Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.2% → 34.8%

Time: 2.3min

Alternatives: 40

Speedup: 3.7×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 34.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y0 - i \cdot y1\\ t_2 := z \cdot t - x \cdot y\\ t_3 := t \cdot j - y \cdot k\\ t_4 := \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_5 := a \cdot y5 - c \cdot y4\\ t_6 := t \cdot t_5\\ t_7 := z \cdot \left(k \cdot t_1 + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ t_8 := a \cdot b - c \cdot i\\ t_9 := y \cdot t_8\\ t_10 := c \cdot y0 - a \cdot y1\\ t_11 := y2 \cdot t_10\\ \mathbf{if}\;y5 \leq -3 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -5.2 \cdot 10^{+59}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -4.8 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_3\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -8.2 \cdot 10^{-161}:\\ \;\;\;\;y2 \cdot \left(\left(\left(k \cdot \left(y1 \cdot y4\right) + y0 \cdot \left(x \cdot c - k \cdot y5\right)\right) - a \cdot \left(x \cdot y1\right)\right) + t_6\right)\\ \mathbf{elif}\;y5 \leq -6.4 \cdot 10^{-186}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -4.1 \cdot 10^{-271}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y5 \leq -3.3 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot t_8\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 4.2 \cdot 10^{-176}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y5 \leq 8.5 \cdot 10^{-108}:\\ \;\;\;\;\left(x \cdot t_9 + \left(x \cdot t_11 + \left(\left(b \cdot y4 - i \cdot y5\right) \cdot t_3 + t_4\right)\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot t_5 - j \cdot \left(x \cdot t_1\right)\right)\\ \mathbf{elif}\;y5 \leq 8.6 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1 + \left(c \cdot t_2 - y5 \cdot t_3\right)\right)\\ \mathbf{elif}\;y5 \leq 5.4 \cdot 10^{+183}:\\ \;\;\;\;c \cdot \left(i \cdot t_2 + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(t_4 - \left(y \cdot y3 - t \cdot y2\right) \cdot t_5\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{+238}:\\ \;\;\;\;x \cdot \left(t_9 + t_11\right)\\ \mathbf{else}:\\ \;\;\;\;t_4 + y2 \cdot \left(x \cdot t_10 + 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 (- (* b y0) (* i y1)))
        (t_2 (- (* z t) (* x y)))
        (t_3 (- (* t j) (* y k)))
        (t_4 (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5))))
        (t_5 (- (* a y5) (* c y4)))
        (t_6 (* t t_5))
        (t_7
         (*
          z
          (+
           (* k t_1)
           (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0)))))))
        (t_8 (- (* a b) (* c i)))
        (t_9 (* y t_8))
        (t_10 (- (* c y0) (* a y1)))
        (t_11 (* y2 t_10)))
   (if (<= y5 -3e+258)
     (* (* y2 y4) (- (* k y1) (* t c)))
     (if (<= y5 -5.2e+59)
       (* (* y2 y5) (- (* t a) (* k y0)))
       (if (<= y5 -4.8e-56)
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 t_3))
           (* y0 (- (* z k) (* x j)))))
         (if (<= y5 -8.2e-161)
           (*
            y2
            (+
             (- (+ (* k (* y1 y4)) (* y0 (- (* x c) (* k y5)))) (* a (* x y1)))
             t_6))
           (if (<= y5 -6.4e-186)
             (* y1 (* j (- (* x i) (* y3 y4))))
             (if (<= y5 -4.1e-271)
               t_7
               (if (<= y5 -3.3e-302)
                 (*
                  y
                  (+
                   (+ (* k (- (* i y5) (* b y4))) (* x t_8))
                   (* y3 (- (* c y4) (* a y5)))))
                 (if (<= y5 4.2e-176)
                   t_7
                   (if (<= y5 8.5e-108)
                     (+
                      (+
                       (* x t_9)
                       (+ (* x t_11) (+ (* (- (* b y4) (* i y5)) t_3) t_4)))
                      (- (* (- (* t y2) (* y y3)) t_5) (* j (* x t_1))))
                     (if (<= y5 8.6e-41)
                       (*
                        i
                        (+
                         (* (- (* x j) (* z k)) y1)
                         (- (* c t_2) (* y5 t_3))))
                       (if (<= y5 5.4e+183)
                         (+
                          (* c (+ (* i t_2) (* y0 (- (* x y2) (* z y3)))))
                          (- t_4 (* (- (* y y3) (* t y2)) t_5)))
                         (if (<= y5 1.15e+238)
                           (* x (+ t_9 t_11))
                           (+ t_4 (* y2 (+ (* x t_10) 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 = (b * y0) - (i * y1);
	double t_2 = (z * t) - (x * y);
	double t_3 = (t * j) - (y * k);
	double t_4 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	double t_5 = (a * y5) - (c * y4);
	double t_6 = t * t_5;
	double t_7 = z * ((k * t_1) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	double t_8 = (a * b) - (c * i);
	double t_9 = y * t_8;
	double t_10 = (c * y0) - (a * y1);
	double t_11 = y2 * t_10;
	double tmp;
	if (y5 <= -3e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -5.2e+59) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -4.8e-56) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -8.2e-161) {
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_6);
	} else if (y5 <= -6.4e-186) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= -4.1e-271) {
		tmp = t_7;
	} else if (y5 <= -3.3e-302) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_8)) + (y3 * ((c * y4) - (a * y5))));
	} else if (y5 <= 4.2e-176) {
		tmp = t_7;
	} else if (y5 <= 8.5e-108) {
		tmp = ((x * t_9) + ((x * t_11) + ((((b * y4) - (i * y5)) * t_3) + t_4))) + ((((t * y2) - (y * y3)) * t_5) - (j * (x * t_1)));
	} else if (y5 <= 8.6e-41) {
		tmp = i * ((((x * j) - (z * k)) * y1) + ((c * t_2) - (y5 * t_3)));
	} else if (y5 <= 5.4e+183) {
		tmp = (c * ((i * t_2) + (y0 * ((x * y2) - (z * y3))))) + (t_4 - (((y * y3) - (t * y2)) * t_5));
	} else if (y5 <= 1.15e+238) {
		tmp = x * (t_9 + t_11);
	} else {
		tmp = t_4 + (y2 * ((x * t_10) + 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_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 = (b * y0) - (i * y1)
    t_2 = (z * t) - (x * y)
    t_3 = (t * j) - (y * k)
    t_4 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))
    t_5 = (a * y5) - (c * y4)
    t_6 = t * t_5
    t_7 = z * ((k * t_1) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    t_8 = (a * b) - (c * i)
    t_9 = y * t_8
    t_10 = (c * y0) - (a * y1)
    t_11 = y2 * t_10
    if (y5 <= (-3d+258)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (y5 <= (-5.2d+59)) then
        tmp = (y2 * y5) * ((t * a) - (k * y0))
    else if (y5 <= (-4.8d-56)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= (-8.2d-161)) then
        tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_6)
    else if (y5 <= (-6.4d-186)) then
        tmp = y1 * (j * ((x * i) - (y3 * y4)))
    else if (y5 <= (-4.1d-271)) then
        tmp = t_7
    else if (y5 <= (-3.3d-302)) then
        tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_8)) + (y3 * ((c * y4) - (a * y5))))
    else if (y5 <= 4.2d-176) then
        tmp = t_7
    else if (y5 <= 8.5d-108) then
        tmp = ((x * t_9) + ((x * t_11) + ((((b * y4) - (i * y5)) * t_3) + t_4))) + ((((t * y2) - (y * y3)) * t_5) - (j * (x * t_1)))
    else if (y5 <= 8.6d-41) then
        tmp = i * ((((x * j) - (z * k)) * y1) + ((c * t_2) - (y5 * t_3)))
    else if (y5 <= 5.4d+183) then
        tmp = (c * ((i * t_2) + (y0 * ((x * y2) - (z * y3))))) + (t_4 - (((y * y3) - (t * y2)) * t_5))
    else if (y5 <= 1.15d+238) then
        tmp = x * (t_9 + t_11)
    else
        tmp = t_4 + (y2 * ((x * t_10) + 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 = (b * y0) - (i * y1);
	double t_2 = (z * t) - (x * y);
	double t_3 = (t * j) - (y * k);
	double t_4 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	double t_5 = (a * y5) - (c * y4);
	double t_6 = t * t_5;
	double t_7 = z * ((k * t_1) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	double t_8 = (a * b) - (c * i);
	double t_9 = y * t_8;
	double t_10 = (c * y0) - (a * y1);
	double t_11 = y2 * t_10;
	double tmp;
	if (y5 <= -3e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -5.2e+59) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -4.8e-56) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -8.2e-161) {
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_6);
	} else if (y5 <= -6.4e-186) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= -4.1e-271) {
		tmp = t_7;
	} else if (y5 <= -3.3e-302) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_8)) + (y3 * ((c * y4) - (a * y5))));
	} else if (y5 <= 4.2e-176) {
		tmp = t_7;
	} else if (y5 <= 8.5e-108) {
		tmp = ((x * t_9) + ((x * t_11) + ((((b * y4) - (i * y5)) * t_3) + t_4))) + ((((t * y2) - (y * y3)) * t_5) - (j * (x * t_1)));
	} else if (y5 <= 8.6e-41) {
		tmp = i * ((((x * j) - (z * k)) * y1) + ((c * t_2) - (y5 * t_3)));
	} else if (y5 <= 5.4e+183) {
		tmp = (c * ((i * t_2) + (y0 * ((x * y2) - (z * y3))))) + (t_4 - (((y * y3) - (t * y2)) * t_5));
	} else if (y5 <= 1.15e+238) {
		tmp = x * (t_9 + t_11);
	} else {
		tmp = t_4 + (y2 * ((x * t_10) + 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 = (b * y0) - (i * y1)
	t_2 = (z * t) - (x * y)
	t_3 = (t * j) - (y * k)
	t_4 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))
	t_5 = (a * y5) - (c * y4)
	t_6 = t * t_5
	t_7 = z * ((k * t_1) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	t_8 = (a * b) - (c * i)
	t_9 = y * t_8
	t_10 = (c * y0) - (a * y1)
	t_11 = y2 * t_10
	tmp = 0
	if y5 <= -3e+258:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif y5 <= -5.2e+59:
		tmp = (y2 * y5) * ((t * a) - (k * y0))
	elif y5 <= -4.8e-56:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
	elif y5 <= -8.2e-161:
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_6)
	elif y5 <= -6.4e-186:
		tmp = y1 * (j * ((x * i) - (y3 * y4)))
	elif y5 <= -4.1e-271:
		tmp = t_7
	elif y5 <= -3.3e-302:
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_8)) + (y3 * ((c * y4) - (a * y5))))
	elif y5 <= 4.2e-176:
		tmp = t_7
	elif y5 <= 8.5e-108:
		tmp = ((x * t_9) + ((x * t_11) + ((((b * y4) - (i * y5)) * t_3) + t_4))) + ((((t * y2) - (y * y3)) * t_5) - (j * (x * t_1)))
	elif y5 <= 8.6e-41:
		tmp = i * ((((x * j) - (z * k)) * y1) + ((c * t_2) - (y5 * t_3)))
	elif y5 <= 5.4e+183:
		tmp = (c * ((i * t_2) + (y0 * ((x * y2) - (z * y3))))) + (t_4 - (((y * y3) - (t * y2)) * t_5))
	elif y5 <= 1.15e+238:
		tmp = x * (t_9 + t_11)
	else:
		tmp = t_4 + (y2 * ((x * t_10) + 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(b * y0) - Float64(i * y1))
	t_2 = Float64(Float64(z * t) - Float64(x * y))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	t_4 = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	t_5 = Float64(Float64(a * y5) - Float64(c * y4))
	t_6 = Float64(t * t_5)
	t_7 = Float64(z * Float64(Float64(k * t_1) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_8 = Float64(Float64(a * b) - Float64(c * i))
	t_9 = Float64(y * t_8)
	t_10 = Float64(Float64(c * y0) - Float64(a * y1))
	t_11 = Float64(y2 * t_10)
	tmp = 0.0
	if (y5 <= -3e+258)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (y5 <= -5.2e+59)
		tmp = Float64(Float64(y2 * y5) * Float64(Float64(t * a) - Float64(k * y0)));
	elseif (y5 <= -4.8e-56)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_3)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= -8.2e-161)
		tmp = Float64(y2 * Float64(Float64(Float64(Float64(k * Float64(y1 * y4)) + Float64(y0 * Float64(Float64(x * c) - Float64(k * y5)))) - Float64(a * Float64(x * y1))) + t_6));
	elseif (y5 <= -6.4e-186)
		tmp = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y5 <= -4.1e-271)
		tmp = t_7;
	elseif (y5 <= -3.3e-302)
		tmp = Float64(y * Float64(Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(x * t_8)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y5 <= 4.2e-176)
		tmp = t_7;
	elseif (y5 <= 8.5e-108)
		tmp = Float64(Float64(Float64(x * t_9) + Float64(Float64(x * t_11) + Float64(Float64(Float64(Float64(b * y4) - Float64(i * y5)) * t_3) + t_4))) + Float64(Float64(Float64(Float64(t * y2) - Float64(y * y3)) * t_5) - Float64(j * Float64(x * t_1))));
	elseif (y5 <= 8.6e-41)
		tmp = Float64(i * Float64(Float64(Float64(Float64(x * j) - Float64(z * k)) * y1) + Float64(Float64(c * t_2) - Float64(y5 * t_3))));
	elseif (y5 <= 5.4e+183)
		tmp = Float64(Float64(c * Float64(Float64(i * t_2) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))) + Float64(t_4 - Float64(Float64(Float64(y * y3) - Float64(t * y2)) * t_5)));
	elseif (y5 <= 1.15e+238)
		tmp = Float64(x * Float64(t_9 + t_11));
	else
		tmp = Float64(t_4 + Float64(y2 * Float64(Float64(x * t_10) + 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 = (b * y0) - (i * y1);
	t_2 = (z * t) - (x * y);
	t_3 = (t * j) - (y * k);
	t_4 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	t_5 = (a * y5) - (c * y4);
	t_6 = t * t_5;
	t_7 = z * ((k * t_1) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	t_8 = (a * b) - (c * i);
	t_9 = y * t_8;
	t_10 = (c * y0) - (a * y1);
	t_11 = y2 * t_10;
	tmp = 0.0;
	if (y5 <= -3e+258)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (y5 <= -5.2e+59)
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	elseif (y5 <= -4.8e-56)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= -8.2e-161)
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_6);
	elseif (y5 <= -6.4e-186)
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	elseif (y5 <= -4.1e-271)
		tmp = t_7;
	elseif (y5 <= -3.3e-302)
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_8)) + (y3 * ((c * y4) - (a * y5))));
	elseif (y5 <= 4.2e-176)
		tmp = t_7;
	elseif (y5 <= 8.5e-108)
		tmp = ((x * t_9) + ((x * t_11) + ((((b * y4) - (i * y5)) * t_3) + t_4))) + ((((t * y2) - (y * y3)) * t_5) - (j * (x * t_1)));
	elseif (y5 <= 8.6e-41)
		tmp = i * ((((x * j) - (z * k)) * y1) + ((c * t_2) - (y5 * t_3)));
	elseif (y5 <= 5.4e+183)
		tmp = (c * ((i * t_2) + (y0 * ((x * y2) - (z * y3))))) + (t_4 - (((y * y3) - (t * y2)) * t_5));
	elseif (y5 <= 1.15e+238)
		tmp = x * (t_9 + t_11);
	else
		tmp = t_4 + (y2 * ((x * t_10) + 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[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(z * N[(N[(k * t$95$1), $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]}, Block[{t$95$8 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(y * t$95$8), $MachinePrecision]}, Block[{t$95$10 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$11 = N[(y2 * t$95$10), $MachinePrecision]}, If[LessEqual[y5, -3e+258], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -5.2e+59], N[(N[(y2 * y5), $MachinePrecision] * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.8e-56], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8.2e-161], N[(y2 * N[(N[(N[(N[(k * N[(y1 * y4), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6.4e-186], N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.1e-271], t$95$7, If[LessEqual[y5, -3.3e-302], N[(y * N[(N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$8), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.2e-176], t$95$7, If[LessEqual[y5, 8.5e-108], N[(N[(N[(x * t$95$9), $MachinePrecision] + N[(N[(x * t$95$11), $MachinePrecision] + N[(N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision] - N[(j * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 8.6e-41], N[(i * N[(N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision] + N[(N[(c * t$95$2), $MachinePrecision] - N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5.4e+183], N[(N[(c * N[(N[(i * t$95$2), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 - N[(N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.15e+238], N[(x * N[(t$95$9 + t$95$11), $MachinePrecision]), $MachinePrecision], N[(t$95$4 + N[(y2 * N[(N[(x * t$95$10), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if y5 < -3e258

   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 y2 around inf 11.1%

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

   3. Taylor expanded in y4 around inf 78.8%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   if -3e258 < y5 < -5.19999999999999999e59

   1. Initial program 13.8%

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

   2. Taylor expanded in y2 around inf 50.2%

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

   3. Taylor expanded in y0 around -inf 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y5 around -inf 60.9%

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

      1. associate-*r* 60.8%

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

      2. +-commutative 60.8%

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

      3. mul-1-neg 60.8%

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

      4. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   if -5.19999999999999999e59 < y5 < -4.80000000000000001e-56

   1. Initial program 30.7%

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

   2. Taylor expanded in b around inf 66.1%

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

   if -4.80000000000000001e-56 < y5 < -8.1999999999999994e-161

   1. Initial program 30.4%

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

   2. Taylor expanded in y2 around inf 52.3%

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

   3. Taylor expanded in y0 around -inf 61.0%

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

   5. Simplified 61.0%

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

   if -8.1999999999999994e-161 < y5 < -6.4000000000000001e-186

   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 y1 around inf 42.9%

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

      1. +-commutative 42.9%

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

      2. mul-1-neg 42.9%

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

      3. unsub-neg 42.9%

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

      4. *-commutative 42.9%

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

      5. *-commutative 42.9%

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

      6. *-commutative 42.9%

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

      7. mul-1-neg 42.9%

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

      8. *-commutative 42.9%

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

   4. Simplified 42.9%

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

   5. Taylor expanded in j around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -6.4000000000000001e-186 < y5 < -4.1000000000000003e-271 or -3.3000000000000002e-302 < y5 < 4.19999999999999984e-176

   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 64.6%

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

   if -4.1000000000000003e-271 < y5 < -3.3000000000000002e-302

   1. Initial program 54.5%

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

   2. Taylor expanded in y around inf 64.2%

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

   if 4.19999999999999984e-176 < y5 < 8.49999999999999986e-108

   1. Initial program 33.2%

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

   2. Taylor expanded in z around 0 59.9%

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

   if 8.49999999999999986e-108 < y5 < 8.5999999999999997e-41

   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 i around -inf 50.7%

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

   if 8.5999999999999997e-41 < y5 < 5.39999999999999964e183

   1. Initial program 45.7%

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

   3. Simplified 45.7%

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

   4. Taylor expanded in c around inf 60.6%

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

   if 5.39999999999999964e183 < y5 < 1.15000000000000001e238

   1. Initial program 26.7%

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

   2. Taylor expanded in x around inf 40.5%

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

   3. Taylor expanded in j around 0 67.2%

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

   if 1.15000000000000001e238 < y5

   1. Initial program 57.2%

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

   2. Taylor expanded in y2 around inf 71.6%

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

      1. *-commutative 71.6%

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

   4. Simplified 71.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot x - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Recombined 12 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -5.2 \cdot 10^{+59}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -4.8 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -8.2 \cdot 10^{-161}:\\ \;\;\;\;y2 \cdot \left(\left(\left(k \cdot \left(y1 \cdot y4\right) + y0 \cdot \left(x \cdot c - k \cdot y5\right)\right) - a \cdot \left(x \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -6.4 \cdot 10^{-186}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -4.1 \cdot 10^{-271}:\\ \;\;\;\;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}\;y5 \leq -3.3 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 4.2 \cdot 10^{-176}:\\ \;\;\;\;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}\;y5 \leq 8.5 \cdot 10^{-108}:\\ \;\;\;\;\left(x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right) - j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 8.6 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1 + \left(c \cdot \left(z \cdot t - x \cdot y\right) - y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 5.4 \cdot 10^{+183}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(y \cdot y3 - t \cdot y2\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{+238}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 2: 52.6% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))))
        (t_2 (* (- (* x j) (* z k)) (- (* i y1) (* b y0))))
        (t_3 (- (* a y5) (* c y4)))
        (t_4 (- (* a b) (* c i)))
        (t_5 (* (- (* b y4) (* i y5)) (- (* t j) (* y k))))
        (t_6 (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))))
   (if (<=
        (+
         (+
          (+ (+ (+ (* t_4 (- (* x y) (* z t))) t_2) t_1) t_5)
          (* (- (* t y2) (* y y3)) t_3))
         t_6)
        INFINITY)
     (+
      (+ (+ (* t_4 (fma x y (* z (- t)))) t_2) (+ t_1 t_5))
      (- t_6 (* (- (* y y3) (* t y2)) t_3)))
     (*
      z
      (+
       (* k (- (* b y0) (* i y1)))
       (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((x * y2) - (z * y3)) * ((c * y0) - (a * y1));
	double t_2 = ((x * j) - (z * k)) * ((i * y1) - (b * y0));
	double t_3 = (a * y5) - (c * y4);
	double t_4 = (a * b) - (c * i);
	double t_5 = ((b * y4) - (i * y5)) * ((t * j) - (y * k));
	double t_6 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	double tmp;
	if (((((((t_4 * ((x * y) - (z * t))) + t_2) + t_1) + t_5) + (((t * y2) - (y * y3)) * t_3)) + t_6) <= ((double) INFINITY)) {
		tmp = (((t_4 * fma(x, y, (z * -t))) + t_2) + (t_1 + t_5)) + (t_6 - (((y * y3) - (t * y2)) * t_3));
	} else {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))
	t_2 = Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(i * y1) - Float64(b * y0)))
	t_3 = Float64(Float64(a * y5) - Float64(c * y4))
	t_4 = Float64(Float64(a * b) - Float64(c * i))
	t_5 = Float64(Float64(Float64(b * y4) - Float64(i * y5)) * Float64(Float64(t * j) - Float64(y * k)))
	t_6 = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(t_4 * Float64(Float64(x * y) - Float64(z * t))) + t_2) + t_1) + t_5) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * t_3)) + t_6) <= Inf)
		tmp = Float64(Float64(Float64(Float64(t_4 * fma(x, y, Float64(z * Float64(-t)))) + t_2) + Float64(t_1 + t_5)) + Float64(t_6 - Float64(Float64(Float64(y * y3) - Float64(t * y2)) * t_3)));
	else
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))));
	end
	return tmp
end

Wolfram

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

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 90.7%

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

   3. Simplified 90.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around -inf 41.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.6%

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

Alternative 3: 52.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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 90.7%

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

   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 z around -inf 41.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.6%

