j * (y3 * -y4));
	} else if ((y2 <= 6.9e+165) || !(y2 <= 8.8e+222)) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y1 * (y4 * (k * y2))
    if (y2 <= (-1.86d-56)) then
        tmp = t_1
    else if (y2 <= 5.8d-12) then
        tmp = y1 * (j * (y3 * -y4))
    else if ((y2 <= 6.9d+165) .or. (.not. (y2 <= 8.8d+222))) then
        tmp = a * (y5 * (t * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (y4 * (k * y2));
	double tmp;
	if (y2 <= -1.86e-56) {
		tmp = t_1;
	} else if (y2 <= 5.8e-12) {
		tmp = y1 * (j * (y3 * -y4));
	} else if ((y2 <= 6.9e+165) || !(y2 <= 8.8e+222)) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (y4 * (k * y2))
	tmp = 0
	if y2 <= -1.86e-56:
		tmp = t_1
	elif y2 <= 5.8e-12:
		tmp = y1 * (j * (y3 * -y4))
	elif (y2 <= 6.9e+165) or not (y2 <= 8.8e+222):
		tmp = a * (y5 * (t * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(y4 * Float64(k * y2)))
	tmp = 0.0
	if (y2 <= -1.86e-56)
		tmp = t_1;
	elseif (y2 <= 5.8e-12)
		tmp = Float64(y1 * Float64(j * Float64(y3 * Float64(-y4))));
	elseif ((y2 <= 6.9e+165) || !(y2 <= 8.8e+222))
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (y4 * (k * y2));
	tmp = 0.0;
	if (y2 <= -1.86e-56)
		tmp = t_1;
	elseif (y2 <= 5.8e-12)
		tmp = y1 * (j * (y3 * -y4));
	elseif ((y2 <= 6.9e+165) || ~((y2 <= 8.8e+222)))
		tmp = a * (y5 * (t * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.86e-56], t$95$1, If[LessEqual[y2, 5.8e-12], N[(y1 * N[(j * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y2, 6.9e+165], N[Not[LessEqual[y2, 8.8e+222]], $MachinePrecision]], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -1.85999999999999997e-56 or 6.90000000000000006e165 < y2 < 8.8000000000000004e222

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 47.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 39.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 33.0%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 37.5%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   6. Simplified 37.5%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   if -1.85999999999999997e-56 < y2 < 5.8000000000000003e-12

   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. Taylor expanded in z around -inf 44.7%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 23.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around 0 25.5%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]

   if 5.8000000000000003e-12 < y2 < 6.90000000000000006e165 or 8.8000000000000004e222 < y2

   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. Taylor expanded in y4 around inf 38.8%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 38.8%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 38.8%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 38.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 38.9%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 38.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around inf 35.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.86 \cdot 10^{-56}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 5.8 \cdot 10^{-12}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.9 \cdot 10^{+165} \lor \neg \left(y2 \leq 8.8 \cdot 10^{+222}\right):\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]

Alternative 32: 27.8% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{if}\;y4 \leq -1.55 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq 2.7 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 3.9 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (* y3 (- y4))))))
   (if (<= y4 -1.55e+17)
     t_1
     (if (<= y4 2.7e+72)
       (* a (* y5 (- (* t y2) (* y y3))))
       (if (<= y4 3.9e+174) t_1 (* y1 (* y4 (* k y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y1 * (y3 * -y4));
	double tmp;
	if (y4 <= -1.55e+17) {
		tmp = t_1;
	} else if (y4 <= 2.7e+72) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y4 <= 3.9e+174) {
		tmp = t_1;
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y1 * (y3 * -y4))
    if (y4 <= (-1.55d+17)) then
        tmp = t_1
    else if (y4 <= 2.7d+72) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y4 <= 3.9d+174) then
        tmp = t_1
    else
        tmp = y1 * (y4 * (k * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y1 * (y3 * -y4));
	double tmp;
	if (y4 <= -1.55e+17) {
		tmp = t_1;
	} else if (y4 <= 2.7e+72) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y4 <= 3.9e+174) {
		tmp = t_1;
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y1 * (y3 * -y4))
	tmp = 0
	if y4 <= -1.55e+17:
		tmp = t_1
	elif y4 <= 2.7e+72:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y4 <= 3.9e+174:
		tmp = t_1
	else:
		tmp = y1 * (y4 * (k * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y1 * Float64(y3 * Float64(-y4))))
	tmp = 0.0
	if (y4 <= -1.55e+17)
		tmp = t_1;
	elseif (y4 <= 2.7e+72)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y4 <= 3.9e+174)
		tmp = t_1;
	else
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y1 * (y3 * -y4));
	tmp = 0.0;
	if (y4 <= -1.55e+17)
		tmp = t_1;
	elseif (y4 <= 2.7e+72)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y4 <= 3.9e+174)
		tmp = t_1;
	else
		tmp = y1 * (y4 * (k * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y1 * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.55e+17], t$95$1, If[LessEqual[y4, 2.7e+72], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.9e+174], t$95$1, N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -1.55e17 or 2.7000000000000001e72 < y4 < 3.89999999999999981e174