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

Alternative 4: 35.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 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)\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := a \cdot b - c \cdot i\\ t_4 := y \cdot t_3 + y2 \cdot t_2\\ t_5 := i \cdot y1 - b \cdot y0\\ t_6 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{if}\;y5 \leq -3 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -5.7 \cdot 10^{+59}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -9.9 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -5.5 \cdot 10^{-160}:\\ \;\;\;\;y2 \cdot \left(\left(\left(k \cdot \left(y1 \cdot y4\right) + y0 \cdot \left(x \cdot c - k \cdot y5\right)\right) - a \cdot \left(x \cdot y1\right)\right) + t_6\right)\\ \mathbf{elif}\;y5 \leq -1.75 \cdot 10^{-189}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1.95 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -4.3 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot t_3\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t_5\right)\\ \mathbf{elif}\;y5 \leq 1.26 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.45 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(t_4 + j \cdot t_5\right)\\ \mathbf{elif}\;y5 \leq 7 \cdot 10^{+237}:\\ \;\;\;\;x \cdot t_4\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(x \cdot t_2 + 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
          (+
           (* k (- (* b y0) (* i y1)))
           (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0)))))))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* a b) (* c i)))
        (t_4 (+ (* y t_3) (* y2 t_2)))
        (t_5 (- (* i y1) (* b y0)))
        (t_6 (* t (- (* a y5) (* c y4)))))
   (if (<= y5 -3e+258)
     (* (* y2 y4) (- (* k y1) (* t c)))
     (if (<= y5 -5.7e+59)
       (* (* y2 y5) (- (* t a) (* k y0)))
       (if (<= y5 -9.9e-57)
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))
         (if (<= y5 -5.5e-160)
           (*
            y2
            (+
             (- (+ (* k (* y1 y4)) (* y0 (- (* x c) (* k y5)))) (* a (* x y1)))
             t_6))
           (if (<= y5 -1.75e-189)
             (* y1 (* j (- (* x i) (* y3 y4))))
             (if (<= y5 -1.95e-271)
               t_1
               (if (<= y5 -4.3e-302)
                 (*
                  y
                  (+
                   (+ (* k (- (* i y5) (* b y4))) (* x t_3))
                   (* y3 (- (* c y4) (* a y5)))))
                 (if (<= y5 1.4e-194)
                   t_1
                   (if (<= y5 5.5e-131)
                     (*
                      j
                      (+
                       (+
                        (* t (- (* b y4) (* i y5)))
                        (* y3 (- (* y0 y5) (* y1 y4))))
                       (* x t_5)))
                     (if (<= y5 1.26e-78)
                       (*
                        c
                        (+
                         (+
                          (* i (- (* z t) (* x y)))
                          (* y0 (- (* x y2) (* z y3))))
                         (* y4 (- (* y y3) (* t y2)))))
                       (if (<= y5 1.45e+168)
                         (* x (+ t_4 (* j t_5)))
                         (if (<= y5 7e+237)
                           (* x t_4)
                           (+
                            (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
                            (* y2 (+ (* x t_2) 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 * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (a * b) - (c * i);
	double t_4 = (y * t_3) + (y2 * t_2);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = t * ((a * y5) - (c * y4));
	double tmp;
	if (y5 <= -3e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -5.7e+59) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -9.9e-57) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -5.5e-160) {
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_6);
	} else if (y5 <= -1.75e-189) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= -1.95e-271) {
		tmp = t_1;
	} else if (y5 <= -4.3e-302) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_3)) + (y3 * ((c * y4) - (a * y5))));
	} else if (y5 <= 1.4e-194) {
		tmp = t_1;
	} else if (y5 <= 5.5e-131) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5));
	} else if (y5 <= 1.26e-78) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.45e+168) {
		tmp = x * (t_4 + (j * t_5));
	} else if (y5 <= 7e+237) {
		tmp = x * t_4;
	} else {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * ((x * t_2) + 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_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    t_2 = (c * y0) - (a * y1)
    t_3 = (a * b) - (c * i)
    t_4 = (y * t_3) + (y2 * t_2)
    t_5 = (i * y1) - (b * y0)
    t_6 = t * ((a * y5) - (c * y4))
    if (y5 <= (-3d+258)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (y5 <= (-5.7d+59)) then
        tmp = (y2 * y5) * ((t * a) - (k * y0))
    else if (y5 <= (-9.9d-57)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= (-5.5d-160)) then
        tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_6)
    else if (y5 <= (-1.75d-189)) then
        tmp = y1 * (j * ((x * i) - (y3 * y4)))
    else if (y5 <= (-1.95d-271)) then
        tmp = t_1
    else if (y5 <= (-4.3d-302)) then
        tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_3)) + (y3 * ((c * y4) - (a * y5))))
    else if (y5 <= 1.4d-194) then
        tmp = t_1
    else if (y5 <= 5.5d-131) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5))
    else if (y5 <= 1.26d-78) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 1.45d+168) then
        tmp = x * (t_4 + (j * t_5))
    else if (y5 <= 7d+237) then
        tmp = x * t_4
    else
        tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * ((x * t_2) + 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 * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (a * b) - (c * i);
	double t_4 = (y * t_3) + (y2 * t_2);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = t * ((a * y5) - (c * y4));
	double tmp;
	if (y5 <= -3e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -5.7e+59) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -9.9e-57) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -5.5e-160) {
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_6);
	} else if (y5 <= -1.75e-189) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= -1.95e-271) {
		tmp = t_1;
	} else if (y5 <= -4.3e-302) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_3)) + (y3 * ((c * y4) - (a * y5))));
	} else if (y5 <= 1.4e-194) {
		tmp = t_1;
	} else if (y5 <= 5.5e-131) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5));
	} else if (y5 <= 1.26e-78) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.45e+168) {
		tmp = x * (t_4 + (j * t_5));
	} else if (y5 <= 7e+237) {
		tmp = x * t_4;
	} else {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * ((x * t_2) + 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 * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	t_2 = (c * y0) - (a * y1)
	t_3 = (a * b) - (c * i)
	t_4 = (y * t_3) + (y2 * t_2)
	t_5 = (i * y1) - (b * y0)
	t_6 = t * ((a * y5) - (c * y4))
	tmp = 0
	if y5 <= -3e+258:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif y5 <= -5.7e+59:
		tmp = (y2 * y5) * ((t * a) - (k * y0))
	elif y5 <= -9.9e-57:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y5 <= -5.5e-160:
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_6)
	elif y5 <= -1.75e-189:
		tmp = y1 * (j * ((x * i) - (y3 * y4)))
	elif y5 <= -1.95e-271:
		tmp = t_1
	elif y5 <= -4.3e-302:
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_3)) + (y3 * ((c * y4) - (a * y5))))
	elif y5 <= 1.4e-194:
		tmp = t_1
	elif y5 <= 5.5e-131:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5))
	elif y5 <= 1.26e-78:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 1.45e+168:
		tmp = x * (t_4 + (j * t_5))
	elif y5 <= 7e+237:
		tmp = x * t_4
	else:
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * ((x * t_2) + 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(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(a * b) - Float64(c * i))
	t_4 = Float64(Float64(y * t_3) + Float64(y2 * t_2))
	t_5 = Float64(Float64(i * y1) - Float64(b * y0))
	t_6 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	tmp = 0.0
	if (y5 <= -3e+258)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (y5 <= -5.7e+59)
		tmp = Float64(Float64(y2 * y5) * Float64(Float64(t * a) - Float64(k * y0)));
	elseif (y5 <= -9.9e-57)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= -5.5e-160)
		tmp = Float64(y2 * Float64(Float64(Float64(Float64(k * Float64(y1 * y4)) + Float64(y0 * Float64(Float64(x * c) - Float64(k * y5)))) - Float64(a * Float64(x * y1))) + t_6));
	elseif (y5 <= -1.75e-189)
		tmp = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y5 <= -1.95e-271)
		tmp = t_1;
	elseif (y5 <= -4.3e-302)
		tmp = Float64(y * Float64(Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(x * t_3)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y5 <= 1.4e-194)
		tmp = t_1;
	elseif (y5 <= 5.5e-131)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_5)));
	elseif (y5 <= 1.26e-78)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 1.45e+168)
		tmp = Float64(x * Float64(t_4 + Float64(j * t_5)));
	elseif (y5 <= 7e+237)
		tmp = Float64(x * t_4);
	else
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y2 * Float64(Float64(x * t_2) + 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 * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	t_2 = (c * y0) - (a * y1);
	t_3 = (a * b) - (c * i);
	t_4 = (y * t_3) + (y2 * t_2);
	t_5 = (i * y1) - (b * y0);
	t_6 = t * ((a * y5) - (c * y4));
	tmp = 0.0;
	if (y5 <= -3e+258)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (y5 <= -5.7e+59)
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	elseif (y5 <= -9.9e-57)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= -5.5e-160)
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_6);
	elseif (y5 <= -1.75e-189)
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	elseif (y5 <= -1.95e-271)
		tmp = t_1;
	elseif (y5 <= -4.3e-302)
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_3)) + (y3 * ((c * y4) - (a * y5))));
	elseif (y5 <= 1.4e-194)
		tmp = t_1;
	elseif (y5 <= 5.5e-131)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5));
	elseif (y5 <= 1.26e-78)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 1.45e+168)
		tmp = x * (t_4 + (j * t_5));
	elseif (y5 <= 7e+237)
		tmp = x * t_4;
	else
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * ((x * t_2) + 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[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $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]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * t$95$3), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3e+258], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -5.7e+59], N[(N[(y2 * y5), $MachinePrecision] * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -9.9e-57], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -5.5e-160], N[(y2 * N[(N[(N[(N[(k * N[(y1 * y4), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.75e-189], N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.95e-271], t$95$1, If[LessEqual[y5, -4.3e-302], N[(y * N[(N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.4e-194], t$95$1, If[LessEqual[y5, 5.5e-131], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.26e-78], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.45e+168], N[(x * N[(t$95$4 + N[(j * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7e+237], N[(x * t$95$4), $MachinePrecision], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(x * t$95$2), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if y5 < -3e258

   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 y2 around inf 11.1%

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

   3. Taylor expanded in y4 around inf 78.8%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   if -3e258 < y5 < -5.7000000000000001e59

   1. Initial program 13.8%

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

   2. Taylor expanded in y2 around inf 50.2%

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

   3. Taylor expanded in y0 around -inf 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y5 around -inf 60.9%

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

      1. associate-*r* 60.8%

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

      2. +-commutative 60.8%

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

      3. mul-1-neg 60.8%

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

      4. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   if -5.7000000000000001e59 < y5 < -9.8999999999999995e-57

   1. Initial program 30.7%

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

   2. Taylor expanded in b around inf 66.1%

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

   if -9.8999999999999995e-57 < y5 < -5.5e-160

   1. Initial program 30.4%

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

   2. Taylor expanded in y2 around inf 52.3%

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

   3. Taylor expanded in y0 around -inf 61.0%

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

   5. Simplified 61.0%

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

   if -5.5e-160 < y5 < -1.7500000000000001e-189

   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 y1 around inf 42.9%

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

      1. +-commutative 42.9%

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

      2. mul-1-neg 42.9%

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

      3. unsub-neg 42.9%

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

      4. *-commutative 42.9%

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

      5. *-commutative 42.9%

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

      6. *-commutative 42.9%

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

      7. mul-1-neg 42.9%

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

      8. *-commutative 42.9%

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

   4. Simplified 42.9%

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

   5. Taylor expanded in j around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -1.7500000000000001e-189 < y5 < -1.94999999999999999e-271 or -4.3000000000000002e-302 < y5 < 1.40000000000000006e-194

   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 66.0%

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

   if -1.94999999999999999e-271 < y5 < -4.3000000000000002e-302

   1. Initial program 54.5%

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

   2. Taylor expanded in y around inf 64.2%

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

   if 1.40000000000000006e-194 < y5 < 5.4999999999999997e-131

   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 j around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. *-commutative 58.0%

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

   4. Simplified 58.0%

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

   if 5.4999999999999997e-131 < y5 < 1.26000000000000008e-78

   1. Initial program 46.0%

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

   2. Taylor expanded in c around inf 62.4%

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

   4. Simplified 62.4%

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

   if 1.26000000000000008e-78 < y5 < 1.45e168

   1. Initial program 43.4%

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

   2. Taylor expanded in x around inf 57.5%

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

   if 1.45e168 < y5 < 6.99999999999999976e237

   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 x around inf 38.0%

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

   3. Taylor expanded in j around 0 63.0%

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

   if 6.99999999999999976e237 < y5

   1. Initial program 57.2%

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

   2. Taylor expanded in y2 around inf 71.6%

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

      1. *-commutative 71.6%

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

   4. Simplified 71.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot x - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Recombined 12 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -5.7 \cdot 10^{+59}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -9.9 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -5.5 \cdot 10^{-160}:\\ \;\;\;\;y2 \cdot \left(\left(\left(k \cdot \left(y1 \cdot y4\right) + y0 \cdot \left(x \cdot c - k \cdot y5\right)\right) - a \cdot \left(x \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1.75 \cdot 10^{-189}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1.95 \cdot 10^{-271}:\\ \;\;\;\;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}\;y5 \leq -4.3 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4 \cdot 10^{-194}:\\ \;\;\;\;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}\;y5 \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.26 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.45 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 7 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 5: 36.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_5 := y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t_4\right)\\ t_6 := c \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{if}\;y1 \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq -4.8 \cdot 10^{-114}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t_3\right) + t_6\right)\\ \mathbf{elif}\;y1 \leq -1.05 \cdot 10^{-209}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y1 \leq -5.2 \cdot 10^{-287}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y1 \leq 3.3 \cdot 10^{-246}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.35 \cdot 10^{-195}:\\ \;\;\;\;y4 \cdot t_6\\ \mathbf{elif}\;y1 \leq 1.22 \cdot 10^{-107}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 1.66 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq 9.2 \cdot 10^{+128}:\\ \;\;\;\;y2 \cdot \left(x \cdot t_1 + t_4\right)\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{+198}:\\ \;\;\;\;y1 \cdot \left(\left(y4 \cdot t_3 - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_1))
           (* j (- (* i y1) (* b y0))))))
        (t_3 (- (* k y2) (* j y3)))
        (t_4 (* t (- (* a y5) (* c y4))))
        (t_5 (* y2 (+ (* y0 (- (* x c) (* k y5))) t_4)))
        (t_6 (* c (- (* y y3) (* t y2)))))
   (if (<= y1 -6.8e+31)
     t_2
     (if (<= y1 -4.8e-114)
       (* y4 (+ (+ (* b (- (* t j) (* y k))) (* y1 t_3)) t_6))
       (if (<= y1 -1.05e-209)
         t_5
         (if (<= y1 -3.8e-251)
           (+
            (* x (* c (- (* y0 y2) (* y i))))
            (* (* x a) (- (* y b) (* y1 y2))))
           (if (<= y1 -5.2e-287)
             t_5
             (if (<= y1 3.3e-246)
               (*
                y3
                (+
                 (* y (- (* c y4) (* a y5)))
                 (+
                  (* z (- (* a y1) (* c y0)))
                  (* j (- (* y0 y5) (* y1 y4))))))
               (if (<= y1 1.35e-195)
                 (* y4 t_6)
                 (if (<= y1 1.22e-107)
                   (*
                    k
                    (+
                     (+
                      (* y2 (- (* y1 y4) (* y0 y5)))
                      (* y (- (* i y5) (* b y4))))
                     (* z (- (* b y0) (* i y1)))))
                   (if (<= y1 1.66e-28)
                     t_2
                     (if (<= y1 9.2e+128)
                       (* y2 (+ (* x t_1) t_4))
                       (if (<= y1 2e+198)
                         (*
                          y1
                          (+
                           (- (* y4 t_3) (* a (- (* x y2) (* z y3))))
                           (* i (- (* x j) (* z k)))))
                         (* (* z y1) (- (* a y3) (* i k))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double t_3 = (k * y2) - (j * y3);
	double t_4 = t * ((a * y5) - (c * y4));
	double t_5 = y2 * ((y0 * ((x * c) - (k * y5))) + t_4);
	double t_6 = c * ((y * y3) - (t * y2));
	double tmp;
	if (y1 <= -6.8e+31) {
		tmp = t_2;
	} else if (y1 <= -4.8e-114) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + t_6);
	} else if (y1 <= -1.05e-209) {
		tmp = t_5;
	} else if (y1 <= -3.8e-251) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y1 <= -5.2e-287) {
		tmp = t_5;
	} else if (y1 <= 3.3e-246) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))));
	} else if (y1 <= 1.35e-195) {
		tmp = y4 * t_6;
	} else if (y1 <= 1.22e-107) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (y1 <= 1.66e-28) {
		tmp = t_2;
	} else if (y1 <= 9.2e+128) {
		tmp = y2 * ((x * t_1) + t_4);
	} else if (y1 <= 2e+198) {
		tmp = y1 * (((y4 * t_3) - (a * ((x * y2) - (z * y3)))) + (i * ((x * j) - (z * k))));
	} else {
		tmp = (z * y1) * ((a * y3) - (i * k));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
    t_3 = (k * y2) - (j * y3)
    t_4 = t * ((a * y5) - (c * y4))
    t_5 = y2 * ((y0 * ((x * c) - (k * y5))) + t_4)
    t_6 = c * ((y * y3) - (t * y2))
    if (y1 <= (-6.8d+31)) then
        tmp = t_2
    else if (y1 <= (-4.8d-114)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + t_6)
    else if (y1 <= (-1.05d-209)) then
        tmp = t_5
    else if (y1 <= (-3.8d-251)) then
        tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
    else if (y1 <= (-5.2d-287)) then
        tmp = t_5
    else if (y1 <= 3.3d-246) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))))
    else if (y1 <= 1.35d-195) then
        tmp = y4 * t_6
    else if (y1 <= 1.22d-107) then
        tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    else if (y1 <= 1.66d-28) then
        tmp = t_2
    else if (y1 <= 9.2d+128) then
        tmp = y2 * ((x * t_1) + t_4)
    else if (y1 <= 2d+198) then
        tmp = y1 * (((y4 * t_3) - (a * ((x * y2) - (z * y3)))) + (i * ((x * j) - (z * k))))
    else
        tmp = (z * y1) * ((a * y3) - (i * k))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double t_3 = (k * y2) - (j * y3);
	double t_4 = t * ((a * y5) - (c * y4));
	double t_5 = y2 * ((y0 * ((x * c) - (k * y5))) + t_4);
	double t_6 = c * ((y * y3) - (t * y2));
	double tmp;
	if (y1 <= -6.8e+31) {
		tmp = t_2;
	} else if (y1 <= -4.8e-114) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + t_6);
	} else if (y1 <= -1.05e-209) {
		tmp = t_5;
	} else if (y1 <= -3.8e-251) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y1 <= -5.2e-287) {
		tmp = t_5;
	} else if (y1 <= 3.3e-246) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))));
	} else if (y1 <= 1.35e-195) {
		tmp = y4 * t_6;
	} else if (y1 <= 1.22e-107) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (y1 <= 1.66e-28) {
		tmp = t_2;
	} else if (y1 <= 9.2e+128) {
		tmp = y2 * ((x * t_1) + t_4);
	} else if (y1 <= 2e+198) {
		tmp = y1 * (((y4 * t_3) - (a * ((x * y2) - (z * y3)))) + (i * ((x * j) - (z * k))));
	} else {
		tmp = (z * y1) * ((a * y3) - (i * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
	t_3 = (k * y2) - (j * y3)
	t_4 = t * ((a * y5) - (c * y4))
	t_5 = y2 * ((y0 * ((x * c) - (k * y5))) + t_4)
	t_6 = c * ((y * y3) - (t * y2))
	tmp = 0
	if y1 <= -6.8e+31:
		tmp = t_2
	elif y1 <= -4.8e-114:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + t_6)
	elif y1 <= -1.05e-209:
		tmp = t_5
	elif y1 <= -3.8e-251:
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
	elif y1 <= -5.2e-287:
		tmp = t_5
	elif y1 <= 3.3e-246:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))))
	elif y1 <= 1.35e-195:
		tmp = y4 * t_6
	elif y1 <= 1.22e-107:
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	elif y1 <= 1.66e-28:
		tmp = t_2
	elif y1 <= 9.2e+128:
		tmp = y2 * ((x * t_1) + t_4)
	elif y1 <= 2e+198:
		tmp = y1 * (((y4 * t_3) - (a * ((x * y2) - (z * y3)))) + (i * ((x * j) - (z * k))))
	else:
		tmp = (z * y1) * ((a * y3) - (i * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_5 = Float64(y2 * Float64(Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))) + t_4))
	t_6 = Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))
	tmp = 0.0
	if (y1 <= -6.8e+31)
		tmp = t_2;
	elseif (y1 <= -4.8e-114)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_3)) + t_6));
	elseif (y1 <= -1.05e-209)
		tmp = t_5;
	elseif (y1 <= -3.8e-251)
		tmp = Float64(Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i)))) + Float64(Float64(x * a) * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y1 <= -5.2e-287)
		tmp = t_5;
	elseif (y1 <= 3.3e-246)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(z * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))))));
	elseif (y1 <= 1.35e-195)
		tmp = Float64(y4 * t_6);
	elseif (y1 <= 1.22e-107)
		tmp = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y1 <= 1.66e-28)
		tmp = t_2;
	elseif (y1 <= 9.2e+128)
		tmp = Float64(y2 * Float64(Float64(x * t_1) + t_4));
	elseif (y1 <= 2e+198)
		tmp = Float64(y1 * Float64(Float64(Float64(y4 * t_3) - Float64(a * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(i * Float64(Float64(x * j) - Float64(z * k)))));
	else
		tmp = Float64(Float64(z * y1) * Float64(Float64(a * y3) - Float64(i * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	t_3 = (k * y2) - (j * y3);
	t_4 = t * ((a * y5) - (c * y4));
	t_5 = y2 * ((y0 * ((x * c) - (k * y5))) + t_4);
	t_6 = c * ((y * y3) - (t * y2));
	tmp = 0.0;
	if (y1 <= -6.8e+31)
		tmp = t_2;
	elseif (y1 <= -4.8e-114)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + t_6);
	elseif (y1 <= -1.05e-209)
		tmp = t_5;
	elseif (y1 <= -3.8e-251)
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	elseif (y1 <= -5.2e-287)
		tmp = t_5;
	elseif (y1 <= 3.3e-246)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))));
	elseif (y1 <= 1.35e-195)
		tmp = y4 * t_6;
	elseif (y1 <= 1.22e-107)
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	elseif (y1 <= 1.66e-28)
		tmp = t_2;
	elseif (y1 <= 9.2e+128)
		tmp = y2 * ((x * t_1) + t_4);
	elseif (y1 <= 2e+198)
		tmp = y1 * (((y4 * t_3) - (a * ((x * y2) - (z * y3)))) + (i * ((x * j) - (z * k))));
	else
		tmp = (z * y1) * ((a * y3) - (i * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y2 * N[(N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -6.8e+31], t$95$2, If[LessEqual[y1, -4.8e-114], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.05e-209], t$95$5, If[LessEqual[y1, -3.8e-251], N[(N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * a), $MachinePrecision] * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5.2e-287], t$95$5, If[LessEqual[y1, 3.3e-246], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.35e-195], N[(y4 * t$95$6), $MachinePrecision], If[LessEqual[y1, 1.22e-107], 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[y1, 1.66e-28], t$95$2, If[LessEqual[y1, 9.2e+128], N[(y2 * N[(N[(x * t$95$1), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2e+198], N[(y1 * N[(N[(N[(y4 * t$95$3), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y1), $MachinePrecision] * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y1 < -6.7999999999999996e31 or 1.22000000000000001e-107 < y1 < 1.66000000000000003e-28

   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 x around inf 58.7%

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

   if -6.7999999999999996e31 < y1 < -4.8000000000000002e-114

   1. Initial program 35.6%

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

   2. Taylor expanded in y4 around inf 52.5%

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

   if -4.8000000000000002e-114 < y1 < -1.04999999999999998e-209 or -3.7999999999999997e-251 < y1 < -5.1999999999999999e-287

   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 y2 around inf 61.6%

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

   3. Taylor expanded in y0 around -inf 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in y1 around 0 68.4%

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

   if -1.04999999999999998e-209 < y1 < -3.7999999999999997e-251

   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 x around inf 66.6%

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

   3. Taylor expanded in j around 0 67.2%

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

   4. Taylor expanded in a around -inf 77.9%

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

      1. +-commutative 77.9%

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

      2. mul-1-neg 77.9%

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

      3. unsub-neg 77.9%

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

      4. mul-1-neg 77.9%

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

      5. distribute-rgt-neg-in 77.9%

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

      6. mul-1-neg 77.9%

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

      7. distribute-lft-in 77.9%

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

      8. +-commutative 77.9%

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

      9. mul-1-neg 77.9%

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

      10. unsub-neg 77.9%

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

      11. *-commutative 77.9%

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

      12. associate-*r* 89.0%

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

      13. *-commutative 89.0%

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

   6. Simplified 89.0%

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

   if -5.1999999999999999e-287 < y1 < 3.3000000000000001e-246

   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 y3 around -inf 57.7%

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

   if 3.3000000000000001e-246 < y1 < 1.35e-195

   1. Initial program 22.3%

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

   2. Taylor expanded in y4 around inf 45.0%

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

   3. Taylor expanded in c around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. *-commutative 57.2%

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

   5. Simplified 57.2%

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

   if 1.35e-195 < y1 < 1.22000000000000001e-107

   1. Initial program 33.2%

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

   2. Taylor expanded in k around inf 61.6%

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

      1. +-commutative 61.6%

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

      2. mul-1-neg 61.6%

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

      3. unsub-neg 61.6%

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

      4. *-commutative 61.6%

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

      5. mul-1-neg 61.6%

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

   4. Simplified 61.6%

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

   if 1.66000000000000003e-28 < y1 < 9.19999999999999992e128

   1. Initial program 34.7%

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

   2. Taylor expanded in y2 around inf 48.9%

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

   3. Taylor expanded in k around 0 52.3%

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

   if 9.19999999999999992e128 < y1 < 2.00000000000000004e198

   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 80.0%

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

      1. +-commutative 80.0%

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

      2. mul-1-neg 80.0%

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

      3. unsub-neg 80.0%

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

      4. *-commutative 80.0%

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

      5. *-commutative 80.0%

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

      6. *-commutative 80.0%

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

      7. mul-1-neg 80.0%

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

      8. *-commutative 80.0%

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

   4. Simplified 80.0%

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

   if 2.00000000000000004e198 < y1

   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 y1 around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. mul-1-neg 51.6%

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

      3. unsub-neg 51.6%

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

      4. *-commutative 51.6%

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

      5. *-commutative 51.6%

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

      6. *-commutative 51.6%

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

      7. mul-1-neg 51.6%

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

      8. *-commutative 51.6%

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

   4. Simplified 51.6%

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

   5. Taylor expanded in z around inf 62.1%

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

      1. associate-*r* 65.1%

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

      2. distribute-lft-out-- 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -4.8 \cdot 10^{-114}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.05 \cdot 10^{-209}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y1 \leq -5.2 \cdot 10^{-287}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 3.3 \cdot 10^{-246}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.35 \cdot 10^{-195}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 1.22 \cdot 10^{-107}:\\ \;\;\;\;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}\;y1 \leq 1.66 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 9.2 \cdot 10^{+128}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{+198}:\\ \;\;\;\;y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \end{array} \]

Alternative 6: 35.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t_2\right)\\ t_4 := z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ t_5 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_1\right) + j \cdot t_2\right)\\ \mathbf{if}\;y5 \leq -2.2 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -1.92 \cdot 10^{+58}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -6.2 \cdot 10^{-76}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1.75 \cdot 10^{-142}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y5 \leq -1.2 \cdot 10^{-186}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq -6.5 \cdot 10^{-295}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq -5.6 \cdot 10^{-302}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y5 \leq 1.85 \cdot 10^{-190}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq 4.9 \cdot 10^{-132}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq 1.26 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 7.4 \cdot 10^{+65}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot t_1 + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* i y1) (* b y0)))
        (t_3
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x t_2))))
        (t_4
         (*
          z
          (+
           (* k (- (* b y0) (* i y1)))
           (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0)))))))
        (t_5 (* x (+ (+ (* y (- (* a b) (* c i))) (* y2 t_1)) (* j t_2)))))
   (if (<= y5 -2.2e+258)
     (* (* y2 y4) (- (* k y1) (* t c)))
     (if (<= y5 -1.92e+58)
       (* (* y2 y5) (- (* t a) (* k y0)))
       (if (<= y5 -6.2e-76)
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))
         (if (<= y5 -1.75e-142)
           (* y1 (* y2 (- (* k y4) (* x a))))
           (if (<= y5 -1.2e-186)
             t_3
             (if (<= y5 -6.5e-295)
               t_4
               (if (<= y5 -5.6e-302)
                 t_5
                 (if (<= y5 1.85e-190)
                   t_4
                   (if (<= y5 4.9e-132)
                     t_3
                     (if (<= y5 1.26e-78)
                       (*
                        c
                        (+
                         (+
                          (* i (- (* z t) (* x y)))
                          (* y0 (- (* x y2) (* z y3))))
                         (* y4 (- (* y y3) (* t y2)))))
                       (if (<= y5 7.4e+65)
                         t_5
                         (*
                          y2
                          (+
                           (* k (- (* y1 y4) (* y0 y5)))
                           (+
                            (* x t_1)
                            (* t (- (* a y5) (* c y4)))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	double t_4 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	double t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	double tmp;
	if (y5 <= -2.2e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -1.92e+58) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -6.2e-76) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -1.75e-142) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y5 <= -1.2e-186) {
		tmp = t_3;
	} else if (y5 <= -6.5e-295) {
		tmp = t_4;
	} else if (y5 <= -5.6e-302) {
		tmp = t_5;
	} else if (y5 <= 1.85e-190) {
		tmp = t_4;
	} else if (y5 <= 4.9e-132) {
		tmp = t_3;
	} else if (y5 <= 1.26e-78) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 7.4e+65) {
		tmp = t_5;
	} else {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_1) + (t * ((a * y5) - (c * y4)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (i * y1) - (b * y0)
    t_3 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2))
    t_4 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2))
    if (y5 <= (-2.2d+258)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (y5 <= (-1.92d+58)) then
        tmp = (y2 * y5) * ((t * a) - (k * y0))
    else if (y5 <= (-6.2d-76)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= (-1.75d-142)) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (y5 <= (-1.2d-186)) then
        tmp = t_3
    else if (y5 <= (-6.5d-295)) then
        tmp = t_4
    else if (y5 <= (-5.6d-302)) then
        tmp = t_5
    else if (y5 <= 1.85d-190) then
        tmp = t_4
    else if (y5 <= 4.9d-132) then
        tmp = t_3
    else if (y5 <= 1.26d-78) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 7.4d+65) then
        tmp = t_5
    else
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_1) + (t * ((a * y5) - (c * y4)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	double t_4 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	double t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	double tmp;
	if (y5 <= -2.2e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -1.92e+58) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -6.2e-76) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -1.75e-142) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y5 <= -1.2e-186) {
		tmp = t_3;
	} else if (y5 <= -6.5e-295) {
		tmp = t_4;
	} else if (y5 <= -5.6e-302) {
		tmp = t_5;
	} else if (y5 <= 1.85e-190) {
		tmp = t_4;
	} else if (y5 <= 4.9e-132) {
		tmp = t_3;
	} else if (y5 <= 1.26e-78) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 7.4e+65) {
		tmp = t_5;
	} else {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_1) + (t * ((a * y5) - (c * y4)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (i * y1) - (b * y0)
	t_3 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2))
	t_4 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2))
	tmp = 0
	if y5 <= -2.2e+258:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif y5 <= -1.92e+58:
		tmp = (y2 * y5) * ((t * a) - (k * y0))
	elif y5 <= -6.2e-76:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y5 <= -1.75e-142:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif y5 <= -1.2e-186:
		tmp = t_3
	elif y5 <= -6.5e-295:
		tmp = t_4
	elif y5 <= -5.6e-302:
		tmp = t_5
	elif y5 <= 1.85e-190:
		tmp = t_4
	elif y5 <= 4.9e-132:
		tmp = t_3
	elif y5 <= 1.26e-78:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 7.4e+65:
		tmp = t_5
	else:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_1) + (t * ((a * y5) - (c * y4)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	t_3 = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_2)))
	t_4 = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_5 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)) + Float64(j * t_2)))
	tmp = 0.0
	if (y5 <= -2.2e+258)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (y5 <= -1.92e+58)
		tmp = Float64(Float64(y2 * y5) * Float64(Float64(t * a) - Float64(k * y0)));
	elseif (y5 <= -6.2e-76)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= -1.75e-142)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y5 <= -1.2e-186)
		tmp = t_3;
	elseif (y5 <= -6.5e-295)
		tmp = t_4;
	elseif (y5 <= -5.6e-302)
		tmp = t_5;
	elseif (y5 <= 1.85e-190)
		tmp = t_4;
	elseif (y5 <= 4.9e-132)
		tmp = t_3;
	elseif (y5 <= 1.26e-78)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 7.4e+65)
		tmp = t_5;
	else
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(x * t_1) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (i * y1) - (b * y0);
	t_3 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	t_4 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	tmp = 0.0;
	if (y5 <= -2.2e+258)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (y5 <= -1.92e+58)
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	elseif (y5 <= -6.2e-76)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= -1.75e-142)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (y5 <= -1.2e-186)
		tmp = t_3;
	elseif (y5 <= -6.5e-295)
		tmp = t_4;
	elseif (y5 <= -5.6e-302)
		tmp = t_5;
	elseif (y5 <= 1.85e-190)
		tmp = t_4;
	elseif (y5 <= 4.9e-132)
		tmp = t_3;
	elseif (y5 <= 1.26e-78)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 7.4e+65)
		tmp = t_5;
	else
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_1) + (t * ((a * y5) - (c * y4)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $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]}, Block[{t$95$5 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.2e+258], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.92e+58], N[(N[(y2 * y5), $MachinePrecision] * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6.2e-76], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.75e-142], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.2e-186], t$95$3, If[LessEqual[y5, -6.5e-295], t$95$4, If[LessEqual[y5, -5.6e-302], t$95$5, If[LessEqual[y5, 1.85e-190], t$95$4, If[LessEqual[y5, 4.9e-132], t$95$3, If[LessEqual[y5, 1.26e-78], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.4e+65], t$95$5, N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * t$95$1), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y5 < -2.19999999999999983e258

   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 y2 around inf 11.1%

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

   3. Taylor expanded in y4 around inf 78.8%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   if -2.19999999999999983e258 < y5 < -1.92000000000000004e58

   1. Initial program 13.8%

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

   2. Taylor expanded in y2 around inf 50.2%

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

   3. Taylor expanded in y0 around -inf 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y5 around -inf 60.9%

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

      1. associate-*r* 60.8%

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

      2. +-commutative 60.8%

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

      3. mul-1-neg 60.8%

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

      4. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   if -1.92000000000000004e58 < y5 < -6.19999999999999939e-76

   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 b around inf 56.1%

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

   if -6.19999999999999939e-76 < y5 < -1.75000000000000007e-142

   1. Initial program 35.7%

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

   2. Taylor expanded in y2 around inf 57.4%

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

   3. Taylor expanded in y1 around inf 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. sub-neg 71.9%

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

      4. *-commutative 71.9%

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

      5. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   if -1.75000000000000007e-142 < y5 < -1.20000000000000002e-186 or 1.8500000000000001e-190 < y5 < 4.89999999999999981e-132

   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 j around inf 67.5%

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

      1. +-commutative 67.5%

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

      2. mul-1-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

   4. Simplified 67.5%

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

   if -1.20000000000000002e-186 < y5 < -6.4999999999999998e-295 or -5.6e-302 < y5 < 1.8500000000000001e-190

   1. Initial program 37.0%

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

   2. Taylor expanded in z around -inf 62.0%

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

   if -6.4999999999999998e-295 < y5 < -5.6e-302 or 1.26000000000000008e-78 < y5 < 7.39999999999999989e65

   1. Initial program 51.7%

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

   2. Taylor expanded in x around inf 67.2%

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

   if 4.89999999999999981e-132 < y5 < 1.26000000000000008e-78

   1. Initial program 46.0%

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

   2. Taylor expanded in c around inf 62.4%

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

   4. Simplified 62.4%

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

   if 7.39999999999999989e65 < y5

   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 y2 around inf 52.3%

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

      1. associate--l+ 52.3%

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

   4. Applied egg-rr 52.3%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.2 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -1.92 \cdot 10^{+58}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -6.2 \cdot 10^{-76}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1.75 \cdot 10^{-142}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y5 \leq -1.2 \cdot 10^{-186}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -6.5 \cdot 10^{-295}:\\ \;\;\;\;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}\;y5 \leq -5.6 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.85 \cdot 10^{-190}:\\ \;\;\;\;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}\;y5 \leq 4.9 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.26 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 7.4 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \end{array} \]

Alternative 7: 35.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 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)\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := i \cdot y1 - b \cdot y0\\ t_4 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_2\right) + j \cdot t_3\right)\\ t_5 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{if}\;y5 \leq -2.9 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{+57}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -2.65 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -8.2 \cdot 10^{-161}:\\ \;\;\;\;y2 \cdot \left(\left(\left(k \cdot \left(y1 \cdot y4\right) + y0 \cdot \left(x \cdot c - k \cdot y5\right)\right) - a \cdot \left(x \cdot y1\right)\right) + t_5\right)\\ \mathbf{elif}\;y5 \leq -2.75 \cdot 10^{-189}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -3.5 \cdot 10^{-302}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq 1.46 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 1.05 \cdot 10^{-131}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t_3\right)\\ \mathbf{elif}\;y5 \leq 2.2 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.26 \cdot 10^{+66}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot t_2 + t_5\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
         (*
          z
          (+
           (* k (- (* b y0) (* i y1)))
           (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0)))))))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* i y1) (* b y0)))
        (t_4 (* x (+ (+ (* y (- (* a b) (* c i))) (* y2 t_2)) (* j t_3))))
        (t_5 (* t (- (* a y5) (* c y4)))))
   (if (<= y5 -2.9e+258)
     (* (* y2 y4) (- (* k y1) (* t c)))
     (if (<= y5 -1.45e+57)
       (* (* y2 y5) (- (* t a) (* k y0)))
       (if (<= y5 -2.65e-59)
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))
         (if (<= y5 -8.2e-161)
           (*
            y2
            (+
             (- (+ (* k (* y1 y4)) (* y0 (- (* x c) (* k y5)))) (* a (* x y1)))
             t_5))
           (if (<= y5 -2.75e-189)
             (* y1 (* j (- (* x i) (* y3 y4))))
             (if (<= y5 -2.8e-272)
               t_1
               (if (<= y5 -3.5e-302)
                 t_4
                 (if (<= y5 1.46e-189)
                   t_1
                   (if (<= y5 1.05e-131)
                     (*
                      j
                      (+
                       (+
                        (* t (- (* b y4) (* i y5)))
                        (* y3 (- (* y0 y5) (* y1 y4))))
                       (* x t_3)))
                     (if (<= y5 2.2e-77)
                       (*
                        c
                        (+
                         (+
                          (* i (- (* z t) (* x y)))
                          (* y0 (- (* x y2) (* z y3))))
                         (* y4 (- (* y y3) (* t y2)))))
                       (if (<= y5 1.26e+66)
                         t_4
                         (*
                          y2
                          (+
                           (* k (- (* y1 y4) (* y0 y5)))
                           (+ (* x t_2) t_5))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_3));
	double t_5 = t * ((a * y5) - (c * y4));
	double tmp;
	if (y5 <= -2.9e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -1.45e+57) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -2.65e-59) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -8.2e-161) {
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_5);
	} else if (y5 <= -2.75e-189) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= -2.8e-272) {
		tmp = t_1;
	} else if (y5 <= -3.5e-302) {
		tmp = t_4;
	} else if (y5 <= 1.46e-189) {
		tmp = t_1;
	} else if (y5 <= 1.05e-131) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	} else if (y5 <= 2.2e-77) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.26e+66) {
		tmp = t_4;
	} else {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_2) + t_5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    t_2 = (c * y0) - (a * y1)
    t_3 = (i * y1) - (b * y0)
    t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_3))
    t_5 = t * ((a * y5) - (c * y4))
    if (y5 <= (-2.9d+258)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (y5 <= (-1.45d+57)) then
        tmp = (y2 * y5) * ((t * a) - (k * y0))
    else if (y5 <= (-2.65d-59)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= (-8.2d-161)) then
        tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_5)
    else if (y5 <= (-2.75d-189)) then
        tmp = y1 * (j * ((x * i) - (y3 * y4)))
    else if (y5 <= (-2.8d-272)) then
        tmp = t_1
    else if (y5 <= (-3.5d-302)) then
        tmp = t_4
    else if (y5 <= 1.46d-189) then
        tmp = t_1
    else if (y5 <= 1.05d-131) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
    else if (y5 <= 2.2d-77) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 1.26d+66) then
        tmp = t_4
    else
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_2) + t_5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_3));
	double t_5 = t * ((a * y5) - (c * y4));
	double tmp;
	if (y5 <= -2.9e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -1.45e+57) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -2.65e-59) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -8.2e-161) {
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_5);
	} else if (y5 <= -2.75e-189) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= -2.8e-272) {
		tmp = t_1;
	} else if (y5 <= -3.5e-302) {
		tmp = t_4;
	} else if (y5 <= 1.46e-189) {
		tmp = t_1;
	} else if (y5 <= 1.05e-131) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	} else if (y5 <= 2.2e-77) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.26e+66) {
		tmp = t_4;
	} else {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_2) + t_5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	t_2 = (c * y0) - (a * y1)
	t_3 = (i * y1) - (b * y0)
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_3))
	t_5 = t * ((a * y5) - (c * y4))
	tmp = 0
	if y5 <= -2.9e+258:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif y5 <= -1.45e+57:
		tmp = (y2 * y5) * ((t * a) - (k * y0))
	elif y5 <= -2.65e-59:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y5 <= -8.2e-161:
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_5)
	elif y5 <= -2.75e-189:
		tmp = y1 * (j * ((x * i) - (y3 * y4)))
	elif y5 <= -2.8e-272:
		tmp = t_1
	elif y5 <= -3.5e-302:
		tmp = t_4
	elif y5 <= 1.46e-189:
		tmp = t_1
	elif y5 <= 1.05e-131:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
	elif y5 <= 2.2e-77:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 1.26e+66:
		tmp = t_4
	else:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_2) + t_5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(i * y1) - Float64(b * y0))
	t_4 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * t_3)))
	t_5 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	tmp = 0.0
	if (y5 <= -2.9e+258)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (y5 <= -1.45e+57)
		tmp = Float64(Float64(y2 * y5) * Float64(Float64(t * a) - Float64(k * y0)));
	elseif (y5 <= -2.65e-59)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= -8.2e-161)
		tmp = Float64(y2 * Float64(Float64(Float64(Float64(k * Float64(y1 * y4)) + Float64(y0 * Float64(Float64(x * c) - Float64(k * y5)))) - Float64(a * Float64(x * y1))) + t_5));
	elseif (y5 <= -2.75e-189)
		tmp = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y5 <= -2.8e-272)
		tmp = t_1;
	elseif (y5 <= -3.5e-302)
		tmp = t_4;
	elseif (y5 <= 1.46e-189)
		tmp = t_1;
	elseif (y5 <= 1.05e-131)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_3)));
	elseif (y5 <= 2.2e-77)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 1.26e+66)
		tmp = t_4;
	else
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(x * t_2) + t_5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	t_2 = (c * y0) - (a * y1);
	t_3 = (i * y1) - (b * y0);
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_3));
	t_5 = t * ((a * y5) - (c * y4));
	tmp = 0.0;
	if (y5 <= -2.9e+258)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (y5 <= -1.45e+57)
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	elseif (y5 <= -2.65e-59)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= -8.2e-161)
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_5);
	elseif (y5 <= -2.75e-189)
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	elseif (y5 <= -2.8e-272)
		tmp = t_1;
	elseif (y5 <= -3.5e-302)
		tmp = t_4;
	elseif (y5 <= 1.46e-189)
		tmp = t_1;
	elseif (y5 <= 1.05e-131)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	elseif (y5 <= 2.2e-77)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 1.26e+66)
		tmp = t_4;
	else
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_2) + t_5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $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]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.9e+258], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.45e+57], N[(N[(y2 * y5), $MachinePrecision] * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.65e-59], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8.2e-161], N[(y2 * N[(N[(N[(N[(k * N[(y1 * y4), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.75e-189], N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.8e-272], t$95$1, If[LessEqual[y5, -3.5e-302], t$95$4, If[LessEqual[y5, 1.46e-189], t$95$1, If[LessEqual[y5, 1.05e-131], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.2e-77], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.26e+66], t$95$4, N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * t$95$2), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y5 < -2.9000000000000001e258

   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 y2 around inf 11.1%

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

   3. Taylor expanded in y4 around inf 78.8%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   if -2.9000000000000001e258 < y5 < -1.4500000000000001e57

   1. Initial program 13.8%

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

   2. Taylor expanded in y2 around inf 50.2%

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

   3. Taylor expanded in y0 around -inf 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y5 around -inf 60.9%

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

      1. associate-*r* 60.8%

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

      2. +-commutative 60.8%

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

      3. mul-1-neg 60.8%

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

      4. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   if -1.4500000000000001e57 < y5 < -2.6500000000000002e-59

   1. Initial program 30.7%

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

   2. Taylor expanded in b around inf 66.1%

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

   if -2.6500000000000002e-59 < y5 < -8.1999999999999994e-161

   1. Initial program 30.4%

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

   2. Taylor expanded in y2 around inf 52.3%

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

   3. Taylor expanded in y0 around -inf 61.0%

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

   5. Simplified 61.0%

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

   if -8.1999999999999994e-161 < y5 < -2.7499999999999999e-189

   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 y1 around inf 42.9%

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

      1. +-commutative 42.9%

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

      2. mul-1-neg 42.9%

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

      3. unsub-neg 42.9%

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

      4. *-commutative 42.9%

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

      5. *-commutative 42.9%

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

      6. *-commutative 42.9%

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

      7. mul-1-neg 42.9%

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

      8. *-commutative 42.9%

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

   4. Simplified 42.9%

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

   5. Taylor expanded in j around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -2.7499999999999999e-189 < y5 < -2.79999999999999994e-272 or -3.5000000000000001e-302 < y5 < 1.45999999999999995e-189

   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 z around -inf 66.7%

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

   if -2.79999999999999994e-272 < y5 < -3.5000000000000001e-302 or 2.20000000000000007e-77 < y5 < 1.25999999999999999e66

   1. Initial program 50.1%

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

   2. Taylor expanded in x around inf 61.0%

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

   if 1.45999999999999995e-189 < y5 < 1.04999999999999999e-131

   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 j around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. *-commutative 58.0%

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

   4. Simplified 58.0%

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

   if 1.04999999999999999e-131 < y5 < 2.20000000000000007e-77

   1. Initial program 46.0%

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

   2. Taylor expanded in c around inf 62.4%

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

   4. Simplified 62.4%

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

   if 1.25999999999999999e66 < y5

   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 y2 around inf 52.3%

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

      1. associate--l+ 52.3%

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

   4. Applied egg-rr 52.3%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.9 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{+57}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -2.65 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -8.2 \cdot 10^{-161}:\\ \;\;\;\;y2 \cdot \left(\left(\left(k \cdot \left(y1 \cdot y4\right) + y0 \cdot \left(x \cdot c - k \cdot y5\right)\right) - a \cdot \left(x \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -2.75 \cdot 10^{-189}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-272}:\\ \;\;\;\;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}\;y5 \leq -3.5 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.46 \cdot 10^{-189}:\\ \;\;\;\;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}\;y5 \leq 1.05 \cdot 10^{-131}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 2.2 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.26 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \end{array} \]

Alternative 8: 35.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 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)\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := a \cdot b - c \cdot i\\ t_4 := i \cdot y1 - b \cdot y0\\ t_5 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{if}\;y5 \leq -2.9 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -5.7 \cdot 10^{+59}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -3.95 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -9 \cdot 10^{-160}:\\ \;\;\;\;y2 \cdot \left(\left(\left(k \cdot \left(y1 \cdot y4\right) + y0 \cdot \left(x \cdot c - k \cdot y5\right)\right) - a \cdot \left(x \cdot y1\right)\right) + t_5\right)\\ \mathbf{elif}\;y5 \leq -9.5 \cdot 10^{-187}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1.75 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -2.1 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot t_3\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 1.2 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 9.8 \cdot 10^{-129}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t_4\right)\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.5 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t_3 + y2 \cdot t_2\right) + j \cdot t_4\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot t_2 + t_5\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
         (*
          z
          (+
           (* k (- (* b y0) (* i y1)))
           (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0)))))))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* a b) (* c i)))
        (t_4 (- (* i y1) (* b y0)))
        (t_5 (* t (- (* a y5) (* c y4)))))
   (if (<= y5 -2.9e+258)
     (* (* y2 y4) (- (* k y1) (* t c)))
     (if (<= y5 -5.7e+59)
       (* (* y2 y5) (- (* t a) (* k y0)))
       (if (<= y5 -3.95e-53)
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))
         (if (<= y5 -9e-160)
           (*
            y2
            (+
             (- (+ (* k (* y1 y4)) (* y0 (- (* x c) (* k y5)))) (* a (* x y1)))
             t_5))
           (if (<= y5 -9.5e-187)
             (* y1 (* j (- (* x i) (* y3 y4))))
             (if (<= y5 -1.75e-271)
               t_1
               (if (<= y5 -2.1e-302)
                 (*
                  y
                  (+
                   (+ (* k (- (* i y5) (* b y4))) (* x t_3))
                   (* y3 (- (* c y4) (* a y5)))))
                 (if (<= y5 1.2e-189)
                   t_1
                   (if (<= y5 9.8e-129)
                     (*
                      j
                      (+
                       (+
                        (* t (- (* b y4) (* i y5)))
                        (* y3 (- (* y0 y5) (* y1 y4))))
                       (* x t_4)))
                     (if (<= y5 7.5e-78)
                       (*
                        c
                        (+
                         (+
                          (* i (- (* z t) (* x y)))
                          (* y0 (- (* x y2) (* z y3))))
                         (* y4 (- (* y y3) (* t y2)))))
                       (if (<= y5 1.5e+65)
                         (* x (+ (+ (* y t_3) (* y2 t_2)) (* j t_4)))
                         (*
                          y2
                          (+
                           (* k (- (* y1 y4) (* y0 y5)))
                           (+ (* x t_2) t_5))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (a * b) - (c * i);
	double t_4 = (i * y1) - (b * y0);
	double t_5 = t * ((a * y5) - (c * y4));
	double tmp;
	if (y5 <= -2.9e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -5.7e+59) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -3.95e-53) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -9e-160) {
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_5);
	} else if (y5 <= -9.5e-187) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= -1.75e-271) {
		tmp = t_1;
	} else if (y5 <= -2.1e-302) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_3)) + (y3 * ((c * y4) - (a * y5))));
	} else if (y5 <= 1.2e-189) {
		tmp = t_1;
	} else if (y5 <= 9.8e-129) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_4));
	} else if (y5 <= 7.5e-78) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.5e+65) {
		tmp = x * (((y * t_3) + (y2 * t_2)) + (j * t_4));
	} else {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_2) + t_5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
    t_2 = (c * y0) - (a * y1)
    t_3 = (a * b) - (c * i)
    t_4 = (i * y1) - (b * y0)
    t_5 = t * ((a * y5) - (c * y4))
    if (y5 <= (-2.9d+258)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (y5 <= (-5.7d+59)) then
        tmp = (y2 * y5) * ((t * a) - (k * y0))
    else if (y5 <= (-3.95d-53)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y5 <= (-9d-160)) then
        tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_5)
    else if (y5 <= (-9.5d-187)) then
        tmp = y1 * (j * ((x * i) - (y3 * y4)))
    else if (y5 <= (-1.75d-271)) then
        tmp = t_1
    else if (y5 <= (-2.1d-302)) then
        tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_3)) + (y3 * ((c * y4) - (a * y5))))
    else if (y5 <= 1.2d-189) then
        tmp = t_1
    else if (y5 <= 9.8d-129) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_4))
    else if (y5 <= 7.5d-78) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 1.5d+65) then
        tmp = x * (((y * t_3) + (y2 * t_2)) + (j * t_4))
    else
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_2) + t_5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (a * b) - (c * i);
	double t_4 = (i * y1) - (b * y0);
	double t_5 = t * ((a * y5) - (c * y4));
	double tmp;
	if (y5 <= -2.9e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -5.7e+59) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -3.95e-53) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y5 <= -9e-160) {
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_5);
	} else if (y5 <= -9.5e-187) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= -1.75e-271) {
		tmp = t_1;
	} else if (y5 <= -2.1e-302) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_3)) + (y3 * ((c * y4) - (a * y5))));
	} else if (y5 <= 1.2e-189) {
		tmp = t_1;
	} else if (y5 <= 9.8e-129) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_4));
	} else if (y5 <= 7.5e-78) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.5e+65) {
		tmp = x * (((y * t_3) + (y2 * t_2)) + (j * t_4));
	} else {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_2) + t_5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))))
	t_2 = (c * y0) - (a * y1)
	t_3 = (a * b) - (c * i)
	t_4 = (i * y1) - (b * y0)
	t_5 = t * ((a * y5) - (c * y4))
	tmp = 0
	if y5 <= -2.9e+258:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif y5 <= -5.7e+59:
		tmp = (y2 * y5) * ((t * a) - (k * y0))
	elif y5 <= -3.95e-53:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y5 <= -9e-160:
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_5)
	elif y5 <= -9.5e-187:
		tmp = y1 * (j * ((x * i) - (y3 * y4)))
	elif y5 <= -1.75e-271:
		tmp = t_1
	elif y5 <= -2.1e-302:
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_3)) + (y3 * ((c * y4) - (a * y5))))
	elif y5 <= 1.2e-189:
		tmp = t_1
	elif y5 <= 9.8e-129:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_4))
	elif y5 <= 7.5e-78:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 1.5e+65:
		tmp = x * (((y * t_3) + (y2 * t_2)) + (j * t_4))
	else:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_2) + t_5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(a * b) - Float64(c * i))
	t_4 = Float64(Float64(i * y1) - Float64(b * y0))
	t_5 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	tmp = 0.0
	if (y5 <= -2.9e+258)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (y5 <= -5.7e+59)
		tmp = Float64(Float64(y2 * y5) * Float64(Float64(t * a) - Float64(k * y0)));
	elseif (y5 <= -3.95e-53)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y5 <= -9e-160)
		tmp = Float64(y2 * Float64(Float64(Float64(Float64(k * Float64(y1 * y4)) + Float64(y0 * Float64(Float64(x * c) - Float64(k * y5)))) - Float64(a * Float64(x * y1))) + t_5));
	elseif (y5 <= -9.5e-187)
		tmp = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y5 <= -1.75e-271)
		tmp = t_1;
	elseif (y5 <= -2.1e-302)
		tmp = Float64(y * Float64(Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(x * t_3)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y5 <= 1.2e-189)
		tmp = t_1;
	elseif (y5 <= 9.8e-129)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_4)));
	elseif (y5 <= 7.5e-78)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 1.5e+65)
		tmp = Float64(x * Float64(Float64(Float64(y * t_3) + Float64(y2 * t_2)) + Float64(j * t_4)));
	else
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(x * t_2) + t_5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))));
	t_2 = (c * y0) - (a * y1);
	t_3 = (a * b) - (c * i);
	t_4 = (i * y1) - (b * y0);
	t_5 = t * ((a * y5) - (c * y4));
	tmp = 0.0;
	if (y5 <= -2.9e+258)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (y5 <= -5.7e+59)
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	elseif (y5 <= -3.95e-53)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y5 <= -9e-160)
		tmp = y2 * ((((k * (y1 * y4)) + (y0 * ((x * c) - (k * y5)))) - (a * (x * y1))) + t_5);
	elseif (y5 <= -9.5e-187)
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	elseif (y5 <= -1.75e-271)
		tmp = t_1;
	elseif (y5 <= -2.1e-302)
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_3)) + (y3 * ((c * y4) - (a * y5))));
	elseif (y5 <= 1.2e-189)
		tmp = t_1;
	elseif (y5 <= 9.8e-129)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_4));
	elseif (y5 <= 7.5e-78)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 1.5e+65)
		tmp = x * (((y * t_3) + (y2 * t_2)) + (j * t_4));
	else
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_2) + t_5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $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]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.9e+258], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -5.7e+59], N[(N[(y2 * y5), $MachinePrecision] * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3.95e-53], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -9e-160], N[(y2 * N[(N[(N[(N[(k * N[(y1 * y4), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -9.5e-187], N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.75e-271], t$95$1, If[LessEqual[y5, -2.1e-302], N[(y * N[(N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.2e-189], t$95$1, If[LessEqual[y5, 9.8e-129], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.5e-78], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.5e+65], N[(x * N[(N[(N[(y * t$95$3), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * t$95$2), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y5 < -2.9000000000000001e258