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 48.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 39.3%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around 0 43.2%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 43.2%

         \[\leadsto \color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

      2. neg-mul-1 43.2%

         \[\leadsto \color{blue}{\left(-j\right)} \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right) \]

   6. Simplified 43.2%

      \[\leadsto \color{blue}{\left(-j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

   if -1.55e17 < y4 < 2.7000000000000001e72

   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. Taylor expanded in y4 around inf 27.0%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 27.0%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 27.0%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 31.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 31.6%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 31.6%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 31.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if 3.89999999999999981e174 < y4

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 27.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 50.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 47.4%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   6. Simplified 47.4%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.55 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.7 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 3.9 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]

Alternative 33: 21.7% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.5 \cdot 10^{+23} \lor \neg \left(y3 \leq 4.6 \cdot 10^{+15}\right):\\ \;\;\;\;a \cdot \left(\left(y \cdot y3\right) \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y3 -1.5e+23) (not (<= y3 4.6e+15)))
   (* a (* (* y y3) (- y5)))
   (* a (* y5 (* t y2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y3 <= -1.5e+23) || !(y3 <= 4.6e+15)) {
		tmp = a * ((y * y3) * -y5);
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y3 <= (-1.5d+23)) .or. (.not. (y3 <= 4.6d+15))) then
        tmp = a * ((y * y3) * -y5)
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y3 <= -1.5e+23) || !(y3 <= 4.6e+15)) {
		tmp = a * ((y * y3) * -y5);
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y3 <= -1.5e+23) or not (y3 <= 4.6e+15):
		tmp = a * ((y * y3) * -y5)
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y3 <= -1.5e+23) || !(y3 <= 4.6e+15))
		tmp = Float64(a * Float64(Float64(y * y3) * Float64(-y5)));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y3 <= -1.5e+23) || ~((y3 <= 4.6e+15)))
		tmp = a * ((y * y3) * -y5);
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y3, -1.5e+23], N[Not[LessEqual[y3, 4.6e+15]], $MachinePrecision]], N[(a * N[(N[(y * y3), $MachinePrecision] * (-y5)), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y3 < -1.5e23 or 4.6e15 < y3

   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. Taylor expanded in y4 around inf 27.9%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 27.9%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 27.9%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 35.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.1%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 35.1%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 35.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 34.4%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 34.4%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

      2. distribute-lft-neg-out 34.4%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

      3. *-commutative 34.4%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   10. Simplified 34.4%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   if -1.5e23 < y3 < 4.6e15

   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. Taylor expanded in y4 around inf 35.4%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 35.4%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 22.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 22.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 22.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 22.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around inf 22.2%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.5 \cdot 10^{+23} \lor \neg \left(y3 \leq 4.6 \cdot 10^{+15}\right):\\ \;\;\;\;a \cdot \left(\left(y \cdot y3\right) \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]

Alternative 34: 21.6% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -3.8 \cdot 10^{-18} \lor \neg \left(y3 \leq 3.8 \cdot 10^{+123}\right):\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y3 -3.8e-18) (not (<= y3 3.8e+123)))
   (* c (* y (* y3 y4)))
   (* a (* y5 (* t y2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y3 <= -3.8e-18) || !(y3 <= 3.8e+123)) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y3 <= (-3.8d-18)) .or. (.not. (y3 <= 3.8d+123))) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y3 <= -3.8e-18) || !(y3 <= 3.8e+123)) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y3 <= -3.8e-18) or not (y3 <= 3.8e+123):
		tmp = c * (y * (y3 * y4))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y3 <= -3.8e-18) || !(y3 <= 3.8e+123))
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y3 <= -3.8e-18) || ~((y3 <= 3.8e+123)))
		tmp = c * (y * (y3 * y4));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y3, -3.8e-18], N[Not[LessEqual[y3, 3.8e+123]], $MachinePrecision]], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y3 < -3.7999999999999998e-18 or 3.79999999999999994e123 < y3

   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. Taylor expanded in y4 around inf 24.9%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 24.9%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 24.9%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in c around inf 28.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 28.5%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 28.5%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 28.5%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      4. *-commutative 28.5%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 28.5%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 28.5%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if -3.7999999999999998e-18 < y3 < 3.79999999999999994e123

   1. Initial program 36.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 36.5%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 36.5%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 36.5%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 26.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 26.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 26.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 26.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around inf 23.0%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.8 \cdot 10^{-18} \lor \neg \left(y3 \leq 3.8 \cdot 10^{+123}\right):\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]