   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 y2 around inf 11.1%

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

   3. Taylor expanded in y4 around inf 78.8%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   if -2.9000000000000001e258 < y5 < -5.7000000000000001e59

   1. Initial program 13.8%

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

   2. Taylor expanded in y2 around inf 50.2%

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

   3. Taylor expanded in y0 around -inf 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y5 around -inf 60.9%

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

      1. associate-*r* 60.8%

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

      2. +-commutative 60.8%

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

      3. mul-1-neg 60.8%

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

      4. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   if -5.7000000000000001e59 < y5 < -3.9499999999999999e-53

   1. Initial program 30.7%

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

   2. Taylor expanded in b around inf 66.1%

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

   if -3.9499999999999999e-53 < y5 < -9.00000000000000053e-160

   1. Initial program 30.4%

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

   2. Taylor expanded in y2 around inf 52.3%

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

   3. Taylor expanded in y0 around -inf 61.0%

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

   5. Simplified 61.0%

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

   if -9.00000000000000053e-160 < y5 < -9.49999999999999936e-187

   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 y1 around inf 42.9%

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

      1. +-commutative 42.9%

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

      2. mul-1-neg 42.9%

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

      3. unsub-neg 42.9%

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

      4. *-commutative 42.9%

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

      5. *-commutative 42.9%

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

      6. *-commutative 42.9%

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

      7. mul-1-neg 42.9%

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

      8. *-commutative 42.9%

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

   4. Simplified 42.9%

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

   5. Taylor expanded in j around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -9.49999999999999936e-187 < y5 < -1.75e-271 or -2.10000000000000013e-302 < y5 < 1.1999999999999999e-189

   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 66.0%

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

   if -1.75e-271 < y5 < -2.10000000000000013e-302

   1. Initial program 54.5%

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

   2. Taylor expanded in y around inf 64.2%

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

   if 1.1999999999999999e-189 < y5 < 9.80000000000000004e-129

   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 j around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. *-commutative 58.0%

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

   4. Simplified 58.0%

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

   if 9.80000000000000004e-129 < y5 < 7.50000000000000041e-78

   1. Initial program 46.0%

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

   2. Taylor expanded in c around inf 62.4%

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

   4. Simplified 62.4%

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

   if 7.50000000000000041e-78 < y5 < 1.5000000000000001e65

   1. Initial program 46.6%

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

   2. Taylor expanded in x around inf 61.4%

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

   if 1.5000000000000001e65 < y5

   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 y2 around inf 52.3%

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

      1. associate--l+ 52.3%

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

   4. Applied egg-rr 52.3%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.9 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -5.7 \cdot 10^{+59}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -3.95 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -9 \cdot 10^{-160}:\\ \;\;\;\;y2 \cdot \left(\left(\left(k \cdot \left(y1 \cdot y4\right) + y0 \cdot \left(x \cdot c - k \cdot y5\right)\right) - a \cdot \left(x \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -9.5 \cdot 10^{-187}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1.75 \cdot 10^{-271}:\\ \;\;\;\;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}\;y5 \leq -2.1 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 1.2 \cdot 10^{-189}:\\ \;\;\;\;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}\;y5 \leq 9.8 \cdot 10^{-129}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.5 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \end{array} \]

Alternative 9: 35.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_4 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;y5 \leq -2.9 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -7 \cdot 10^{+56}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -1.2 \cdot 10^{-55}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq -9.5 \cdot 10^{-160}:\\ \;\;\;\;y2 \cdot \left(x \cdot t_1 + t_3\right)\\ \mathbf{elif}\;y5 \leq -6.7 \cdot 10^{-295}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y5 \leq 3.05 \cdot 10^{-190}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t_2\right)\\ \mathbf{elif}\;y5 \leq 1.8 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.55 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_1\right) + j \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* i y1) (* b y0)))
        (t_3 (* t (- (* a y5) (* c y4))))
        (t_4
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= y5 -2.9e+258)
     (* (* y2 y4) (- (* k y1) (* t c)))
     (if (<= y5 -7e+56)
       (* (* y2 y5) (- (* t a) (* k y0)))
       (if (<= y5 -1.2e-55)
         t_4
         (if (<= y5 -9.5e-160)
           (* y2 (+ (* x t_1) t_3))
           (if (<= y5 -6.7e-295)
             (* y1 (* j (- (* x i) (* y3 y4))))
             (if (<= y5 6e-286)
               (+
                (* x (* c (- (* y0 y2) (* y i))))
                (* (* x a) (- (* y b) (* y1 y2))))
               (if (<= y5 3.05e-190)
                 t_4
                 (if (<= y5 1.35e-127)
                   (*
                    j
                    (+
                     (+
                      (* t (- (* b y4) (* i y5)))
                      (* y3 (- (* y0 y5) (* y1 y4))))
                     (* x t_2)))
                   (if (<= y5 1.8e-77)
                     (*
                      c
                      (+
                       (+
                        (* i (- (* z t) (* x y)))
                        (* y0 (- (* x y2) (* z y3))))
                       (* y4 (- (* y y3) (* t y2)))))
                     (if (<= y5 1.55e+36)
                       (*
                        x
                        (+ (+ (* y (- (* a b) (* c i))) (* y2 t_1)) (* j t_2)))
                       (* y2 (+ (* y0 (- (* x c) (* k y5))) t_3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = t * ((a * y5) - (c * y4));
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (y5 <= -2.9e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -7e+56) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -1.2e-55) {
		tmp = t_4;
	} else if (y5 <= -9.5e-160) {
		tmp = y2 * ((x * t_1) + t_3);
	} else if (y5 <= -6.7e-295) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= 6e-286) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y5 <= 3.05e-190) {
		tmp = t_4;
	} else if (y5 <= 1.35e-127) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	} else if (y5 <= 1.8e-77) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.55e+36) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	} else {
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (i * y1) - (b * y0)
    t_3 = t * ((a * y5) - (c * y4))
    t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    if (y5 <= (-2.9d+258)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (y5 <= (-7d+56)) then
        tmp = (y2 * y5) * ((t * a) - (k * y0))
    else if (y5 <= (-1.2d-55)) then
        tmp = t_4
    else if (y5 <= (-9.5d-160)) then
        tmp = y2 * ((x * t_1) + t_3)
    else if (y5 <= (-6.7d-295)) then
        tmp = y1 * (j * ((x * i) - (y3 * y4)))
    else if (y5 <= 6d-286) then
        tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
    else if (y5 <= 3.05d-190) then
        tmp = t_4
    else if (y5 <= 1.35d-127) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2))
    else if (y5 <= 1.8d-77) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 1.55d+36) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2))
    else
        tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = t * ((a * y5) - (c * y4));
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (y5 <= -2.9e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -7e+56) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -1.2e-55) {
		tmp = t_4;
	} else if (y5 <= -9.5e-160) {
		tmp = y2 * ((x * t_1) + t_3);
	} else if (y5 <= -6.7e-295) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= 6e-286) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y5 <= 3.05e-190) {
		tmp = t_4;
	} else if (y5 <= 1.35e-127) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	} else if (y5 <= 1.8e-77) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.55e+36) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	} else {
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (i * y1) - (b * y0)
	t_3 = t * ((a * y5) - (c * y4))
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if y5 <= -2.9e+258:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif y5 <= -7e+56:
		tmp = (y2 * y5) * ((t * a) - (k * y0))
	elif y5 <= -1.2e-55:
		tmp = t_4
	elif y5 <= -9.5e-160:
		tmp = y2 * ((x * t_1) + t_3)
	elif y5 <= -6.7e-295:
		tmp = y1 * (j * ((x * i) - (y3 * y4)))
	elif y5 <= 6e-286:
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
	elif y5 <= 3.05e-190:
		tmp = t_4
	elif y5 <= 1.35e-127:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2))
	elif y5 <= 1.8e-77:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 1.55e+36:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2))
	else:
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	t_3 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_4 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (y5 <= -2.9e+258)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (y5 <= -7e+56)
		tmp = Float64(Float64(y2 * y5) * Float64(Float64(t * a) - Float64(k * y0)));
	elseif (y5 <= -1.2e-55)
		tmp = t_4;
	elseif (y5 <= -9.5e-160)
		tmp = Float64(y2 * Float64(Float64(x * t_1) + t_3));
	elseif (y5 <= -6.7e-295)
		tmp = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y5 <= 6e-286)
		tmp = Float64(Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i)))) + Float64(Float64(x * a) * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y5 <= 3.05e-190)
		tmp = t_4;
	elseif (y5 <= 1.35e-127)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_2)));
	elseif (y5 <= 1.8e-77)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 1.55e+36)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)) + Float64(j * t_2)));
	else
		tmp = Float64(y2 * Float64(Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))) + t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (i * y1) - (b * y0);
	t_3 = t * ((a * y5) - (c * y4));
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (y5 <= -2.9e+258)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (y5 <= -7e+56)
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	elseif (y5 <= -1.2e-55)
		tmp = t_4;
	elseif (y5 <= -9.5e-160)
		tmp = y2 * ((x * t_1) + t_3);
	elseif (y5 <= -6.7e-295)
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	elseif (y5 <= 6e-286)
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	elseif (y5 <= 3.05e-190)
		tmp = t_4;
	elseif (y5 <= 1.35e-127)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_2));
	elseif (y5 <= 1.8e-77)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 1.55e+36)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	else
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.9e+258], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -7e+56], N[(N[(y2 * y5), $MachinePrecision] * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.2e-55], t$95$4, If[LessEqual[y5, -9.5e-160], N[(y2 * N[(N[(x * t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6.7e-295], N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6e-286], N[(N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * a), $MachinePrecision] * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.05e-190], t$95$4, If[LessEqual[y5, 1.35e-127], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.8e-77], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.55e+36], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y5 < -2.9000000000000001e258

   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 y2 around inf 11.1%

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

   3. Taylor expanded in y4 around inf 78.8%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   if -2.9000000000000001e258 < y5 < -6.99999999999999999e56

   1. Initial program 13.8%

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

   2. Taylor expanded in y2 around inf 50.2%

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

   3. Taylor expanded in y0 around -inf 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y5 around -inf 60.9%

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

      1. associate-*r* 60.8%

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

      2. +-commutative 60.8%

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

      3. mul-1-neg 60.8%

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

      4. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   if -6.99999999999999999e56 < y5 < -1.19999999999999996e-55 or 6.0000000000000001e-286 < y5 < 3.05000000000000012e-190

   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 b around inf 64.3%

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

   if -1.19999999999999996e-55 < y5 < -9.5000000000000002e-160

   1. Initial program 30.4%

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

   2. Taylor expanded in y2 around inf 52.3%

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

   3. Taylor expanded in k around 0 52.5%

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

   if -9.5000000000000002e-160 < y5 < -6.70000000000000034e-295

   1. Initial program 28.0%

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

   2. Taylor expanded in y1 around inf 38.2%

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

      1. +-commutative 38.2%

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

      2. mul-1-neg 38.2%

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

      3. unsub-neg 38.2%

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

      4. *-commutative 38.2%

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

      5. *-commutative 38.2%

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

      6. *-commutative 38.2%

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

      7. mul-1-neg 38.2%

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

      8. *-commutative 38.2%

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

   4. Simplified 38.2%

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

   5. Taylor expanded in j around inf 56.0%

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

      1. +-commutative 56.0%

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

      2. mul-1-neg 56.0%

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

      3. unsub-neg 56.0%

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

      4. *-commutative 56.0%

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

      5. *-commutative 56.0%

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

   7. Simplified 56.0%

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

   if -6.70000000000000034e-295 < y5 < 6.0000000000000001e-286

   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 x around inf 64.1%

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

   3. Taylor expanded in j around 0 57.3%

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

   4. Taylor expanded in a around -inf 50.1%

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

      1. +-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. mul-1-neg 50.1%

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

      5. distribute-rgt-neg-in 50.1%

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

      6. mul-1-neg 50.1%

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

      7. distribute-lft-in 57.2%

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

      8. +-commutative 57.2%

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

      9. mul-1-neg 57.2%

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

      10. unsub-neg 57.2%

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

      11. *-commutative 57.2%

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

      12. associate-*r* 64.4%

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

      13. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   if 3.05000000000000012e-190 < y5 < 1.35e-127

   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 j around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. *-commutative 58.0%

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

   4. Simplified 58.0%

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

   if 1.35e-127 < y5 < 1.8e-77

   1. Initial program 46.0%

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

   2. Taylor expanded in c around inf 62.4%

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

   4. Simplified 62.4%

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

   if 1.8e-77 < y5 < 1.55e36

   1. Initial program 54.1%

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

   2. Taylor expanded in x around inf 71.1%

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

   if 1.55e36 < y5

   1. Initial program 37.4%

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

   2. Taylor expanded in y2 around inf 48.9%

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

   3. Taylor expanded in y0 around -inf 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in y1 around 0 47.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y2 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right) + y0 \cdot \left(k \cdot y5 - c \cdot x\right)\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.9 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -7 \cdot 10^{+56}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -1.2 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -9.5 \cdot 10^{-160}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -6.7 \cdot 10^{-295}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y5 \leq 3.05 \cdot 10^{-190}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.8 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.55 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 10: 34.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := x \cdot t_1 + t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_3 := i \cdot y1 - b \cdot y0\\ t_4 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;y5 \leq -5.5 \cdot 10^{+257}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -1.04 \cdot 10^{+52}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -8 \cdot 10^{-59}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq -1.8 \cdot 10^{-160}:\\ \;\;\;\;y2 \cdot t_2\\ \mathbf{elif}\;y5 \leq -6.5 \cdot 10^{-295}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y5 \leq 1.35 \cdot 10^{-190}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq 3.6 \cdot 10^{-128}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t_3\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.5 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_1\right) + j \cdot t_3\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (+ (* x t_1) (* t (- (* a y5) (* c y4)))))
        (t_3 (- (* i y1) (* b y0)))
        (t_4
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= y5 -5.5e+257)
     (* (* y2 y4) (- (* k y1) (* t c)))
     (if (<= y5 -1.04e+52)
       (* (* y2 y5) (- (* t a) (* k y0)))
       (if (<= y5 -8e-59)
         t_4
         (if (<= y5 -1.8e-160)
           (* y2 t_2)
           (if (<= y5 -6.5e-295)
             (* y1 (* j (- (* x i) (* y3 y4))))
             (if (<= y5 2.7e-286)
               (+
                (* x (* c (- (* y0 y2) (* y i))))
                (* (* x a) (- (* y b) (* y1 y2))))
               (if (<= y5 1.35e-190)
                 t_4
                 (if (<= y5 3.6e-128)
                   (*
                    j
                    (+
                     (+
                      (* t (- (* b y4) (* i y5)))
                      (* y3 (- (* y0 y5) (* y1 y4))))
                     (* x t_3)))
                   (if (<= y5 1.3e-77)
                     (*
                      c
                      (+
                       (+
                        (* i (- (* z t) (* x y)))
                        (* y0 (- (* x y2) (* z y3))))
                       (* y4 (- (* y y3) (* t y2)))))
                     (if (<= y5 1.5e+66)
                       (*
                        x
                        (+ (+ (* y (- (* a b) (* c i))) (* y2 t_1)) (* j t_3)))
                       (* y2 (+ (* k (- (* y1 y4) (* y0 y5))) t_2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (x * t_1) + (t * ((a * y5) - (c * y4)));
	double t_3 = (i * y1) - (b * y0);
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (y5 <= -5.5e+257) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -1.04e+52) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -8e-59) {
		tmp = t_4;
	} else if (y5 <= -1.8e-160) {
		tmp = y2 * t_2;
	} else if (y5 <= -6.5e-295) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= 2.7e-286) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y5 <= 1.35e-190) {
		tmp = t_4;
	} else if (y5 <= 3.6e-128) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	} else if (y5 <= 1.3e-77) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.5e+66) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_3));
	} else {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + 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 = (c * y0) - (a * y1)
    t_2 = (x * t_1) + (t * ((a * y5) - (c * y4)))
    t_3 = (i * y1) - (b * y0)
    t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    if (y5 <= (-5.5d+257)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (y5 <= (-1.04d+52)) then
        tmp = (y2 * y5) * ((t * a) - (k * y0))
    else if (y5 <= (-8d-59)) then
        tmp = t_4
    else if (y5 <= (-1.8d-160)) then
        tmp = y2 * t_2
    else if (y5 <= (-6.5d-295)) then
        tmp = y1 * (j * ((x * i) - (y3 * y4)))
    else if (y5 <= 2.7d-286) then
        tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
    else if (y5 <= 1.35d-190) then
        tmp = t_4
    else if (y5 <= 3.6d-128) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
    else if (y5 <= 1.3d-77) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 1.5d+66) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_3))
    else
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (x * t_1) + (t * ((a * y5) - (c * y4)));
	double t_3 = (i * y1) - (b * y0);
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (y5 <= -5.5e+257) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -1.04e+52) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -8e-59) {
		tmp = t_4;
	} else if (y5 <= -1.8e-160) {
		tmp = y2 * t_2;
	} else if (y5 <= -6.5e-295) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= 2.7e-286) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y5 <= 1.35e-190) {
		tmp = t_4;
	} else if (y5 <= 3.6e-128) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	} else if (y5 <= 1.3e-77) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.5e+66) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_3));
	} else {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (x * t_1) + (t * ((a * y5) - (c * y4)))
	t_3 = (i * y1) - (b * y0)
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if y5 <= -5.5e+257:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif y5 <= -1.04e+52:
		tmp = (y2 * y5) * ((t * a) - (k * y0))
	elif y5 <= -8e-59:
		tmp = t_4
	elif y5 <= -1.8e-160:
		tmp = y2 * t_2
	elif y5 <= -6.5e-295:
		tmp = y1 * (j * ((x * i) - (y3 * y4)))
	elif y5 <= 2.7e-286:
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
	elif y5 <= 1.35e-190:
		tmp = t_4
	elif y5 <= 3.6e-128:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3))
	elif y5 <= 1.3e-77:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 1.5e+66:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_3))
	else:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(x * t_1) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))
	t_3 = Float64(Float64(i * y1) - Float64(b * y0))
	t_4 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (y5 <= -5.5e+257)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (y5 <= -1.04e+52)
		tmp = Float64(Float64(y2 * y5) * Float64(Float64(t * a) - Float64(k * y0)));
	elseif (y5 <= -8e-59)
		tmp = t_4;
	elseif (y5 <= -1.8e-160)
		tmp = Float64(y2 * t_2);
	elseif (y5 <= -6.5e-295)
		tmp = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y5 <= 2.7e-286)
		tmp = Float64(Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i)))) + Float64(Float64(x * a) * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y5 <= 1.35e-190)
		tmp = t_4;
	elseif (y5 <= 3.6e-128)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_3)));
	elseif (y5 <= 1.3e-77)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 1.5e+66)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)) + Float64(j * t_3)));
	else
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (x * t_1) + (t * ((a * y5) - (c * y4)));
	t_3 = (i * y1) - (b * y0);
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (y5 <= -5.5e+257)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (y5 <= -1.04e+52)
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	elseif (y5 <= -8e-59)
		tmp = t_4;
	elseif (y5 <= -1.8e-160)
		tmp = y2 * t_2;
	elseif (y5 <= -6.5e-295)
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	elseif (y5 <= 2.7e-286)
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	elseif (y5 <= 1.35e-190)
		tmp = t_4;
	elseif (y5 <= 3.6e-128)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_3));
	elseif (y5 <= 1.3e-77)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 1.5e+66)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_3));
	else
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * t$95$1), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5.5e+257], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.04e+52], N[(N[(y2 * y5), $MachinePrecision] * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8e-59], t$95$4, If[LessEqual[y5, -1.8e-160], N[(y2 * t$95$2), $MachinePrecision], If[LessEqual[y5, -6.5e-295], N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.7e-286], N[(N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * a), $MachinePrecision] * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.35e-190], t$95$4, If[LessEqual[y5, 3.6e-128], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.3e-77], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.5e+66], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y5 < -5.49999999999999957e257

   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 y2 around inf 11.1%

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

   3. Taylor expanded in y4 around inf 78.8%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   if -5.49999999999999957e257 < y5 < -1.04e52

   1. Initial program 13.8%

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

   2. Taylor expanded in y2 around inf 50.2%

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

   3. Taylor expanded in y0 around -inf 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y5 around -inf 60.9%

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

      1. associate-*r* 60.8%

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

      2. +-commutative 60.8%

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

      3. mul-1-neg 60.8%

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

      4. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   if -1.04e52 < y5 < -8.0000000000000002e-59 or 2.7000000000000002e-286 < y5 < 1.35e-190

   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 b around inf 64.3%

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

   if -8.0000000000000002e-59 < y5 < -1.7999999999999999e-160

   1. Initial program 30.4%

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

   2. Taylor expanded in y2 around inf 52.3%

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

   3. Taylor expanded in k around 0 52.5%

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

   if -1.7999999999999999e-160 < y5 < -6.4999999999999998e-295

   1. Initial program 28.0%

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

   2. Taylor expanded in y1 around inf 38.2%

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

      1. +-commutative 38.2%

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

      2. mul-1-neg 38.2%

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

      3. unsub-neg 38.2%

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

      4. *-commutative 38.2%

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

      5. *-commutative 38.2%

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

      6. *-commutative 38.2%

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

      7. mul-1-neg 38.2%

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

      8. *-commutative 38.2%

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

   4. Simplified 38.2%

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

   5. Taylor expanded in j around inf 56.0%

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

      1. +-commutative 56.0%

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

      2. mul-1-neg 56.0%

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

      3. unsub-neg 56.0%

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

      4. *-commutative 56.0%

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

      5. *-commutative 56.0%

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

   7. Simplified 56.0%

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

   if -6.4999999999999998e-295 < y5 < 2.7000000000000002e-286

   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 x around inf 64.1%

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

   3. Taylor expanded in j around 0 57.3%

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

   4. Taylor expanded in a around -inf 50.1%

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

      1. +-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. mul-1-neg 50.1%

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

      5. distribute-rgt-neg-in 50.1%

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

      6. mul-1-neg 50.1%

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

      7. distribute-lft-in 57.2%

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

      8. +-commutative 57.2%

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

      9. mul-1-neg 57.2%

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

      10. unsub-neg 57.2%

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

      11. *-commutative 57.2%

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

      12. associate-*r* 64.4%

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

      13. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   if 1.35e-190 < y5 < 3.60000000000000025e-128

   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 j around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. *-commutative 58.0%

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

   4. Simplified 58.0%

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

   if 3.60000000000000025e-128 < y5 < 1.3000000000000001e-77

   1. Initial program 46.0%

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

   2. Taylor expanded in c around inf 62.4%

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

   4. Simplified 62.4%

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

   if 1.3000000000000001e-77 < y5 < 1.50000000000000001e66

   1. Initial program 46.6%

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

   2. Taylor expanded in x around inf 61.4%

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

   if 1.50000000000000001e66 < y5

   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 y2 around inf 52.3%

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

      1. associate--l+ 52.3%

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

   4. Applied egg-rr 52.3%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -5.5 \cdot 10^{+257}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -1.04 \cdot 10^{+52}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -8 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1.8 \cdot 10^{-160}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -6.5 \cdot 10^{-295}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y5 \leq 1.35 \cdot 10^{-190}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 3.6 \cdot 10^{-128}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.5 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \end{array} \]

Alternative 11: 34.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ t_2 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;y3 \leq -6.8 \cdot 10^{+211}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;y3 \leq -7.5 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq -3.8 \cdot 10^{-127}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y3 \leq -4.4 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 1.05 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y3 \leq 8 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 1.2 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq 6.1 \cdot 10^{-18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y3 \leq 1.65 \cdot 10^{+163}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 7.2 \cdot 10^{+257}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* j (- (* x i) (* y3 y4)))))
        (t_2
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_3
         (* y2 (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4)))))))
   (if (<= y3 -6.8e+211)
     (* (* y1 y3) (- (* z a) (* j y4)))
     (if (<= y3 -7.5e-12)
       t_1
       (if (<= y3 -3.8e-127)
         (* (* y2 y4) (- (* k y1) (* t c)))
         (if (<= y3 -4.4e-257)
           t_2
           (if (<= y3 1.05e-296)
             t_3
             (if (<= y3 8e-265)
               t_2
               (if (<= y3 1.2e-171)
                 (+
                  (* x (* c (- (* y0 y2) (* y i))))
                  (* (* x a) (- (* y b) (* y1 y2))))
                 (if (<= y3 6.1e-18)
                   t_3
                   (if (<= y3 1.65e+163)
                     (*
                      c
                      (+
                       (+
                        (* i (- (* z t) (* x y)))
                        (* y0 (- (* x y2) (* z y3))))
                       (* y4 (- (* y y3) (* t y2)))))
                     (if (<= y3 7.2e+257)
                       (* (* z y1) (- (* a y3) (* i k)))
                       t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (j * ((x * i) - (y3 * y4)));
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_3 = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (y3 <= -6.8e+211) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (y3 <= -7.5e-12) {
		tmp = t_1;
	} else if (y3 <= -3.8e-127) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y3 <= -4.4e-257) {
		tmp = t_2;
	} else if (y3 <= 1.05e-296) {
		tmp = t_3;
	} else if (y3 <= 8e-265) {
		tmp = t_2;
	} else if (y3 <= 1.2e-171) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y3 <= 6.1e-18) {
		tmp = t_3;
	} else if (y3 <= 1.65e+163) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y3 <= 7.2e+257) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y1 * (j * ((x * i) - (y3 * y4)))
    t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_3 = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
    if (y3 <= (-6.8d+211)) then
        tmp = (y1 * y3) * ((z * a) - (j * y4))
    else if (y3 <= (-7.5d-12)) then
        tmp = t_1
    else if (y3 <= (-3.8d-127)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (y3 <= (-4.4d-257)) then
        tmp = t_2
    else if (y3 <= 1.05d-296) then
        tmp = t_3
    else if (y3 <= 8d-265) then
        tmp = t_2
    else if (y3 <= 1.2d-171) then
        tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
    else if (y3 <= 6.1d-18) then
        tmp = t_3
    else if (y3 <= 1.65d+163) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y3 <= 7.2d+257) then
        tmp = (z * y1) * ((a * y3) - (i * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (j * ((x * i) - (y3 * y4)));
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_3 = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (y3 <= -6.8e+211) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (y3 <= -7.5e-12) {
		tmp = t_1;
	} else if (y3 <= -3.8e-127) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y3 <= -4.4e-257) {
		tmp = t_2;
	} else if (y3 <= 1.05e-296) {
		tmp = t_3;
	} else if (y3 <= 8e-265) {
		tmp = t_2;
	} else if (y3 <= 1.2e-171) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y3 <= 6.1e-18) {
		tmp = t_3;
	} else if (y3 <= 1.65e+163) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y3 <= 7.2e+257) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (j * ((x * i) - (y3 * y4)))
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_3 = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
	tmp = 0
	if y3 <= -6.8e+211:
		tmp = (y1 * y3) * ((z * a) - (j * y4))
	elif y3 <= -7.5e-12:
		tmp = t_1
	elif y3 <= -3.8e-127:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif y3 <= -4.4e-257:
		tmp = t_2
	elif y3 <= 1.05e-296:
		tmp = t_3
	elif y3 <= 8e-265:
		tmp = t_2
	elif y3 <= 1.2e-171:
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
	elif y3 <= 6.1e-18:
		tmp = t_3
	elif y3 <= 1.65e+163:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y3 <= 7.2e+257:
		tmp = (z * y1) * ((a * y3) - (i * k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))))
	t_2 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_3 = Float64(y2 * Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	tmp = 0.0
	if (y3 <= -6.8e+211)
		tmp = Float64(Float64(y1 * y3) * Float64(Float64(z * a) - Float64(j * y4)));
	elseif (y3 <= -7.5e-12)
		tmp = t_1;
	elseif (y3 <= -3.8e-127)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (y3 <= -4.4e-257)
		tmp = t_2;
	elseif (y3 <= 1.05e-296)
		tmp = t_3;
	elseif (y3 <= 8e-265)
		tmp = t_2;
	elseif (y3 <= 1.2e-171)
		tmp = Float64(Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i)))) + Float64(Float64(x * a) * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y3 <= 6.1e-18)
		tmp = t_3;
	elseif (y3 <= 1.65e+163)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y3 <= 7.2e+257)
		tmp = Float64(Float64(z * y1) * Float64(Float64(a * y3) - Float64(i * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (j * ((x * i) - (y3 * y4)));
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_3 = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	tmp = 0.0;
	if (y3 <= -6.8e+211)
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	elseif (y3 <= -7.5e-12)
		tmp = t_1;
	elseif (y3 <= -3.8e-127)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (y3 <= -4.4e-257)
		tmp = t_2;
	elseif (y3 <= 1.05e-296)
		tmp = t_3;
	elseif (y3 <= 8e-265)
		tmp = t_2;
	elseif (y3 <= 1.2e-171)
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	elseif (y3 <= 6.1e-18)
		tmp = t_3;
	elseif (y3 <= 1.65e+163)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y3 <= 7.2e+257)
		tmp = (z * y1) * ((a * y3) - (i * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -6.8e+211], N[(N[(y1 * y3), $MachinePrecision] * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -7.5e-12], t$95$1, If[LessEqual[y3, -3.8e-127], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4.4e-257], t$95$2, If[LessEqual[y3, 1.05e-296], t$95$3, If[LessEqual[y3, 8e-265], t$95$2, If[LessEqual[y3, 1.2e-171], N[(N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * a), $MachinePrecision] * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 6.1e-18], t$95$3, If[LessEqual[y3, 1.65e+163], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 7.2e+257], N[(N[(z * y1), $MachinePrecision] * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y3 < -6.7999999999999998e211

   1. Initial program 5.6%

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

   2. Taylor expanded in y1 around inf 50.0%

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

      1. +-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. unsub-neg 50.0%

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

      4. *-commutative 50.0%

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

      5. *-commutative 50.0%

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

      6. *-commutative 50.0%

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

      7. mul-1-neg 50.0%

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

      8. *-commutative 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in y3 around inf 77.8%

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

      1. associate-*r* 72.7%

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

      2. cancel-sign-sub-inv 72.7%

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

      3. metadata-eval 72.7%

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

      4. *-lft-identity 72.7%

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

      5. +-commutative 72.7%

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

      6. mul-1-neg 72.7%

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

      7. unsub-neg 72.7%

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

   7. Simplified 72.7%

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

   if -6.7999999999999998e211 < y3 < -7.5e-12 or 7.19999999999999968e257 < y3

   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 y1 around inf 33.9%

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

      1. +-commutative 33.9%

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

      2. mul-1-neg 33.9%

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

      3. unsub-neg 33.9%

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

      4. *-commutative 33.9%

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

      5. *-commutative 33.9%

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

      6. *-commutative 33.9%

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

      7. mul-1-neg 33.9%

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

      8. *-commutative 33.9%

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

   4. Simplified 33.9%

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

   5. Taylor expanded in j around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. *-commutative 49.9%

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

      5. *-commutative 49.9%

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

   7. Simplified 49.9%

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

   if -7.5e-12 < y3 < -3.80000000000000003e-127

   1. Initial program 31.9%

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

   2. Taylor expanded in y2 around inf 48.6%

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

   3. Taylor expanded in y4 around inf 49.2%

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

      1. associate-*r* 49.5%

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

      2. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   if -3.80000000000000003e-127 < y3 < -4.39999999999999975e-257 or 1.05e-296 < y3 < 7.99999999999999988e-265

   1. Initial program 46.8%

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

   2. Taylor expanded in b around inf 54.9%

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

   if -4.39999999999999975e-257 < y3 < 1.05e-296 or 1.19999999999999993e-171 < y3 < 6.0999999999999999e-18

   1. Initial program 41.3%

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

   2. Taylor expanded in y2 around inf 59.1%

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

   3. Taylor expanded in k around 0 61.4%

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

   if 7.99999999999999988e-265 < y3 < 1.19999999999999993e-171

   1. Initial program 37.4%

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

   2. Taylor expanded in x around inf 62.5%

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

   3. Taylor expanded in j around 0 68.8%

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

   4. Taylor expanded in a around -inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. mul-1-neg 56.4%

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

      5. distribute-rgt-neg-in 56.4%

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

      6. mul-1-neg 56.4%

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

      7. distribute-lft-in 62.6%

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

      8. +-commutative 62.6%

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

      9. mul-1-neg 62.6%

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

      10. unsub-neg 62.6%

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

      11. *-commutative 62.6%

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

      12. associate-*r* 75.1%

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

      13. *-commutative 75.1%

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

   6. Simplified 75.1%

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

   if 6.0999999999999999e-18 < y3 < 1.65e163

   1. Initial program 37.4%

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

   2. Taylor expanded in c around inf 46.6%

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

   4. Simplified 46.6%

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

   if 1.65e163 < y3 < 7.19999999999999968e257

   1. Initial program 19.2%

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

   2. Taylor expanded in y1 around inf 27.7%

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

      1. +-commutative 27.7%

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

      2. mul-1-neg 27.7%

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

      3. unsub-neg 27.7%

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

      4. *-commutative 27.7%

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

      5. *-commutative 27.7%

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

      6. *-commutative 27.7%

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

      7. mul-1-neg 27.7%

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

      8. *-commutative 27.7%

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

   4. Simplified 27.7%

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

   5. Taylor expanded in z around inf 58.7%

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

      1. associate-*r* 58.5%

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

      2. distribute-lft-out-- 58.5%

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

   7. Simplified 58.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -6.8 \cdot 10^{+211}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;y3 \leq -7.5 \cdot 10^{-12}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq -3.8 \cdot 10^{-127}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y3 \leq -4.4 \cdot 10^{-257}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 1.05 \cdot 10^{-296}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 8 \cdot 10^{-265}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 1.2 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq 6.1 \cdot 10^{-18}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.65 \cdot 10^{+163}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 7.2 \cdot 10^{+257}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \end{array} \]

Alternative 12: 34.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_3 := y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t_2\right)\\ t_4 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_5 := x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_1\right)\\ \mathbf{if}\;y5 \leq -2.8 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -1.6 \cdot 10^{+56}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq -7.2 \cdot 10^{-159}:\\ \;\;\;\;y2 \cdot \left(x \cdot t_1 + t_2\right)\\ \mathbf{elif}\;y5 \leq -6.7 \cdot 10^{-295}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.25 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y5 \leq 10^{-192}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1020000000:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{+60}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y5 \leq 3.1 \cdot 10^{+183}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq 8 \cdot 10^{+237}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y5 \leq 6.4 \cdot 10^{+274}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (* t (- (* a y5) (* c y4))))
        (t_3 (* y2 (+ (* y0 (- (* x c) (* k y5))) t_2)))
        (t_4
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_5 (* x (+ (* y (- (* a b) (* c i))) (* y2 t_1)))))
   (if (<= y5 -2.8e+258)
     (* (* y2 y4) (- (* k y1) (* t c)))
     (if (<= y5 -1.6e+56)
       (* (* y2 y5) (- (* t a) (* k y0)))
       (if (<= y5 -4.2e-57)
         t_4
         (if (<= y5 -7.2e-159)
           (* y2 (+ (* x t_1) t_2))
           (if (<= y5 -6.7e-295)
             (* y1 (* j (- (* x i) (* y3 y4))))
             (if (<= y5 1.25e-285)
               (+
                (* x (* c (- (* y0 y2) (* y i))))
                (* (* x a) (- (* y b) (* y1 y2))))
               (if (<= y5 1e-192)
                 t_4
                 (if (<= y5 1.3e-132)
                   (*
                    j
                    (+
                     (+
                      (* t (- (* b y4) (* i y5)))
                      (* y3 (- (* y0 y5) (* y1 y4))))
                     (* x (- (* i y1) (* b y0)))))
                   (if (<= y5 1020000000.0)
                     (*
                      c
                      (+
                       (+
                        (* i (- (* z t) (* x y)))
                        (* y0 (- (* x y2) (* z y3))))
                       (* y4 (- (* y y3) (* t y2)))))
                     (if (<= y5 1e+60)
                       t_5
                       (if (<= y5 3.1e+183)
                         t_3
                         (if (<= y5 8e+237)
                           t_5
                           (if (<= y5 6.4e+274) t_3 (* 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 = (c * y0) - (a * y1);
	double t_2 = t * ((a * y5) - (c * y4));
	double t_3 = y2 * ((y0 * ((x * c) - (k * y5))) + t_2);
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_5 = x * ((y * ((a * b) - (c * i))) + (y2 * t_1));
	double tmp;
	if (y5 <= -2.8e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -1.6e+56) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -4.2e-57) {
		tmp = t_4;
	} else if (y5 <= -7.2e-159) {
		tmp = y2 * ((x * t_1) + t_2);
	} else if (y5 <= -6.7e-295) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= 1.25e-285) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y5 <= 1e-192) {
		tmp = t_4;
	} else if (y5 <= 1.3e-132) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (y5 <= 1020000000.0) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1e+60) {
		tmp = t_5;
	} else if (y5 <= 3.1e+183) {
		tmp = t_3;
	} else if (y5 <= 8e+237) {
		tmp = t_5;
	} else if (y5 <= 6.4e+274) {
		tmp = t_3;
	} else {
		tmp = 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) :: t_5
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = t * ((a * y5) - (c * y4))
    t_3 = y2 * ((y0 * ((x * c) - (k * y5))) + t_2)
    t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_5 = x * ((y * ((a * b) - (c * i))) + (y2 * t_1))
    if (y5 <= (-2.8d+258)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (y5 <= (-1.6d+56)) then
        tmp = (y2 * y5) * ((t * a) - (k * y0))
    else if (y5 <= (-4.2d-57)) then
        tmp = t_4
    else if (y5 <= (-7.2d-159)) then
        tmp = y2 * ((x * t_1) + t_2)
    else if (y5 <= (-6.7d-295)) then
        tmp = y1 * (j * ((x * i) - (y3 * y4)))
    else if (y5 <= 1.25d-285) then
        tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
    else if (y5 <= 1d-192) then
        tmp = t_4
    else if (y5 <= 1.3d-132) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else if (y5 <= 1020000000.0d0) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 1d+60) then
        tmp = t_5
    else if (y5 <= 3.1d+183) then
        tmp = t_3
    else if (y5 <= 8d+237) then
        tmp = t_5
    else if (y5 <= 6.4d+274) then
        tmp = t_3
    else
        tmp = 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 = (c * y0) - (a * y1);
	double t_2 = t * ((a * y5) - (c * y4));
	double t_3 = y2 * ((y0 * ((x * c) - (k * y5))) + t_2);
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_5 = x * ((y * ((a * b) - (c * i))) + (y2 * t_1));
	double tmp;
	if (y5 <= -2.8e+258) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y5 <= -1.6e+56) {
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	} else if (y5 <= -4.2e-57) {
		tmp = t_4;
	} else if (y5 <= -7.2e-159) {
		tmp = y2 * ((x * t_1) + t_2);
	} else if (y5 <= -6.7e-295) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y5 <= 1.25e-285) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y5 <= 1e-192) {
		tmp = t_4;
	} else if (y5 <= 1.3e-132) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (y5 <= 1020000000.0) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 1e+60) {
		tmp = t_5;
	} else if (y5 <= 3.1e+183) {
		tmp = t_3;
	} else if (y5 <= 8e+237) {
		tmp = t_5;
	} else if (y5 <= 6.4e+274) {
		tmp = t_3;
	} else {
		tmp = 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 = (c * y0) - (a * y1)
	t_2 = t * ((a * y5) - (c * y4))
	t_3 = y2 * ((y0 * ((x * c) - (k * y5))) + t_2)
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_5 = x * ((y * ((a * b) - (c * i))) + (y2 * t_1))
	tmp = 0
	if y5 <= -2.8e+258:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif y5 <= -1.6e+56:
		tmp = (y2 * y5) * ((t * a) - (k * y0))
	elif y5 <= -4.2e-57:
		tmp = t_4
	elif y5 <= -7.2e-159:
		tmp = y2 * ((x * t_1) + t_2)
	elif y5 <= -6.7e-295:
		tmp = y1 * (j * ((x * i) - (y3 * y4)))
	elif y5 <= 1.25e-285:
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
	elif y5 <= 1e-192:
		tmp = t_4
	elif y5 <= 1.3e-132:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	elif y5 <= 1020000000.0:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 1e+60:
		tmp = t_5
	elif y5 <= 3.1e+183:
		tmp = t_3
	elif y5 <= 8e+237:
		tmp = t_5
	elif y5 <= 6.4e+274:
		tmp = t_3
	else:
		tmp = 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(c * y0) - Float64(a * y1))
	t_2 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_3 = Float64(y2 * Float64(Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))) + t_2))
	t_4 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_5 = Float64(x * Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)))
	tmp = 0.0
	if (y5 <= -2.8e+258)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (y5 <= -1.6e+56)
		tmp = Float64(Float64(y2 * y5) * Float64(Float64(t * a) - Float64(k * y0)));
	elseif (y5 <= -4.2e-57)
		tmp = t_4;
	elseif (y5 <= -7.2e-159)
		tmp = Float64(y2 * Float64(Float64(x * t_1) + t_2));
	elseif (y5 <= -6.7e-295)
		tmp = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y5 <= 1.25e-285)
		tmp = Float64(Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i)))) + Float64(Float64(x * a) * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y5 <= 1e-192)
		tmp = t_4;
	elseif (y5 <= 1.3e-132)
		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 (y5 <= 1020000000.0)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 1e+60)
		tmp = t_5;
	elseif (y5 <= 3.1e+183)
		tmp = t_3;
	elseif (y5 <= 8e+237)
		tmp = t_5;
	elseif (y5 <= 6.4e+274)
		tmp = t_3;
	else
		tmp = Float64(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 = (c * y0) - (a * y1);
	t_2 = t * ((a * y5) - (c * y4));
	t_3 = y2 * ((y0 * ((x * c) - (k * y5))) + t_2);
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_5 = x * ((y * ((a * b) - (c * i))) + (y2 * t_1));
	tmp = 0.0;
	if (y5 <= -2.8e+258)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (y5 <= -1.6e+56)
		tmp = (y2 * y5) * ((t * a) - (k * y0));
	elseif (y5 <= -4.2e-57)
		tmp = t_4;
	elseif (y5 <= -7.2e-159)
		tmp = y2 * ((x * t_1) + t_2);
	elseif (y5 <= -6.7e-295)
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	elseif (y5 <= 1.25e-285)
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	elseif (y5 <= 1e-192)
		tmp = t_4;
	elseif (y5 <= 1.3e-132)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	elseif (y5 <= 1020000000.0)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 1e+60)
		tmp = t_5;
	elseif (y5 <= 3.1e+183)
		tmp = t_3;
	elseif (y5 <= 8e+237)
		tmp = t_5;
	elseif (y5 <= 6.4e+274)
		tmp = t_3;
	else
		tmp = 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[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.8e+258], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.6e+56], N[(N[(y2 * y5), $MachinePrecision] * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.2e-57], t$95$4, If[LessEqual[y5, -7.2e-159], N[(y2 * N[(N[(x * t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6.7e-295], N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.25e-285], N[(N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * a), $MachinePrecision] * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1e-192], t$95$4, If[LessEqual[y5, 1.3e-132], 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[y5, 1020000000.0], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1e+60], t$95$5, If[LessEqual[y5, 3.1e+183], t$95$3, If[LessEqual[y5, 8e+237], t$95$5, If[LessEqual[y5, 6.4e+274], t$95$3, N[(y2 * t$95$2), $MachinePrecision]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y5 < -2.79999999999999982e258

   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 y2 around inf 11.1%

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

   3. Taylor expanded in y4 around inf 78.8%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   if -2.79999999999999982e258 < y5 < -1.60000000000000002e56

   1. Initial program 13.8%

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

   2. Taylor expanded in y2 around inf 50.2%

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

   3. Taylor expanded in y0 around -inf 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y5 around -inf 60.9%

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

      1. associate-*r* 60.8%

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

      2. +-commutative 60.8%

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

      3. mul-1-neg 60.8%

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

      4. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   if -1.60000000000000002e56 < y5 < -4.1999999999999999e-57 or 1.25000000000000005e-285 < y5 < 1.0000000000000001e-192

   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 b around inf 64.3%

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

   if -4.1999999999999999e-57 < y5 < -7.20000000000000042e-159

   1. Initial program 30.4%

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

   2. Taylor expanded in y2 around inf 52.3%

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

   3. Taylor expanded in k around 0 52.5%

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

   if -7.20000000000000042e-159 < y5 < -6.70000000000000034e-295

   1. Initial program 28.0%

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

   2. Taylor expanded in y1 around inf 38.2%

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

      1. +-commutative 38.2%

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

      2. mul-1-neg 38.2%

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

      3. unsub-neg 38.2%

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

      4. *-commutative 38.2%

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

      5. *-commutative 38.2%

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

      6. *-commutative 38.2%

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

      7. mul-1-neg 38.2%

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

      8. *-commutative 38.2%

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

   4. Simplified 38.2%

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

   5. Taylor expanded in j around inf 56.0%

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

      1. +-commutative 56.0%

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

      2. mul-1-neg 56.0%

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

      3. unsub-neg 56.0%

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

      4. *-commutative 56.0%

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

      5. *-commutative 56.0%

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

   7. Simplified 56.0%

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

   if -6.70000000000000034e-295 < y5 < 1.25000000000000005e-285

   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 x around inf 64.1%

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

   3. Taylor expanded in j around 0 57.3%

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

   4. Taylor expanded in a around -inf 50.1%

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

      1. +-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. mul-1-neg 50.1%

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

      5. distribute-rgt-neg-in 50.1%

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

      6. mul-1-neg 50.1%

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

      7. distribute-lft-in 57.2%

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

      8. +-commutative 57.2%

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

      9. mul-1-neg 57.2%

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

      10. unsub-neg 57.2%

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

      11. *-commutative 57.2%

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

      12. associate-*r* 64.4%

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

      13. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   if 1.0000000000000001e-192 < y5 < 1.3e-132

   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 j around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. *-commutative 58.0%

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

   4. Simplified 58.0%

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

   if 1.3e-132 < y5 < 1.02e9

   1. Initial program 51.7%

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

   2. Taylor expanded in c around inf 55.7%

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

   4. Simplified 55.7%

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

   if 1.02e9 < y5 < 9.9999999999999995e59 or 3.0999999999999998e183 < y5 < 7.99999999999999952e237

   1. Initial program 30.9%

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

   2. Taylor expanded in x around inf 47.1%

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

   3. Taylor expanded in j around 0 62.6%

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

   if 9.9999999999999995e59 < y5 < 3.0999999999999998e183 or 7.99999999999999952e237 < y5 < 6.39999999999999965e274

   1. Initial program 41.6%

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

   2. Taylor expanded in y2 around inf 60.3%

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

   3. Taylor expanded in y0 around -inf 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in y1 around 0 60.4%

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

   if 6.39999999999999965e274 < y5

   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 y2 around inf 40.6%

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

   3. Taylor expanded in t around inf 80.6%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.8 \cdot 10^{+258}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y5 \leq -1.6 \cdot 10^{+56}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a - k \cdot y0\right)\\ \mathbf{elif}\;y5 \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -7.2 \cdot 10^{-159}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -6.7 \cdot 10^{-295}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.25 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y5 \leq 10^{-192}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1020000000:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{+60}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 3.1 \cdot 10^{+183}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 8 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 6.4 \cdot 10^{+274}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 13: 36.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ t_3 := y \cdot y3 - t \cdot y2\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_4\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_6 := k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{if}\;y1 \leq -3.2 \cdot 10^{+31}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y1 \leq -2.5 \cdot 10^{-114}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t_1\right) + c \cdot t_3\right)\\ \mathbf{elif}\;y1 \leq -8.8 \cdot 10^{-191}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t_2\right)\\ \mathbf{elif}\;y1 \leq 1.1 \cdot 10^{-273}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y1 \leq 4 \cdot 10^{-194}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot t_3\\ \mathbf{elif}\;y1 \leq 5.1 \cdot 10^{-107}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{-29}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y1 \leq 1.9 \cdot 10^{+130}:\\ \;\;\;\;y2 \cdot \left(x \cdot t_4 + t_2\right)\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{+198}:\\ \;\;\;\;y1 \cdot \left(\left(y4 \cdot t_1 - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \end{array} \end{array} \]