Alternative 35: 22.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -3.05 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 7 \cdot 10^{+73}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -3.05e-50)
   (* y1 (* k (* y2 y4)))
   (if (<= y2 7e+73) (* c (* y (* y3 y4))) (* a (* y5 (* t y2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -3.05e-50) {
		tmp = y1 * (k * (y2 * y4));
	} else if (y2 <= 7e+73) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-3.05d-50)) then
        tmp = y1 * (k * (y2 * y4))
    else if (y2 <= 7d+73) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -3.05e-50) {
		tmp = y1 * (k * (y2 * y4));
	} else if (y2 <= 7e+73) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -3.05e-50:
		tmp = y1 * (k * (y2 * y4))
	elif y2 <= 7e+73:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -3.05e-50)
		tmp = Float64(y1 * Float64(k * Float64(y2 * y4)));
	elseif (y2 <= 7e+73)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -3.05e-50)
		tmp = y1 * (k * (y2 * y4));
	elseif (y2 <= 7e+73)
		tmp = c * (y * (y3 * y4));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -3.05e-50], N[(y1 * N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7e+73], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -3.0499999999999998e-50

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 48.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 39.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 31.2%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]

   if -3.0499999999999998e-50 < y2 < 7.00000000000000004e73

   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. Taylor expanded in y4 around inf 31.6%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 31.6%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 31.6%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in c around inf 16.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 16.4%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 16.4%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 16.4%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      4. *-commutative 16.4%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 16.4%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 18.4%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if 7.00000000000000004e73 < y2

   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. Taylor expanded in y4 around inf 37.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 37.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 43.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.9%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 43.9%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 43.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around inf 41.9%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 26.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.05 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 7 \cdot 10^{+73}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]

Alternative 36: 22.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -7.5 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 7 \cdot 10^{+73}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -7.5e-50)
   (* y1 (* y4 (* k y2)))
   (if (<= y2 7e+73) (* c (* y (* y3 y4))) (* a (* y5 (* t y2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -7.5e-50) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= 7e+73) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-7.5d-50)) then
        tmp = y1 * (y4 * (k * y2))
    else if (y2 <= 7d+73) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -7.5e-50) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y2 <= 7e+73) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -7.5e-50:
		tmp = y1 * (y4 * (k * y2))
	elif y2 <= 7e+73:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -7.5e-50)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (y2 <= 7e+73)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -7.5e-50)
		tmp = y1 * (y4 * (k * y2));
	elseif (y2 <= 7e+73)
		tmp = c * (y * (y3 * y4));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -7.5e-50], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7e+73], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -7.5e-50

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf 48.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in y4 around inf 39.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   4. Taylor expanded in k around inf 31.2%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 34.1%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   6. Simplified 34.1%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot y2\right) \cdot y4\right)} \]

   if -7.5e-50 < y2 < 7.00000000000000004e73

   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. Taylor expanded in y4 around inf 31.6%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 31.6%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 31.6%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in c around inf 16.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 16.4%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 16.4%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 16.4%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      4. *-commutative 16.4%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 16.4%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 18.4%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if 7.00000000000000004e73 < y2

   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. Taylor expanded in y4 around inf 37.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 37.3%

      \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 43.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.9%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 43.9%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 43.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around inf 41.9%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 26.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -7.5 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 7 \cdot 10^{+73}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]

Alternative 37: 16.7% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* t (* y2 y5))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (t * (y2 * y5));
}

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 * (t * (y2 * y5))
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 * (t * (y2 * y5));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (t * (y2 * y5))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(t * Float64(y2 * y5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (t * (y2 * y5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

2. Taylor expanded in y4 around inf 31.9%

   \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Step-by-step derivation

   1. *-commutative 31.9%

      \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

4. Simplified 31.9%

   \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

5. Taylor expanded in a around inf 28.2%

   \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
6. Step-by-step derivation

   1. *-commutative 28.2%

      \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

   2. *-commutative 28.2%

      \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

7. Simplified 28.2%

   \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

8. Taylor expanded in y2 around inf 16.4%

   \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right)} \]
9. Step-by-step derivation

   1. *-commutative 16.4%

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

10. Simplified 16.4%

    \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2\right)\right)} \]

11. Final simplification 16.4%

    \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]

Alternative 38: 16.5% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y5 (* t y2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y5 * (t * y2));
}

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 * (y5 * (t * y2))
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 * (y5 * (t * y2));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y5 * (t * y2))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y5 * Float64(t * y2)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y5 * (t * y2));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

2. Taylor expanded in y4 around inf 31.9%

   \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Step-by-step derivation

   1. *-commutative 31.9%

      \[\leadsto \left(b \cdot \left(y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

4. Simplified 31.9%

   \[\leadsto \left(\color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

5. Taylor expanded in a around inf 28.2%

   \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
6. Step-by-step derivation

   1. *-commutative 28.2%

      \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

   2. *-commutative 28.2%

      \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

7. Simplified 28.2%

   \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

8. Taylor expanded in y2 around inf 17.2%

   \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

9. Final simplification 17.2%

   \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right) \]

Developer target: 28.2% accurate, 0.8× 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 2023333 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))