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) (* j y3)))
        (t_2 (* t (- (* a y5) (* c y4))))
        (t_3 (- (* y y3) (* t y2)))
        (t_4 (- (* c y0) (* a y1)))
        (t_5
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_4))
           (* j (- (* i y1) (* b y0))))))
        (t_6
         (*
          k
          (+
           (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1)))))))
   (if (<= y1 -3.2e+31)
     t_5
     (if (<= y1 -2.5e-114)
       (* y4 (+ (+ (* b (- (* t j) (* y k))) (* y1 t_1)) (* c t_3)))
       (if (<= y1 -8.8e-191)
         (* y2 (+ (* y0 (- (* x c) (* k y5))) t_2))
         (if (<= y1 1.1e-273)
           t_6
           (if (<= y1 4e-194)
             (* (* c y4) t_3)
             (if (<= y1 5.1e-107)
               t_6
               (if (<= y1 2.3e-29)
                 t_5
                 (if (<= y1 1.9e+130)
                   (* y2 (+ (* x t_4) t_2))
                   (if (<= y1 2.7e+198)
                     (*
                      y1
                      (+
                       (- (* y4 t_1) (* a (- (* x y2) (* z y3))))
                       (* i (- (* x j) (* z k)))))
                     (* (* z y1) (- (* a y3) (* i k))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = t * ((a * y5) - (c * y4));
	double t_3 = (y * y3) - (t * y2);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	double t_6 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double tmp;
	if (y1 <= -3.2e+31) {
		tmp = t_5;
	} else if (y1 <= -2.5e-114) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * t_3));
	} else if (y1 <= -8.8e-191) {
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_2);
	} else if (y1 <= 1.1e-273) {
		tmp = t_6;
	} else if (y1 <= 4e-194) {
		tmp = (c * y4) * t_3;
	} else if (y1 <= 5.1e-107) {
		tmp = t_6;
	} else if (y1 <= 2.3e-29) {
		tmp = t_5;
	} else if (y1 <= 1.9e+130) {
		tmp = y2 * ((x * t_4) + t_2);
	} else if (y1 <= 2.7e+198) {
		tmp = y1 * (((y4 * t_1) - (a * ((x * y2) - (z * y3)))) + (i * ((x * j) - (z * k))));
	} else {
		tmp = (z * y1) * ((a * y3) - (i * k));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = t * ((a * y5) - (c * y4))
    t_3 = (y * y3) - (t * y2)
    t_4 = (c * y0) - (a * y1)
    t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))))
    t_6 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    if (y1 <= (-3.2d+31)) then
        tmp = t_5
    else if (y1 <= (-2.5d-114)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * t_3))
    else if (y1 <= (-8.8d-191)) then
        tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_2)
    else if (y1 <= 1.1d-273) then
        tmp = t_6
    else if (y1 <= 4d-194) then
        tmp = (c * y4) * t_3
    else if (y1 <= 5.1d-107) then
        tmp = t_6
    else if (y1 <= 2.3d-29) then
        tmp = t_5
    else if (y1 <= 1.9d+130) then
        tmp = y2 * ((x * t_4) + t_2)
    else if (y1 <= 2.7d+198) then
        tmp = y1 * (((y4 * t_1) - (a * ((x * y2) - (z * y3)))) + (i * ((x * j) - (z * k))))
    else
        tmp = (z * y1) * ((a * y3) - (i * k))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = t * ((a * y5) - (c * y4));
	double t_3 = (y * y3) - (t * y2);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	double t_6 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double tmp;
	if (y1 <= -3.2e+31) {
		tmp = t_5;
	} else if (y1 <= -2.5e-114) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * t_3));
	} else if (y1 <= -8.8e-191) {
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_2);
	} else if (y1 <= 1.1e-273) {
		tmp = t_6;
	} else if (y1 <= 4e-194) {
		tmp = (c * y4) * t_3;
	} else if (y1 <= 5.1e-107) {
		tmp = t_6;
	} else if (y1 <= 2.3e-29) {
		tmp = t_5;
	} else if (y1 <= 1.9e+130) {
		tmp = y2 * ((x * t_4) + t_2);
	} else if (y1 <= 2.7e+198) {
		tmp = y1 * (((y4 * t_1) - (a * ((x * y2) - (z * y3)))) + (i * ((x * j) - (z * k))));
	} else {
		tmp = (z * y1) * ((a * y3) - (i * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = t * ((a * y5) - (c * y4))
	t_3 = (y * y3) - (t * y2)
	t_4 = (c * y0) - (a * y1)
	t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))))
	t_6 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	tmp = 0
	if y1 <= -3.2e+31:
		tmp = t_5
	elif y1 <= -2.5e-114:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * t_3))
	elif y1 <= -8.8e-191:
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_2)
	elif y1 <= 1.1e-273:
		tmp = t_6
	elif y1 <= 4e-194:
		tmp = (c * y4) * t_3
	elif y1 <= 5.1e-107:
		tmp = t_6
	elif y1 <= 2.3e-29:
		tmp = t_5
	elif y1 <= 1.9e+130:
		tmp = y2 * ((x * t_4) + t_2)
	elif y1 <= 2.7e+198:
		tmp = y1 * (((y4 * t_1) - (a * ((x * y2) - (z * y3)))) + (i * ((x * j) - (z * k))))
	else:
		tmp = (z * y1) * ((a * y3) - (i * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	t_3 = Float64(Float64(y * y3) - Float64(t * y2))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_4)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_6 = 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 (y1 <= -3.2e+31)
		tmp = t_5;
	elseif (y1 <= -2.5e-114)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_1)) + Float64(c * t_3)));
	elseif (y1 <= -8.8e-191)
		tmp = Float64(y2 * Float64(Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))) + t_2));
	elseif (y1 <= 1.1e-273)
		tmp = t_6;
	elseif (y1 <= 4e-194)
		tmp = Float64(Float64(c * y4) * t_3);
	elseif (y1 <= 5.1e-107)
		tmp = t_6;
	elseif (y1 <= 2.3e-29)
		tmp = t_5;
	elseif (y1 <= 1.9e+130)
		tmp = Float64(y2 * Float64(Float64(x * t_4) + t_2));
	elseif (y1 <= 2.7e+198)
		tmp = Float64(y1 * Float64(Float64(Float64(y4 * t_1) - Float64(a * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(i * Float64(Float64(x * j) - Float64(z * k)))));
	else
		tmp = Float64(Float64(z * y1) * Float64(Float64(a * y3) - Float64(i * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y2) - (j * y3);
	t_2 = t * ((a * y5) - (c * y4));
	t_3 = (y * y3) - (t * y2);
	t_4 = (c * y0) - (a * y1);
	t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	t_6 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	tmp = 0.0;
	if (y1 <= -3.2e+31)
		tmp = t_5;
	elseif (y1 <= -2.5e-114)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * t_3));
	elseif (y1 <= -8.8e-191)
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_2);
	elseif (y1 <= 1.1e-273)
		tmp = t_6;
	elseif (y1 <= 4e-194)
		tmp = (c * y4) * t_3;
	elseif (y1 <= 5.1e-107)
		tmp = t_6;
	elseif (y1 <= 2.3e-29)
		tmp = t_5;
	elseif (y1 <= 1.9e+130)
		tmp = y2 * ((x * t_4) + t_2);
	elseif (y1 <= 2.7e+198)
		tmp = y1 * (((y4 * t_1) - (a * ((x * y2) - (z * y3)))) + (i * ((x * j) - (z * k))));
	else
		tmp = (z * y1) * ((a * y3) - (i * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = 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[y1, -3.2e+31], t$95$5, If[LessEqual[y1, -2.5e-114], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -8.8e-191], N[(y2 * N[(N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.1e-273], t$95$6, If[LessEqual[y1, 4e-194], N[(N[(c * y4), $MachinePrecision] * t$95$3), $MachinePrecision], If[LessEqual[y1, 5.1e-107], t$95$6, If[LessEqual[y1, 2.3e-29], t$95$5, If[LessEqual[y1, 1.9e+130], N[(y2 * N[(N[(x * t$95$4), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.7e+198], N[(y1 * N[(N[(N[(y4 * t$95$1), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y1), $MachinePrecision] * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y1 < -3.2000000000000001e31 or 5.1000000000000002e-107 < y1 < 2.29999999999999991e-29

   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 x around inf 58.7%

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

   if -3.2000000000000001e31 < y1 < -2.49999999999999995e-114

   1. Initial program 35.6%

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

   2. Taylor expanded in y4 around inf 52.5%

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

   if -2.49999999999999995e-114 < y1 < -8.79999999999999992e-191

   1. Initial program 23.5%

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

   2. Taylor expanded in y2 around inf 59.9%

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

   3. Taylor expanded in y0 around -inf 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in y1 around 0 65.4%

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

   if -8.79999999999999992e-191 < y1 < 1.0999999999999999e-273 or 4.00000000000000007e-194 < y1 < 5.1000000000000002e-107

   1. Initial program 36.9%

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

   2. Taylor expanded in k around inf 61.5%

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

      1. +-commutative 61.5%

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

      2. mul-1-neg 61.5%

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

      3. unsub-neg 61.5%

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

      4. *-commutative 61.5%

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

      5. mul-1-neg 61.5%

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

   4. Simplified 61.5%

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

   if 1.0999999999999999e-273 < y1 < 4.00000000000000007e-194

   1. Initial program 26.7%

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

   2. Taylor expanded in y4 around inf 47.2%

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

   3. Taylor expanded in c around inf 54.7%

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

      1. associate-*r* 54.7%

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

      2. *-commutative 54.7%

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

      3. *-commutative 54.7%

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

      4. *-commutative 54.7%

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

   5. Simplified 54.7%

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

   if 2.29999999999999991e-29 < y1 < 1.9000000000000001e130

   1. Initial program 34.7%

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

   2. Taylor expanded in y2 around inf 48.9%

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

   3. Taylor expanded in k around 0 52.3%

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

   if 1.9000000000000001e130 < y1 < 2.6999999999999999e198

   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 80.0%

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

      1. +-commutative 80.0%

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

      2. mul-1-neg 80.0%

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

      3. unsub-neg 80.0%

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

      4. *-commutative 80.0%

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

      5. *-commutative 80.0%

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

      6. *-commutative 80.0%

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

      7. mul-1-neg 80.0%

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

      8. *-commutative 80.0%

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

   4. Simplified 80.0%

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

   if 2.6999999999999999e198 < y1

   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 y1 around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. mul-1-neg 51.6%

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

      3. unsub-neg 51.6%

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

      4. *-commutative 51.6%

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

      5. *-commutative 51.6%

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

      6. *-commutative 51.6%

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

      7. mul-1-neg 51.6%

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

      8. *-commutative 51.6%

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

   4. Simplified 51.6%

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

   5. Taylor expanded in z around inf 62.1%

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

      1. associate-*r* 65.1%

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

      2. distribute-lft-out-- 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.2 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -2.5 \cdot 10^{-114}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -8.8 \cdot 10^{-191}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.1 \cdot 10^{-273}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 4 \cdot 10^{-194}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;y1 \leq 5.1 \cdot 10^{-107}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.9 \cdot 10^{+130}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{+198}:\\ \;\;\;\;y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \end{array} \]

Alternative 14: 33.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ t_2 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;y3 \leq -2.05 \cdot 10^{+211}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;y3 \leq -8.6 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq -7 \cdot 10^{-126}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y3 \leq -1.3 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 1.8 \cdot 10^{-297}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y3 \leq 3 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 8.4 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq 48000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 5.2 \cdot 10^{+254}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* j (- (* x i) (* y3 y4)))))
        (t_2
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_3
         (* y2 (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4)))))))
   (if (<= y3 -2.05e+211)
     (* (* y1 y3) (- (* z a) (* j y4)))
     (if (<= y3 -8.6e-10)
       t_1
       (if (<= y3 -7e-126)
         (* (* y2 y4) (- (* k y1) (* t c)))
         (if (<= y3 -1.3e-255)
           t_2
           (if (<= y3 1.8e-297)
             t_3
             (if (<= y3 3e-264)
               t_2
               (if (<= y3 8.4e-172)
                 (+
                  (* x (* c (- (* y0 y2) (* y i))))
                  (* (* x a) (- (* y b) (* y1 y2))))
                 (if (<= y3 48000000000.0)
                   t_3
                   (if (<= y3 1.7e+163)
                     (* t (* i (- (* z c) (* j y5))))
                     (if (<= y3 5.2e+254)
                       (* (* z y1) (- (* a y3) (* i k)))
                       t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (j * ((x * i) - (y3 * y4)));
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_3 = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (y3 <= -2.05e+211) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (y3 <= -8.6e-10) {
		tmp = t_1;
	} else if (y3 <= -7e-126) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y3 <= -1.3e-255) {
		tmp = t_2;
	} else if (y3 <= 1.8e-297) {
		tmp = t_3;
	} else if (y3 <= 3e-264) {
		tmp = t_2;
	} else if (y3 <= 8.4e-172) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y3 <= 48000000000.0) {
		tmp = t_3;
	} else if (y3 <= 1.7e+163) {
		tmp = t * (i * ((z * c) - (j * y5)));
	} else if (y3 <= 5.2e+254) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y1 * (j * ((x * i) - (y3 * y4)))
    t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_3 = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
    if (y3 <= (-2.05d+211)) then
        tmp = (y1 * y3) * ((z * a) - (j * y4))
    else if (y3 <= (-8.6d-10)) then
        tmp = t_1
    else if (y3 <= (-7d-126)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (y3 <= (-1.3d-255)) then
        tmp = t_2
    else if (y3 <= 1.8d-297) then
        tmp = t_3
    else if (y3 <= 3d-264) then
        tmp = t_2
    else if (y3 <= 8.4d-172) then
        tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
    else if (y3 <= 48000000000.0d0) then
        tmp = t_3
    else if (y3 <= 1.7d+163) then
        tmp = t * (i * ((z * c) - (j * y5)))
    else if (y3 <= 5.2d+254) then
        tmp = (z * y1) * ((a * y3) - (i * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (j * ((x * i) - (y3 * y4)));
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_3 = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (y3 <= -2.05e+211) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (y3 <= -8.6e-10) {
		tmp = t_1;
	} else if (y3 <= -7e-126) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (y3 <= -1.3e-255) {
		tmp = t_2;
	} else if (y3 <= 1.8e-297) {
		tmp = t_3;
	} else if (y3 <= 3e-264) {
		tmp = t_2;
	} else if (y3 <= 8.4e-172) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y3 <= 48000000000.0) {
		tmp = t_3;
	} else if (y3 <= 1.7e+163) {
		tmp = t * (i * ((z * c) - (j * y5)));
	} else if (y3 <= 5.2e+254) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (j * ((x * i) - (y3 * y4)))
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_3 = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
	tmp = 0
	if y3 <= -2.05e+211:
		tmp = (y1 * y3) * ((z * a) - (j * y4))
	elif y3 <= -8.6e-10:
		tmp = t_1
	elif y3 <= -7e-126:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif y3 <= -1.3e-255:
		tmp = t_2
	elif y3 <= 1.8e-297:
		tmp = t_3
	elif y3 <= 3e-264:
		tmp = t_2
	elif y3 <= 8.4e-172:
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
	elif y3 <= 48000000000.0:
		tmp = t_3
	elif y3 <= 1.7e+163:
		tmp = t * (i * ((z * c) - (j * y5)))
	elif y3 <= 5.2e+254:
		tmp = (z * y1) * ((a * y3) - (i * k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))))
	t_2 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_3 = Float64(y2 * Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	tmp = 0.0
	if (y3 <= -2.05e+211)
		tmp = Float64(Float64(y1 * y3) * Float64(Float64(z * a) - Float64(j * y4)));
	elseif (y3 <= -8.6e-10)
		tmp = t_1;
	elseif (y3 <= -7e-126)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (y3 <= -1.3e-255)
		tmp = t_2;
	elseif (y3 <= 1.8e-297)
		tmp = t_3;
	elseif (y3 <= 3e-264)
		tmp = t_2;
	elseif (y3 <= 8.4e-172)
		tmp = Float64(Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i)))) + Float64(Float64(x * a) * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y3 <= 48000000000.0)
		tmp = t_3;
	elseif (y3 <= 1.7e+163)
		tmp = Float64(t * Float64(i * Float64(Float64(z * c) - Float64(j * y5))));
	elseif (y3 <= 5.2e+254)
		tmp = Float64(Float64(z * y1) * Float64(Float64(a * y3) - Float64(i * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (j * ((x * i) - (y3 * y4)));
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_3 = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	tmp = 0.0;
	if (y3 <= -2.05e+211)
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	elseif (y3 <= -8.6e-10)
		tmp = t_1;
	elseif (y3 <= -7e-126)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (y3 <= -1.3e-255)
		tmp = t_2;
	elseif (y3 <= 1.8e-297)
		tmp = t_3;
	elseif (y3 <= 3e-264)
		tmp = t_2;
	elseif (y3 <= 8.4e-172)
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	elseif (y3 <= 48000000000.0)
		tmp = t_3;
	elseif (y3 <= 1.7e+163)
		tmp = t * (i * ((z * c) - (j * y5)));
	elseif (y3 <= 5.2e+254)
		tmp = (z * y1) * ((a * y3) - (i * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.05e+211], N[(N[(y1 * y3), $MachinePrecision] * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -8.6e-10], t$95$1, If[LessEqual[y3, -7e-126], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.3e-255], t$95$2, If[LessEqual[y3, 1.8e-297], t$95$3, If[LessEqual[y3, 3e-264], t$95$2, If[LessEqual[y3, 8.4e-172], N[(N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * a), $MachinePrecision] * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 48000000000.0], t$95$3, If[LessEqual[y3, 1.7e+163], N[(t * N[(i * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5.2e+254], N[(N[(z * y1), $MachinePrecision] * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y3 < -2.0499999999999999e211

   1. Initial program 5.6%

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

   2. Taylor expanded in y1 around inf 50.0%

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

      1. +-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. unsub-neg 50.0%

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

      4. *-commutative 50.0%

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

      5. *-commutative 50.0%

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

      6. *-commutative 50.0%

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

      7. mul-1-neg 50.0%

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

      8. *-commutative 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in y3 around inf 77.8%

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

      1. associate-*r* 72.7%

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

      2. cancel-sign-sub-inv 72.7%

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

      3. metadata-eval 72.7%

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

      4. *-lft-identity 72.7%

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

      5. +-commutative 72.7%

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

      6. mul-1-neg 72.7%

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

      7. unsub-neg 72.7%

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

   7. Simplified 72.7%

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

   if -2.0499999999999999e211 < y3 < -8.60000000000000029e-10 or 5.2000000000000002e254 < y3

   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 y1 around inf 33.9%

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

      1. +-commutative 33.9%

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

      2. mul-1-neg 33.9%

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

      3. unsub-neg 33.9%

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

      4. *-commutative 33.9%

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

      5. *-commutative 33.9%

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

      6. *-commutative 33.9%

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

      7. mul-1-neg 33.9%

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

      8. *-commutative 33.9%

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

   4. Simplified 33.9%

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

   5. Taylor expanded in j around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. *-commutative 49.9%

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

      5. *-commutative 49.9%

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

   7. Simplified 49.9%

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

   if -8.60000000000000029e-10 < y3 < -7e-126

   1. Initial program 31.9%

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

   2. Taylor expanded in y2 around inf 48.6%

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

   3. Taylor expanded in y4 around inf 49.2%

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

      1. associate-*r* 49.5%

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

      2. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   if -7e-126 < y3 < -1.3000000000000001e-255 or 1.79999999999999997e-297 < y3 < 3e-264

   1. Initial program 46.8%

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

   2. Taylor expanded in b around inf 54.9%

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

   if -1.3000000000000001e-255 < y3 < 1.79999999999999997e-297 or 8.3999999999999998e-172 < y3 < 4.8e10

   1. Initial program 44.6%

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

   2. 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 k around 0 58.1%

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

   if 3e-264 < y3 < 8.3999999999999998e-172

   1. Initial program 37.4%

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

   2. Taylor expanded in x around inf 62.5%

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

   3. Taylor expanded in j around 0 68.8%

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

   4. Taylor expanded in a around -inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. mul-1-neg 56.4%

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

      5. distribute-rgt-neg-in 56.4%

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

      6. mul-1-neg 56.4%

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

      7. distribute-lft-in 62.6%

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

      8. +-commutative 62.6%

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

      9. mul-1-neg 62.6%

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

      10. unsub-neg 62.6%

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

      11. *-commutative 62.6%

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

      12. associate-*r* 75.1%

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

      13. *-commutative 75.1%

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

   6. Simplified 75.1%

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

   if 4.8e10 < y3 < 1.7000000000000001e163

   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 t around inf 52.4%

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

   3. Taylor expanded in i around inf 41.9%

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

      1. +-commutative 41.9%

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

      2. mul-1-neg 41.9%

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

      3. unsub-neg 41.9%

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

   5. Simplified 41.9%

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

   if 1.7000000000000001e163 < y3 < 5.2000000000000002e254

   1. Initial program 19.2%

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

   2. Taylor expanded in y1 around inf 27.7%

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

      1. +-commutative 27.7%

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

      2. mul-1-neg 27.7%

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

      3. unsub-neg 27.7%

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

      4. *-commutative 27.7%

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

      5. *-commutative 27.7%

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

      6. *-commutative 27.7%

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

      7. mul-1-neg 27.7%

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

      8. *-commutative 27.7%

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

   4. Simplified 27.7%

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

   5. Taylor expanded in z around inf 58.7%

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

      1. associate-*r* 58.5%

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

      2. distribute-lft-out-- 58.5%

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

   7. Simplified 58.5%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.05 \cdot 10^{+211}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;y3 \leq -8.6 \cdot 10^{-10}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq -7 \cdot 10^{-126}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;y3 \leq -1.3 \cdot 10^{-255}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 1.8 \cdot 10^{-297}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 3 \cdot 10^{-264}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 8.4 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq 48000000000:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 5.2 \cdot 10^{+254}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \end{array} \]

Alternative 15: 32.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := y \cdot \left(a \cdot b - c \cdot i\right)\\ t_3 := x \cdot \left(t_2 + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{-48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.95 \cdot 10^{-198}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-218}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-279}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot t_1\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-182}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-66}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+110}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot t_1\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(t_2 + c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (* y (- (* a b) (* c i))))
        (t_3 (* x (+ t_2 (* y2 (- (* c y0) (* a y1)))))))
   (if (<= x -4.2e-48)
     t_3
     (if (<= x -2.95e-198)
       (* y1 (* k (- (* y2 y4) (* z i))))
       (if (<= x -7.8e-218)
         (* (* y1 y3) (- (* z a) (* j y4)))
         (if (<= x 1.05e-279)
           (* y4 (* y1 t_1))
           (if (<= x 1.55e-182)
             t_3
             (if (<= x 9.2e-66)
               (* y1 (* y2 (- (* k y4) (* x a))))
               (if (<= x 8.5e+110)
                 (* y1 (* y4 t_1))
                 (if (<= x 6.4e+214)
                   (* x (+ t_2 (* c (* y0 y2))))
                   (* y1 (* j (* x 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 = (k * y2) - (j * y3);
	double t_2 = y * ((a * b) - (c * i));
	double t_3 = x * (t_2 + (y2 * ((c * y0) - (a * y1))));
	double tmp;
	if (x <= -4.2e-48) {
		tmp = t_3;
	} else if (x <= -2.95e-198) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (x <= -7.8e-218) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (x <= 1.05e-279) {
		tmp = y4 * (y1 * t_1);
	} else if (x <= 1.55e-182) {
		tmp = t_3;
	} else if (x <= 9.2e-66) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (x <= 8.5e+110) {
		tmp = y1 * (y4 * t_1);
	} else if (x <= 6.4e+214) {
		tmp = x * (t_2 + (c * (y0 * y2)));
	} else {
		tmp = y1 * (j * (x * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = y * ((a * b) - (c * i))
    t_3 = x * (t_2 + (y2 * ((c * y0) - (a * y1))))
    if (x <= (-4.2d-48)) then
        tmp = t_3
    else if (x <= (-2.95d-198)) then
        tmp = y1 * (k * ((y2 * y4) - (z * i)))
    else if (x <= (-7.8d-218)) then
        tmp = (y1 * y3) * ((z * a) - (j * y4))
    else if (x <= 1.05d-279) then
        tmp = y4 * (y1 * t_1)
    else if (x <= 1.55d-182) then
        tmp = t_3
    else if (x <= 9.2d-66) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (x <= 8.5d+110) then
        tmp = y1 * (y4 * t_1)
    else if (x <= 6.4d+214) then
        tmp = x * (t_2 + (c * (y0 * y2)))
    else
        tmp = y1 * (j * (x * 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 = (k * y2) - (j * y3);
	double t_2 = y * ((a * b) - (c * i));
	double t_3 = x * (t_2 + (y2 * ((c * y0) - (a * y1))));
	double tmp;
	if (x <= -4.2e-48) {
		tmp = t_3;
	} else if (x <= -2.95e-198) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (x <= -7.8e-218) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (x <= 1.05e-279) {
		tmp = y4 * (y1 * t_1);
	} else if (x <= 1.55e-182) {
		tmp = t_3;
	} else if (x <= 9.2e-66) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (x <= 8.5e+110) {
		tmp = y1 * (y4 * t_1);
	} else if (x <= 6.4e+214) {
		tmp = x * (t_2 + (c * (y0 * y2)));
	} else {
		tmp = y1 * (j * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = y * ((a * b) - (c * i))
	t_3 = x * (t_2 + (y2 * ((c * y0) - (a * y1))))
	tmp = 0
	if x <= -4.2e-48:
		tmp = t_3
	elif x <= -2.95e-198:
		tmp = y1 * (k * ((y2 * y4) - (z * i)))
	elif x <= -7.8e-218:
		tmp = (y1 * y3) * ((z * a) - (j * y4))
	elif x <= 1.05e-279:
		tmp = y4 * (y1 * t_1)
	elif x <= 1.55e-182:
		tmp = t_3
	elif x <= 9.2e-66:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif x <= 8.5e+110:
		tmp = y1 * (y4 * t_1)
	elif x <= 6.4e+214:
		tmp = x * (t_2 + (c * (y0 * y2)))
	else:
		tmp = y1 * (j * (x * 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(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(y * Float64(Float64(a * b) - Float64(c * i)))
	t_3 = Float64(x * Float64(t_2 + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))))
	tmp = 0.0
	if (x <= -4.2e-48)
		tmp = t_3;
	elseif (x <= -2.95e-198)
		tmp = Float64(y1 * Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (x <= -7.8e-218)
		tmp = Float64(Float64(y1 * y3) * Float64(Float64(z * a) - Float64(j * y4)));
	elseif (x <= 1.05e-279)
		tmp = Float64(y4 * Float64(y1 * t_1));
	elseif (x <= 1.55e-182)
		tmp = t_3;
	elseif (x <= 9.2e-66)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (x <= 8.5e+110)
		tmp = Float64(y1 * Float64(y4 * t_1));
	elseif (x <= 6.4e+214)
		tmp = Float64(x * Float64(t_2 + Float64(c * Float64(y0 * y2))));
	else
		tmp = Float64(y1 * Float64(j * Float64(x * 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 = (k * y2) - (j * y3);
	t_2 = y * ((a * b) - (c * i));
	t_3 = x * (t_2 + (y2 * ((c * y0) - (a * y1))));
	tmp = 0.0;
	if (x <= -4.2e-48)
		tmp = t_3;
	elseif (x <= -2.95e-198)
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	elseif (x <= -7.8e-218)
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	elseif (x <= 1.05e-279)
		tmp = y4 * (y1 * t_1);
	elseif (x <= 1.55e-182)
		tmp = t_3;
	elseif (x <= 9.2e-66)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (x <= 8.5e+110)
		tmp = y1 * (y4 * t_1);
	elseif (x <= 6.4e+214)
		tmp = x * (t_2 + (c * (y0 * y2)));
	else
		tmp = y1 * (j * (x * 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[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(t$95$2 + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e-48], t$95$3, If[LessEqual[x, -2.95e-198], N[(y1 * N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.8e-218], N[(N[(y1 * y3), $MachinePrecision] * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-279], N[(y4 * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e-182], t$95$3, If[LessEqual[x, 9.2e-66], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+110], N[(y1 * N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.4e+214], N[(x * N[(t$95$2 + N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(j * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -4.19999999999999977e-48 or 1.05000000000000003e-279 < x < 1.55000000000000004e-182

   1. Initial program 31.8%

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

   2. Taylor expanded in x around inf 52.1%

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

   3. Taylor expanded in j around 0 50.3%

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

   if -4.19999999999999977e-48 < x < -2.94999999999999987e-198

   1. Initial program 38.4%

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

   2. Taylor expanded in y1 around inf 35.5%

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

      1. +-commutative 35.5%

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

      2. mul-1-neg 35.5%

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

      3. unsub-neg 35.5%

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

      4. *-commutative 35.5%

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

      5. *-commutative 35.5%

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

      6. *-commutative 35.5%

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

      7. mul-1-neg 35.5%

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

      8. *-commutative 35.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 35.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in k around inf 45.9%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 45.9%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      2. mul-1-neg 45.9%

         \[\leadsto y1 \cdot \left(k \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      3. unsub-neg 45.9%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)}\right) \]

   7. Simplified 45.9%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   if -2.94999999999999987e-198 < x < -7.8e-218

   1. Initial program 1.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 49.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 49.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 49.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 49.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in y3 around inf 83.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) - -1 \cdot \left(a \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 68.2%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) - -1 \cdot \left(a \cdot z\right)\right)} \]

      2. cancel-sign-sub-inv 68.2%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + \left(--1\right) \cdot \left(a \cdot z\right)\right)} \]

      3. metadata-eval 68.2%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) + \color{blue}{1} \cdot \left(a \cdot z\right)\right) \]

      4. *-lft-identity 68.2%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) + \color{blue}{a \cdot z}\right) \]

      5. +-commutative 68.2%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(a \cdot z + -1 \cdot \left(j \cdot y4\right)\right)} \]

      6. mul-1-neg 68.2%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(a \cdot z + \color{blue}{\left(-j \cdot y4\right)}\right) \]

      7. unsub-neg 68.2%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(a \cdot z - j \cdot y4\right)} \]

   7. Simplified 68.2%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   if -7.8e-218 < x < 1.05000000000000003e-279

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 60.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y1 around inf 50.8%

      \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.8%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(\color{blue}{y2 \cdot k} - j \cdot y3\right)\right) \]

   5. Simplified 50.8%

      \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]

   if 1.55000000000000004e-182 < x < 9.19999999999999967e-66

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 47.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in y1 around inf 44.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.9%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \]

      2. mul-1-neg 44.9%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \]

      3. sub-neg 44.9%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \]

      4. *-commutative 44.9%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(\color{blue}{y4 \cdot k} - a \cdot x\right)\right) \]

      5. *-commutative 44.9%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(y4 \cdot k - \color{blue}{x \cdot a}\right)\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(y4 \cdot k - x \cdot a\right)\right)} \]

   if 9.19999999999999967e-66 < x < 8.5000000000000004e110

   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 y1 around inf 31.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 31.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 31.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 31.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in y4 around inf 40.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.6%

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot k} - j \cdot y3\right)\right) \]

   7. Simplified 40.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]

   if 8.5000000000000004e110 < x < 6.3999999999999999e214

   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 x around inf 48.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around 0 45.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   4. Taylor expanded in c around inf 57.4%

      \[\leadsto x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{c \cdot \left(y0 \cdot y2\right)}\right) \]
   5. Step-by-step derivation

      1. *-commutative 57.4%

         \[\leadsto x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   6. Simplified 57.4%

      \[\leadsto x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{c \cdot \left(y2 \cdot y0\right)}\right) \]

   if 6.3999999999999999e214 < x

   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 52.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 52.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 52.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 56.6%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 56.6%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 56.6%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 56.6%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 56.6%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 56.6%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 56.6%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 68.6%

      \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 68.6%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]

   10. Simplified 68.6%

       \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.95 \cdot 10^{-198}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-218}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-279}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-182}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-66}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+110}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 16: 31.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + c \cdot \left(y0 \cdot y2\right)\right)\\ t_2 := k \cdot y2 - j \cdot y3\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-105}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-208}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-242}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot t_2\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-64}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+110}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot t_2\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+214}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (+ (* y (- (* a b) (* c i))) (* c (* y0 y2)))))
        (t_2 (- (* k y2) (* j y3))))
   (if (<= x -5.2e-25)
     t_1
     (if (<= x -3.3e-105)
       (* (* t y2) (- (* a y5) (* c y4)))
       (if (<= x -3.7e-208)
         (* (* z y1) (- (* a y3) (* i k)))
         (if (<= x 1.12e-242)
           (* y4 (* y1 t_2))
           (if (<= x 3.1e-64)
             (* y1 (* y2 (- (* k y4) (* x a))))
             (if (<= x 8.5e+110)
               (* y1 (* y4 t_2))
               (if (<= x 3.8e+214) t_1 (* y1 (* j (* x 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 = x * ((y * ((a * b) - (c * i))) + (c * (y0 * y2)));
	double t_2 = (k * y2) - (j * y3);
	double tmp;
	if (x <= -5.2e-25) {
		tmp = t_1;
	} else if (x <= -3.3e-105) {
		tmp = (t * y2) * ((a * y5) - (c * y4));
	} else if (x <= -3.7e-208) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else if (x <= 1.12e-242) {
		tmp = y4 * (y1 * t_2);
	} else if (x <= 3.1e-64) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (x <= 8.5e+110) {
		tmp = y1 * (y4 * t_2);
	} else if (x <= 3.8e+214) {
		tmp = t_1;
	} else {
		tmp = y1 * (j * (x * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * ((a * b) - (c * i))) + (c * (y0 * y2)))
    t_2 = (k * y2) - (j * y3)
    if (x <= (-5.2d-25)) then
        tmp = t_1
    else if (x <= (-3.3d-105)) then
        tmp = (t * y2) * ((a * y5) - (c * y4))
    else if (x <= (-3.7d-208)) then
        tmp = (z * y1) * ((a * y3) - (i * k))
    else if (x <= 1.12d-242) then
        tmp = y4 * (y1 * t_2)
    else if (x <= 3.1d-64) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (x <= 8.5d+110) then
        tmp = y1 * (y4 * t_2)
    else if (x <= 3.8d+214) then
        tmp = t_1
    else
        tmp = y1 * (j * (x * 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 = x * ((y * ((a * b) - (c * i))) + (c * (y0 * y2)));
	double t_2 = (k * y2) - (j * y3);
	double tmp;
	if (x <= -5.2e-25) {
		tmp = t_1;
	} else if (x <= -3.3e-105) {
		tmp = (t * y2) * ((a * y5) - (c * y4));
	} else if (x <= -3.7e-208) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else if (x <= 1.12e-242) {
		tmp = y4 * (y1 * t_2);
	} else if (x <= 3.1e-64) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (x <= 8.5e+110) {
		tmp = y1 * (y4 * t_2);
	} else if (x <= 3.8e+214) {
		tmp = t_1;
	} else {
		tmp = y1 * (j * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * ((y * ((a * b) - (c * i))) + (c * (y0 * y2)))
	t_2 = (k * y2) - (j * y3)
	tmp = 0
	if x <= -5.2e-25:
		tmp = t_1
	elif x <= -3.3e-105:
		tmp = (t * y2) * ((a * y5) - (c * y4))
	elif x <= -3.7e-208:
		tmp = (z * y1) * ((a * y3) - (i * k))
	elif x <= 1.12e-242:
		tmp = y4 * (y1 * t_2)
	elif x <= 3.1e-64:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif x <= 8.5e+110:
		tmp = y1 * (y4 * t_2)
	elif x <= 3.8e+214:
		tmp = t_1
	else:
		tmp = y1 * (j * (x * 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(x * Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(c * Float64(y0 * y2))))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	tmp = 0.0
	if (x <= -5.2e-25)
		tmp = t_1;
	elseif (x <= -3.3e-105)
		tmp = Float64(Float64(t * y2) * Float64(Float64(a * y5) - Float64(c * y4)));
	elseif (x <= -3.7e-208)
		tmp = Float64(Float64(z * y1) * Float64(Float64(a * y3) - Float64(i * k)));
	elseif (x <= 1.12e-242)
		tmp = Float64(y4 * Float64(y1 * t_2));
	elseif (x <= 3.1e-64)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (x <= 8.5e+110)
		tmp = Float64(y1 * Float64(y4 * t_2));
	elseif (x <= 3.8e+214)
		tmp = t_1;
	else
		tmp = Float64(y1 * Float64(j * Float64(x * 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 = x * ((y * ((a * b) - (c * i))) + (c * (y0 * y2)));
	t_2 = (k * y2) - (j * y3);
	tmp = 0.0;
	if (x <= -5.2e-25)
		tmp = t_1;
	elseif (x <= -3.3e-105)
		tmp = (t * y2) * ((a * y5) - (c * y4));
	elseif (x <= -3.7e-208)
		tmp = (z * y1) * ((a * y3) - (i * k));
	elseif (x <= 1.12e-242)
		tmp = y4 * (y1 * t_2);
	elseif (x <= 3.1e-64)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (x <= 8.5e+110)
		tmp = y1 * (y4 * t_2);
	elseif (x <= 3.8e+214)
		tmp = t_1;
	else
		tmp = y1 * (j * (x * 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[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e-25], t$95$1, If[LessEqual[x, -3.3e-105], N[(N[(t * y2), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.7e-208], N[(N[(z * y1), $MachinePrecision] * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e-242], N[(y4 * N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e-64], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+110], N[(y1 * N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+214], t$95$1, N[(y1 * N[(j * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -5.2e-25 or 8.5000000000000004e110 < x < 3.79999999999999997e214

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 51.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around 0 47.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   4. Taylor expanded in c around inf 47.0%

      \[\leadsto x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{c \cdot \left(y0 \cdot y2\right)}\right) \]
   5. Step-by-step derivation

      1. *-commutative 47.0%

         \[\leadsto x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   6. Simplified 47.0%

      \[\leadsto x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{c \cdot \left(y2 \cdot y0\right)}\right) \]

   if -5.2e-25 < x < -3.2999999999999999e-105

   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 51.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in y0 around -inf 59.6%

      \[\leadsto y2 \cdot \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y1\right)\right) + \left(-1 \cdot \left(y0 \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) + k \cdot \left(y1 \cdot y4\right)\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

   5. Simplified 59.6%

      \[\leadsto y2 \cdot \color{blue}{\left(\left(\left(k \cdot \left(y1 \cdot y4\right) - y0 \cdot \left(k \cdot y5 - x \cdot c\right)\right) - a \cdot \left(x \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in t around inf 59.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 67.4%

         \[\leadsto \color{blue}{\left(t \cdot y2\right) \cdot \left(a \cdot y5 - c \cdot y4\right)} \]

      2. *-commutative 67.4%

         \[\leadsto \color{blue}{\left(y2 \cdot t\right)} \cdot \left(a \cdot y5 - c \cdot y4\right) \]

      3. *-commutative 67.4%

         \[\leadsto \left(y2 \cdot t\right) \cdot \left(a \cdot y5 - \color{blue}{y4 \cdot c}\right) \]

   8. Simplified 67.4%

      \[\leadsto \color{blue}{\left(y2 \cdot t\right) \cdot \left(a \cdot y5 - y4 \cdot c\right)} \]

   if -3.2999999999999999e-105 < x < -3.7000000000000002e-208

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 46.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 46.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 46.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 46.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 46.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 46.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 46.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 46.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 46.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in z around inf 51.1%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(-1 \cdot \left(i \cdot k\right) - -1 \cdot \left(a \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 51.0%

         \[\leadsto \color{blue}{\left(y1 \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot k\right) - -1 \cdot \left(a \cdot y3\right)\right)} \]

      2. distribute-lft-out-- 51.0%

         \[\leadsto \left(y1 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

   7. Simplified 51.0%

      \[\leadsto \color{blue}{\left(y1 \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

   if -3.7000000000000002e-208 < x < 1.11999999999999997e-242

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 48.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   3. Taylor expanded in y1 around inf 46.0%

      \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 46.0%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(\color{blue}{y2 \cdot k} - j \cdot y3\right)\right) \]

   5. Simplified 46.0%

      \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]

   if 1.11999999999999997e-242 < x < 3.10000000000000025e-64

   1. Initial program 36.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 45.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in y1 around inf 40.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.8%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \]

      2. mul-1-neg 40.8%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \]

      3. sub-neg 40.8%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \]

      4. *-commutative 40.8%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(\color{blue}{y4 \cdot k} - a \cdot x\right)\right) \]

      5. *-commutative 40.8%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(y4 \cdot k - \color{blue}{x \cdot a}\right)\right) \]

   5. Simplified 40.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(y4 \cdot k - x \cdot a\right)\right)} \]

   if 3.10000000000000025e-64 < x < 8.5000000000000004e110

   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 y1 around inf 31.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 31.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 31.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 31.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 31.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in y4 around inf 40.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.6%

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot k} - j \cdot y3\right)\right) \]

   7. Simplified 40.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]

   if 3.79999999999999997e214 < x

   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 52.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 52.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 52.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 52.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 56.6%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 56.6%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 56.6%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 56.6%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 56.6%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 56.6%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 56.6%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 68.6%

      \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 68.6%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]

   10. Simplified 68.6%

       \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-105}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-208}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-242}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-64}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+110}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 17: 33.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ t_2 := t \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{if}\;y3 \leq -4.1 \cdot 10^{+211}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;y3 \leq -9.2 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 1.5 \cdot 10^{-288}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t_2\right)\\ \mathbf{elif}\;y3 \leq 2.3 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq 45000000000:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t_2\right)\\ \mathbf{elif}\;y3 \leq 1.85 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 1.8 \cdot 10^{+255}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* j (- (* x i) (* y3 y4)))))
        (t_2 (* t (- (* a y5) (* c y4)))))
   (if (<= y3 -4.1e+211)
     (* (* y1 y3) (- (* z a) (* j y4)))
     (if (<= y3 -9.2e-10)
       t_1
       (if (<= y3 1.5e-288)
         (* y2 (+ (* y0 (- (* x c) (* k y5))) t_2))
         (if (<= y3 2.3e-171)
           (+
            (* x (* c (- (* y0 y2) (* y i))))
            (* (* x a) (- (* y b) (* y1 y2))))
           (if (<= y3 45000000000.0)
             (* y2 (+ (* x (- (* c y0) (* a y1))) t_2))
             (if (<= y3 1.85e+163)
               (* t (* i (- (* z c) (* j y5))))
               (if (<= y3 1.8e+255)
                 (* (* z y1) (- (* a y3) (* i k)))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (j * ((x * i) - (y3 * y4)));
	double t_2 = t * ((a * y5) - (c * y4));
	double tmp;
	if (y3 <= -4.1e+211) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (y3 <= -9.2e-10) {
		tmp = t_1;
	} else if (y3 <= 1.5e-288) {
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_2);
	} else if (y3 <= 2.3e-171) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y3 <= 45000000000.0) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + t_2);
	} else if (y3 <= 1.85e+163) {
		tmp = t * (i * ((z * c) - (j * y5)));
	} else if (y3 <= 1.8e+255) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y1 * (j * ((x * i) - (y3 * y4)))
    t_2 = t * ((a * y5) - (c * y4))
    if (y3 <= (-4.1d+211)) then
        tmp = (y1 * y3) * ((z * a) - (j * y4))
    else if (y3 <= (-9.2d-10)) then
        tmp = t_1
    else if (y3 <= 1.5d-288) then
        tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_2)
    else if (y3 <= 2.3d-171) then
        tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
    else if (y3 <= 45000000000.0d0) then
        tmp = y2 * ((x * ((c * y0) - (a * y1))) + t_2)
    else if (y3 <= 1.85d+163) then
        tmp = t * (i * ((z * c) - (j * y5)))
    else if (y3 <= 1.8d+255) then
        tmp = (z * y1) * ((a * y3) - (i * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (j * ((x * i) - (y3 * y4)));
	double t_2 = t * ((a * y5) - (c * y4));
	double tmp;
	if (y3 <= -4.1e+211) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (y3 <= -9.2e-10) {
		tmp = t_1;
	} else if (y3 <= 1.5e-288) {
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_2);
	} else if (y3 <= 2.3e-171) {
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	} else if (y3 <= 45000000000.0) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + t_2);
	} else if (y3 <= 1.85e+163) {
		tmp = t * (i * ((z * c) - (j * y5)));
	} else if (y3 <= 1.8e+255) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (j * ((x * i) - (y3 * y4)))
	t_2 = t * ((a * y5) - (c * y4))
	tmp = 0
	if y3 <= -4.1e+211:
		tmp = (y1 * y3) * ((z * a) - (j * y4))
	elif y3 <= -9.2e-10:
		tmp = t_1
	elif y3 <= 1.5e-288:
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_2)
	elif y3 <= 2.3e-171:
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)))
	elif y3 <= 45000000000.0:
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + t_2)
	elif y3 <= 1.85e+163:
		tmp = t * (i * ((z * c) - (j * y5)))
	elif y3 <= 1.8e+255:
		tmp = (z * y1) * ((a * y3) - (i * k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))))
	t_2 = Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))
	tmp = 0.0
	if (y3 <= -4.1e+211)
		tmp = Float64(Float64(y1 * y3) * Float64(Float64(z * a) - Float64(j * y4)));
	elseif (y3 <= -9.2e-10)
		tmp = t_1;
	elseif (y3 <= 1.5e-288)
		tmp = Float64(y2 * Float64(Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))) + t_2));
	elseif (y3 <= 2.3e-171)
		tmp = Float64(Float64(x * Float64(c * Float64(Float64(y0 * y2) - Float64(y * i)))) + Float64(Float64(x * a) * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y3 <= 45000000000.0)
		tmp = Float64(y2 * Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + t_2));
	elseif (y3 <= 1.85e+163)
		tmp = Float64(t * Float64(i * Float64(Float64(z * c) - Float64(j * y5))));
	elseif (y3 <= 1.8e+255)
		tmp = Float64(Float64(z * y1) * Float64(Float64(a * y3) - Float64(i * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (j * ((x * i) - (y3 * y4)));
	t_2 = t * ((a * y5) - (c * y4));
	tmp = 0.0;
	if (y3 <= -4.1e+211)
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	elseif (y3 <= -9.2e-10)
		tmp = t_1;
	elseif (y3 <= 1.5e-288)
		tmp = y2 * ((y0 * ((x * c) - (k * y5))) + t_2);
	elseif (y3 <= 2.3e-171)
		tmp = (x * (c * ((y0 * y2) - (y * i)))) + ((x * a) * ((y * b) - (y1 * y2)));
	elseif (y3 <= 45000000000.0)
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + t_2);
	elseif (y3 <= 1.85e+163)
		tmp = t * (i * ((z * c) - (j * y5)));
	elseif (y3 <= 1.8e+255)
		tmp = (z * y1) * ((a * y3) - (i * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -4.1e+211], N[(N[(y1 * y3), $MachinePrecision] * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -9.2e-10], t$95$1, If[LessEqual[y3, 1.5e-288], N[(y2 * N[(N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.3e-171], N[(N[(x * N[(c * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * a), $MachinePrecision] * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 45000000000.0], N[(y2 * N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.85e+163], N[(t * N[(i * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.8e+255], N[(N[(z * y1), $MachinePrecision] * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y3 < -4.0999999999999999e211

   1. Initial program 5.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 50.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 50.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 50.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in y3 around inf 77.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) - -1 \cdot \left(a \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) - -1 \cdot \left(a \cdot z\right)\right)} \]

      2. cancel-sign-sub-inv 72.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + \left(--1\right) \cdot \left(a \cdot z\right)\right)} \]

      3. metadata-eval 72.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) + \color{blue}{1} \cdot \left(a \cdot z\right)\right) \]

      4. *-lft-identity 72.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) + \color{blue}{a \cdot z}\right) \]

      5. +-commutative 72.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(a \cdot z + -1 \cdot \left(j \cdot y4\right)\right)} \]

      6. mul-1-neg 72.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(a \cdot z + \color{blue}{\left(-j \cdot y4\right)}\right) \]

      7. unsub-neg 72.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(a \cdot z - j \cdot y4\right)} \]

   7. Simplified 72.7%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   if -4.0999999999999999e211 < y3 < -9.20000000000000028e-10 or 1.7999999999999999e255 < y3

   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 y1 around inf 33.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 33.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 33.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 33.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 33.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 33.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 33.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 33.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 33.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 33.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 49.9%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 49.9%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 49.9%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 49.9%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 49.9%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 49.9%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 49.9%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   if -9.20000000000000028e-10 < y3 < 1.5e-288

   1. Initial program 44.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 47.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in y0 around -inf 48.8%

      \[\leadsto y2 \cdot \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y1\right)\right) + \left(-1 \cdot \left(y0 \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right) + k \cdot \left(y1 \cdot y4\right)\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

   5. Simplified 48.8%

      \[\leadsto y2 \cdot \color{blue}{\left(\left(\left(k \cdot \left(y1 \cdot y4\right) - y0 \cdot \left(k \cdot y5 - x \cdot c\right)\right) - a \cdot \left(x \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in y1 around 0 42.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y2 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right) + y0 \cdot \left(k \cdot y5 - c \cdot x\right)\right)\right)} \]

   if 1.5e-288 < y3 < 2.29999999999999978e-171

   1. Initial program 45.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 55.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around 0 59.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   4. Taylor expanded in a around -inf 50.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)\right) + x \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot y\right)\right) + c \cdot \left(y0 \cdot y2\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.5%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot y\right)\right) + c \cdot \left(y0 \cdot y2\right)\right) + -1 \cdot \left(a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 50.5%

         \[\leadsto x \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot y\right)\right) + c \cdot \left(y0 \cdot y2\right)\right) + \color{blue}{\left(-a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)\right)} \]

      3. unsub-neg 50.5%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(c \cdot \left(i \cdot y\right)\right) + c \cdot \left(y0 \cdot y2\right)\right) - a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)} \]

      4. mul-1-neg 50.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(-c \cdot \left(i \cdot y\right)\right)} + c \cdot \left(y0 \cdot y2\right)\right) - a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]

      5. distribute-rgt-neg-in 50.5%

         \[\leadsto x \cdot \left(\color{blue}{c \cdot \left(-i \cdot y\right)} + c \cdot \left(y0 \cdot y2\right)\right) - a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]

      6. mul-1-neg 50.5%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} + c \cdot \left(y0 \cdot y2\right)\right) - a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]

      7. distribute-lft-in 55.0%

         \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} - a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]

      8. +-commutative 55.0%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) - a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]

      9. mul-1-neg 55.0%

         \[\leadsto x \cdot \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) - a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]

      10. unsub-neg 55.0%

          \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) - a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]

      11. *-commutative 55.0%

          \[\leadsto x \cdot \left(c \cdot \left(\color{blue}{y2 \cdot y0} - i \cdot y\right)\right) - a \cdot \left(x \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right) \]

      12. associate-*r* 64.1%

          \[\leadsto x \cdot \left(c \cdot \left(y2 \cdot y0 - i \cdot y\right)\right) - \color{blue}{\left(a \cdot x\right) \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)} \]

      13. *-commutative 64.1%

          \[\leadsto x \cdot \left(c \cdot \left(y2 \cdot y0 - i \cdot y\right)\right) - \color{blue}{\left(x \cdot a\right)} \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right) \]

   6. Simplified 64.1%

      \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y2 \cdot y0 - i \cdot y\right)\right) - \left(x \cdot a\right) \cdot \left(y2 \cdot y1 - b \cdot y\right)} \]

   if 2.29999999999999978e-171 < y3 < 4.5e10

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 52.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in k around 0 54.9%

      \[\leadsto \color{blue}{y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 4.5e10 < y3 < 1.84999999999999996e163

   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 t around inf 52.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in i around inf 41.9%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.9%

         \[\leadsto t \cdot \left(i \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 41.9%

         \[\leadsto t \cdot \left(i \cdot \left(c \cdot z + \color{blue}{\left(-j \cdot y5\right)}\right)\right) \]

      3. unsub-neg 41.9%

         \[\leadsto t \cdot \left(i \cdot \color{blue}{\left(c \cdot z - j \cdot y5\right)}\right) \]

   5. Simplified 41.9%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   if 1.84999999999999996e163 < y3 < 1.7999999999999999e255

   1. Initial program 19.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 27.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 27.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 27.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 27.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in z around inf 58.7%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(-1 \cdot \left(i \cdot k\right) - -1 \cdot \left(a \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto \color{blue}{\left(y1 \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot k\right) - -1 \cdot \left(a \cdot y3\right)\right)} \]

      2. distribute-lft-out-- 58.5%

         \[\leadsto \left(y1 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

   7. Simplified 58.5%

      \[\leadsto \color{blue}{\left(y1 \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -4.1 \cdot 10^{+211}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;y3 \leq -9.2 \cdot 10^{-10}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.5 \cdot 10^{-288}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.3 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2 - y \cdot i\right)\right) + \left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;y3 \leq 45000000000:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.85 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 1.8 \cdot 10^{+255}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \end{array} \]

Alternative 18: 27.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{if}\;y2 \leq -8.5 \cdot 10^{+217}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -3.9 \cdot 10^{+145}:\\ \;\;\;\;c \cdot \left(x \cdot \left(i \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.45 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -5.8 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 9.6 \cdot 10^{-241}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y1 \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.95 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 5.4 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (- (* x j) (* z k)) y1))))
   (if (<= y2 -8.5e+217)
     (* t (* y4 (- (* b j) (* c y2))))
     (if (<= y2 -3.9e+145)
       (* c (* x (* i (- y))))
       (if (<= y2 -2.45e-91)
         (* c (* y2 (- (* x y0) (* t y4))))
         (if (<= y2 -5.8e-285)
           t_1
           (if (<= y2 2.8e-294)
             (* b (* y0 (- (* z k) (* x j))))
             (if (<= y2 9.6e-241)
               (* (* y3 y4) (* y1 (- j)))
               (if (<= y2 1.95e-5)
                 (* x (* y (- (* a b) (* c i))))
                 (if (<= y2 5.4e+107) t_1 (* c (* x (* y0 y2)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (((x * j) - (z * k)) * y1);
	double tmp;
	if (y2 <= -8.5e+217) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y2 <= -3.9e+145) {
		tmp = c * (x * (i * -y));
	} else if (y2 <= -2.45e-91) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -5.8e-285) {
		tmp = t_1;
	} else if (y2 <= 2.8e-294) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= 9.6e-241) {
		tmp = (y3 * y4) * (y1 * -j);
	} else if (y2 <= 1.95e-5) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y2 <= 5.4e+107) {
		tmp = t_1;
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (((x * j) - (z * k)) * y1)
    if (y2 <= (-8.5d+217)) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (y2 <= (-3.9d+145)) then
        tmp = c * (x * (i * -y))
    else if (y2 <= (-2.45d-91)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y2 <= (-5.8d-285)) then
        tmp = t_1
    else if (y2 <= 2.8d-294) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y2 <= 9.6d-241) then
        tmp = (y3 * y4) * (y1 * -j)
    else if (y2 <= 1.95d-5) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y2 <= 5.4d+107) then
        tmp = t_1
    else
        tmp = c * (x * (y0 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (((x * j) - (z * k)) * y1);
	double tmp;
	if (y2 <= -8.5e+217) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y2 <= -3.9e+145) {
		tmp = c * (x * (i * -y));
	} else if (y2 <= -2.45e-91) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -5.8e-285) {
		tmp = t_1;
	} else if (y2 <= 2.8e-294) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y2 <= 9.6e-241) {
		tmp = (y3 * y4) * (y1 * -j);
	} else if (y2 <= 1.95e-5) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y2 <= 5.4e+107) {
		tmp = t_1;
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (((x * j) - (z * k)) * y1)
	tmp = 0
	if y2 <= -8.5e+217:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif y2 <= -3.9e+145:
		tmp = c * (x * (i * -y))
	elif y2 <= -2.45e-91:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y2 <= -5.8e-285:
		tmp = t_1
	elif y2 <= 2.8e-294:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y2 <= 9.6e-241:
		tmp = (y3 * y4) * (y1 * -j)
	elif y2 <= 1.95e-5:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y2 <= 5.4e+107:
		tmp = t_1
	else:
		tmp = c * (x * (y0 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(Float64(Float64(x * j) - Float64(z * k)) * y1))
	tmp = 0.0
	if (y2 <= -8.5e+217)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y2 <= -3.9e+145)
		tmp = Float64(c * Float64(x * Float64(i * Float64(-y))));
	elseif (y2 <= -2.45e-91)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y2 <= -5.8e-285)
		tmp = t_1;
	elseif (y2 <= 2.8e-294)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y2 <= 9.6e-241)
		tmp = Float64(Float64(y3 * y4) * Float64(y1 * Float64(-j)));
	elseif (y2 <= 1.95e-5)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y2 <= 5.4e+107)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (((x * j) - (z * k)) * y1);
	tmp = 0.0;
	if (y2 <= -8.5e+217)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (y2 <= -3.9e+145)
		tmp = c * (x * (i * -y));
	elseif (y2 <= -2.45e-91)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y2 <= -5.8e-285)
		tmp = t_1;
	elseif (y2 <= 2.8e-294)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y2 <= 9.6e-241)
		tmp = (y3 * y4) * (y1 * -j);
	elseif (y2 <= 1.95e-5)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y2 <= 5.4e+107)
		tmp = t_1;
	else
		tmp = c * (x * (y0 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -8.5e+217], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.9e+145], N[(c * N[(x * N[(i * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.45e-91], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.8e-285], t$95$1, If[LessEqual[y2, 2.8e-294], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.6e-241], N[(N[(y3 * y4), $MachinePrecision] * N[(y1 * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.95e-5], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.4e+107], t$95$1, N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y2 < -8.50000000000000021e217

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in t around inf 50.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in y4 around inf 70.6%

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto t \cdot \left(y4 \cdot \left(\color{blue}{j \cdot b} - c \cdot y2\right)\right) \]

      2. *-commutative 70.6%

         \[\leadsto t \cdot \left(y4 \cdot \left(j \cdot b - \color{blue}{y2 \cdot c}\right)\right) \]

   5. Simplified 70.6%

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(j \cdot b - y2 \cdot c\right)\right)} \]

   if -8.50000000000000021e217 < y2 < -3.8999999999999998e145

   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 x around inf 38.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 62.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 62.8%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 62.8%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 62.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 62.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 62.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 62.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 62.8%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around inf 51.0%

      \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y\right)}\right) \]

   if -3.8999999999999998e145 < y2 < -2.4499999999999999e-91

   1. Initial program 51.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 49.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 39.4%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if -2.4499999999999999e-91 < y2 < -5.7999999999999999e-285 or 1.95e-5 < y2 < 5.4000000000000003e107

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 47.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 47.1%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 47.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 47.1%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 47.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 47.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 47.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 47.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 47.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 47.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in i around inf 44.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.0%

         \[\leadsto i \cdot \left(y1 \cdot \left(\color{blue}{x \cdot j} - k \cdot z\right)\right) \]

   7. Simplified 44.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(x \cdot j - k \cdot z\right)\right)} \]

   if -5.7999999999999999e-285 < y2 < 2.79999999999999991e-294

   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 b around inf 46.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y0 around inf 65.1%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 65.1%

         \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - \color{blue}{x \cdot j}\right)\right) \]

   5. Simplified 65.1%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - x \cdot j\right)\right)} \]

   if 2.79999999999999991e-294 < y2 < 9.6e-241

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 14.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 14.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 14.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 14.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 14.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 14.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 14.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 14.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 14.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 14.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 43.3%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 43.3%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 43.3%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 43.3%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 43.3%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 43.3%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 43.3%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around 0 29.8%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 29.8%

         \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

      2. associate-*r* 36.6%

         \[\leadsto -\color{blue}{\left(j \cdot y1\right) \cdot \left(y3 \cdot y4\right)} \]

      3. *-commutative 36.6%

         \[\leadsto -\left(j \cdot y1\right) \cdot \color{blue}{\left(y4 \cdot y3\right)} \]

      4. distribute-lft-neg-in 36.6%

         \[\leadsto \color{blue}{\left(-j \cdot y1\right) \cdot \left(y4 \cdot y3\right)} \]

      5. *-commutative 36.6%

         \[\leadsto \left(-\color{blue}{y1 \cdot j}\right) \cdot \left(y4 \cdot y3\right) \]

      6. distribute-rgt-neg-in 36.6%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(-j\right)\right)} \cdot \left(y4 \cdot y3\right) \]

   10. Simplified 36.6%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(-j\right)\right) \cdot \left(y4 \cdot y3\right)} \]

   if 9.6e-241 < y2 < 1.95e-5

   1. Initial program 42.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 56.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in y around inf 40.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if 5.4000000000000003e107 < y2

   1. Initial program 16.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 36.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 42.9%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 42.9%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 42.9%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 42.9%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 42.9%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 42.9%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 42.9%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 42.9%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around 0 47.7%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   8. Simplified 47.7%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -8.5 \cdot 10^{+217}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -3.9 \cdot 10^{+145}:\\ \;\;\;\;c \cdot \left(x \cdot \left(i \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.45 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -5.8 \cdot 10^{-285}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 9.6 \cdot 10^{-241}:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y1 \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.95 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 5.4 \cdot 10^{+107}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 19: 30.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ t_2 := y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+16}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-96}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-224}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+78}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (* y0 (- (* x c) (* k y5)))))
        (t_2 (* y1 (* k (- (* y2 y4) (* z i))))))
   (if (<= x -1.1e+174)
     t_1
     (if (<= x -3.8e+16)
       (* (* x c) (- (* y0 y2) (* y i)))
       (if (<= x -8e-96)
         (* y2 (* t (- (* a y5) (* c y4))))
         (if (<= x -5.2e-197)
           t_2
           (if (<= x -2e-224)
             (* (* y1 y3) (- (* z a) (* j y4)))
             (if (<= x 1.8e-130)
               t_2
               (if (<= x 2.6e+78)
                 (* y1 (* y4 (- (* k y2) (* j y3))))
                 (if (<= x 1.08e+198) t_1 (* y1 (* j (* x 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 = y2 * (y0 * ((x * c) - (k * y5)));
	double t_2 = y1 * (k * ((y2 * y4) - (z * i)));
	double tmp;
	if (x <= -1.1e+174) {
		tmp = t_1;
	} else if (x <= -3.8e+16) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (x <= -8e-96) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (x <= -5.2e-197) {
		tmp = t_2;
	} else if (x <= -2e-224) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (x <= 1.8e-130) {
		tmp = t_2;
	} else if (x <= 2.6e+78) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 1.08e+198) {
		tmp = t_1;
	} else {
		tmp = y1 * (j * (x * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y2 * (y0 * ((x * c) - (k * y5)))
    t_2 = y1 * (k * ((y2 * y4) - (z * i)))
    if (x <= (-1.1d+174)) then
        tmp = t_1
    else if (x <= (-3.8d+16)) then
        tmp = (x * c) * ((y0 * y2) - (y * i))
    else if (x <= (-8d-96)) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (x <= (-5.2d-197)) then
        tmp = t_2
    else if (x <= (-2d-224)) then
        tmp = (y1 * y3) * ((z * a) - (j * y4))
    else if (x <= 1.8d-130) then
        tmp = t_2
    else if (x <= 2.6d+78) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (x <= 1.08d+198) then
        tmp = t_1
    else
        tmp = y1 * (j * (x * 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 = y2 * (y0 * ((x * c) - (k * y5)));
	double t_2 = y1 * (k * ((y2 * y4) - (z * i)));
	double tmp;
	if (x <= -1.1e+174) {
		tmp = t_1;
	} else if (x <= -3.8e+16) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (x <= -8e-96) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (x <= -5.2e-197) {
		tmp = t_2;
	} else if (x <= -2e-224) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (x <= 1.8e-130) {
		tmp = t_2;
	} else if (x <= 2.6e+78) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 1.08e+198) {
		tmp = t_1;
	} else {
		tmp = y1 * (j * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (y0 * ((x * c) - (k * y5)))
	t_2 = y1 * (k * ((y2 * y4) - (z * i)))
	tmp = 0
	if x <= -1.1e+174:
		tmp = t_1
	elif x <= -3.8e+16:
		tmp = (x * c) * ((y0 * y2) - (y * i))
	elif x <= -8e-96:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif x <= -5.2e-197:
		tmp = t_2
	elif x <= -2e-224:
		tmp = (y1 * y3) * ((z * a) - (j * y4))
	elif x <= 1.8e-130:
		tmp = t_2
	elif x <= 2.6e+78:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif x <= 1.08e+198:
		tmp = t_1
	else:
		tmp = y1 * (j * (x * 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(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))))
	t_2 = Float64(y1 * Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))))
	tmp = 0.0
	if (x <= -1.1e+174)
		tmp = t_1;
	elseif (x <= -3.8e+16)
		tmp = Float64(Float64(x * c) * Float64(Float64(y0 * y2) - Float64(y * i)));
	elseif (x <= -8e-96)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= -5.2e-197)
		tmp = t_2;
	elseif (x <= -2e-224)
		tmp = Float64(Float64(y1 * y3) * Float64(Float64(z * a) - Float64(j * y4)));
	elseif (x <= 1.8e-130)
		tmp = t_2;
	elseif (x <= 2.6e+78)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (x <= 1.08e+198)
		tmp = t_1;
	else
		tmp = Float64(y1 * Float64(j * Float64(x * 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 = y2 * (y0 * ((x * c) - (k * y5)));
	t_2 = y1 * (k * ((y2 * y4) - (z * i)));
	tmp = 0.0;
	if (x <= -1.1e+174)
		tmp = t_1;
	elseif (x <= -3.8e+16)
		tmp = (x * c) * ((y0 * y2) - (y * i));
	elseif (x <= -8e-96)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (x <= -5.2e-197)
		tmp = t_2;
	elseif (x <= -2e-224)
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	elseif (x <= 1.8e-130)
		tmp = t_2;
	elseif (x <= 2.6e+78)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (x <= 1.08e+198)
		tmp = t_1;
	else
		tmp = y1 * (j * (x * 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[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+174], t$95$1, If[LessEqual[x, -3.8e+16], N[(N[(x * c), $MachinePrecision] * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e-96], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.2e-197], t$95$2, If[LessEqual[x, -2e-224], N[(N[(y1 * y3), $MachinePrecision] * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e-130], t$95$2, If[LessEqual[x, 2.6e+78], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.08e+198], t$95$1, N[(y1 * N[(j * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.1000000000000001e174 or 2.6e78 < x < 1.08e198

   1. Initial program 19.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 41.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in y0 around inf 55.5%

      \[\leadsto y2 \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.5%

         \[\leadsto y2 \cdot \left(y0 \cdot \color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 55.5%

         \[\leadsto y2 \cdot \left(y0 \cdot \left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right)\right) \]

      3. unsub-neg 55.5%

         \[\leadsto y2 \cdot \left(y0 \cdot \color{blue}{\left(c \cdot x - k \cdot y5\right)}\right) \]

      4. *-commutative 55.5%

         \[\leadsto y2 \cdot \left(y0 \cdot \left(\color{blue}{x \cdot c} - k \cdot y5\right)\right) \]

   5. Simplified 55.5%

      \[\leadsto y2 \cdot \color{blue}{\left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)} \]

   if -1.1000000000000001e174 < x < -3.8e16

   1. Initial program 21.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 50.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around inf 44.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 42.3%

         \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)} \]

      2. *-commutative 42.3%

         \[\leadsto \color{blue}{\left(x \cdot c\right)} \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \]

      3. +-commutative 42.3%

         \[\leadsto \left(x \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)} \]

      4. mul-1-neg 42.3%

         \[\leadsto \left(x \cdot c\right) \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right) \]

      5. unsub-neg 42.3%

         \[\leadsto \left(x \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)} \]

      6. *-commutative 42.3%

         \[\leadsto \left(x \cdot c\right) \cdot \left(\color{blue}{y2 \cdot y0} - i \cdot y\right) \]

   5. Simplified 42.3%

      \[\leadsto \color{blue}{\left(x \cdot c\right) \cdot \left(y2 \cdot y0 - i \cdot y\right)} \]

   if -3.8e16 < x < -7.9999999999999993e-96

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. 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 t around inf 43.3%

      \[\leadsto y2 \cdot \color{blue}{\left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -7.9999999999999993e-96 < x < -5.2000000000000003e-197 or -2e-224 < x < 1.8000000000000001e-130

   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 y1 around inf 45.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 45.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 45.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in k around inf 45.4%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 45.4%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      2. mul-1-neg 45.4%

         \[\leadsto y1 \cdot \left(k \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      3. unsub-neg 45.4%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)}\right) \]

   7. Simplified 45.4%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   if -5.2000000000000003e-197 < x < -2e-224

   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 42.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 42.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 42.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 42.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in y3 around inf 72.0%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) - -1 \cdot \left(a \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 58.7%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) - -1 \cdot \left(a \cdot z\right)\right)} \]

      2. cancel-sign-sub-inv 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + \left(--1\right) \cdot \left(a \cdot z\right)\right)} \]

      3. metadata-eval 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) + \color{blue}{1} \cdot \left(a \cdot z\right)\right) \]

      4. *-lft-identity 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) + \color{blue}{a \cdot z}\right) \]

      5. +-commutative 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(a \cdot z + -1 \cdot \left(j \cdot y4\right)\right)} \]

      6. mul-1-neg 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(a \cdot z + \color{blue}{\left(-j \cdot y4\right)}\right) \]

      7. unsub-neg 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(a \cdot z - j \cdot y4\right)} \]

   7. Simplified 58.7%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   if 1.8000000000000001e-130 < x < 2.6e78

   1. Initial program 48.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 34.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 34.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in y4 around inf 39.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot k} - j \cdot y3\right)\right) \]

   7. Simplified 39.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]

   if 1.08e198 < x

   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 y1 around inf 50.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.1%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 50.1%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 50.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 57.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 57.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 64.9%

      \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 64.9%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]

   10. Simplified 64.9%

       \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+174}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+16}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-96}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-197}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-224}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-130}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+78}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+198}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 20: 35.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y3 \leq -2.5 \cdot 10^{+206}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;y3 \leq -6.4:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_1\right)\\ \mathbf{elif}\;y3 \leq 38000000000:\\ \;\;\;\;y2 \cdot \left(x \cdot t_1 + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{+162}:\\ \;\;\;\;t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{+254}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1))))
   (if (<= y3 -2.5e+206)
     (* (* y1 y3) (- (* z a) (* j y4)))
     (if (<= y3 -6.4)
       (* x (+ (* y (- (* a b) (* c i))) (* y2 t_1)))
       (if (<= y3 38000000000.0)
         (* y2 (+ (* x t_1) (* t (- (* a y5) (* c y4)))))
         (if (<= y3 2.5e+162)
           (* t (* i (- (* z c) (* j y5))))
           (if (<= y3 4.5e+254)
             (* (* z y1) (- (* a y3) (* i k)))
             (* y1 (* j (- (* x i) (* y3 y4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double tmp;
	if (y3 <= -2.5e+206) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (y3 <= -6.4) {
		tmp = x * ((y * ((a * b) - (c * i))) + (y2 * t_1));
	} else if (y3 <= 38000000000.0) {
		tmp = y2 * ((x * t_1) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= 2.5e+162) {
		tmp = t * (i * ((z * c) - (j * y5)));
	} else if (y3 <= 4.5e+254) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    if (y3 <= (-2.5d+206)) then
        tmp = (y1 * y3) * ((z * a) - (j * y4))
    else if (y3 <= (-6.4d0)) then
        tmp = x * ((y * ((a * b) - (c * i))) + (y2 * t_1))
    else if (y3 <= 38000000000.0d0) then
        tmp = y2 * ((x * t_1) + (t * ((a * y5) - (c * y4))))
    else if (y3 <= 2.5d+162) then
        tmp = t * (i * ((z * c) - (j * y5)))
    else if (y3 <= 4.5d+254) then
        tmp = (z * y1) * ((a * y3) - (i * k))
    else
        tmp = y1 * (j * ((x * i) - (y3 * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double tmp;
	if (y3 <= -2.5e+206) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (y3 <= -6.4) {
		tmp = x * ((y * ((a * b) - (c * i))) + (y2 * t_1));
	} else if (y3 <= 38000000000.0) {
		tmp = y2 * ((x * t_1) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= 2.5e+162) {
		tmp = t * (i * ((z * c) - (j * y5)));
	} else if (y3 <= 4.5e+254) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	tmp = 0
	if y3 <= -2.5e+206:
		tmp = (y1 * y3) * ((z * a) - (j * y4))
	elif y3 <= -6.4:
		tmp = x * ((y * ((a * b) - (c * i))) + (y2 * t_1))
	elif y3 <= 38000000000.0:
		tmp = y2 * ((x * t_1) + (t * ((a * y5) - (c * y4))))
	elif y3 <= 2.5e+162:
		tmp = t * (i * ((z * c) - (j * y5)))
	elif y3 <= 4.5e+254:
		tmp = (z * y1) * ((a * y3) - (i * k))
	else:
		tmp = y1 * (j * ((x * i) - (y3 * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y3 <= -2.5e+206)
		tmp = Float64(Float64(y1 * y3) * Float64(Float64(z * a) - Float64(j * y4)));
	elseif (y3 <= -6.4)
		tmp = Float64(x * Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)));
	elseif (y3 <= 38000000000.0)
		tmp = Float64(y2 * Float64(Float64(x * t_1) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y3 <= 2.5e+162)
		tmp = Float64(t * Float64(i * Float64(Float64(z * c) - Float64(j * y5))));
	elseif (y3 <= 4.5e+254)
		tmp = Float64(Float64(z * y1) * Float64(Float64(a * y3) - Float64(i * k)));
	else
		tmp = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y3 <= -2.5e+206)
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	elseif (y3 <= -6.4)
		tmp = x * ((y * ((a * b) - (c * i))) + (y2 * t_1));
	elseif (y3 <= 38000000000.0)
		tmp = y2 * ((x * t_1) + (t * ((a * y5) - (c * y4))));
	elseif (y3 <= 2.5e+162)
		tmp = t * (i * ((z * c) - (j * y5)));
	elseif (y3 <= 4.5e+254)
		tmp = (z * y1) * ((a * y3) - (i * k));
	else
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.5e+206], N[(N[(y1 * y3), $MachinePrecision] * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -6.4], N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 38000000000.0], N[(y2 * N[(N[(x * t$95$1), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.5e+162], N[(t * N[(i * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.5e+254], N[(N[(z * y1), $MachinePrecision] * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y3 < -2.5000000000000001e206

   1. Initial program 5.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 45.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 45.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 45.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 45.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 45.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 45.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 45.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 45.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 45.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in y3 around inf 75.0%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) - -1 \cdot \left(a \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 70.4%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) - -1 \cdot \left(a \cdot z\right)\right)} \]

      2. cancel-sign-sub-inv 70.4%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + \left(--1\right) \cdot \left(a \cdot z\right)\right)} \]

      3. metadata-eval 70.4%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) + \color{blue}{1} \cdot \left(a \cdot z\right)\right) \]

      4. *-lft-identity 70.4%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) + \color{blue}{a \cdot z}\right) \]

      5. +-commutative 70.4%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(a \cdot z + -1 \cdot \left(j \cdot y4\right)\right)} \]

      6. mul-1-neg 70.4%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(a \cdot z + \color{blue}{\left(-j \cdot y4\right)}\right) \]

      7. unsub-neg 70.4%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(a \cdot z - j \cdot y4\right)} \]

   7. Simplified 70.4%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   if -2.5000000000000001e206 < y3 < -6.4000000000000004

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 46.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around 0 43.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   if -6.4000000000000004 < y3 < 3.8e10

   1. Initial program 40.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 47.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in k around 0 45.6%

      \[\leadsto \color{blue}{y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 3.8e10 < y3 < 2.4999999999999998e162

   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 t around inf 52.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in i around inf 41.9%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.9%

         \[\leadsto t \cdot \left(i \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 41.9%

         \[\leadsto t \cdot \left(i \cdot \left(c \cdot z + \color{blue}{\left(-j \cdot y5\right)}\right)\right) \]

      3. unsub-neg 41.9%

         \[\leadsto t \cdot \left(i \cdot \color{blue}{\left(c \cdot z - j \cdot y5\right)}\right) \]

   5. Simplified 41.9%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   if 2.4999999999999998e162 < y3 < 4.4999999999999998e254

   1. Initial program 19.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 27.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 27.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 27.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 27.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 27.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in z around inf 58.7%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(-1 \cdot \left(i \cdot k\right) - -1 \cdot \left(a \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto \color{blue}{\left(y1 \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot k\right) - -1 \cdot \left(a \cdot y3\right)\right)} \]

      2. distribute-lft-out-- 58.5%

         \[\leadsto \left(y1 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

   7. Simplified 58.5%

      \[\leadsto \color{blue}{\left(y1 \cdot z\right) \cdot \left(-1 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

   if 4.4999999999999998e254 < y3

   1. Initial program 10.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 30.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 30.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 30.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 30.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 30.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 30.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 30.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 30.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 30.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 30.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 80.0%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 80.0%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 80.0%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 80.0%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 80.0%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 80.0%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 80.0%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.5 \cdot 10^{+206}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;y3 \leq -6.4:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 38000000000:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{+162}:\\ \;\;\;\;t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{+254}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \end{array} \]

Alternative 21: 29.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ t_2 := b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-223}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+75}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (- (* x j) (* z k)) y1)))
        (t_2 (* b (* y0 (- (* z k) (* x j))))))
   (if (<= b -1.15e+160)
     t_2
     (if (<= b -1.35e+90)
       (* t (* i (- (* z c) (* j y5))))
       (if (<= b -5e+23)
         t_2
         (if (<= b -1.4e-89)
           t_1
           (if (<= b -2.1e-223)
             (* y1 (* j (* y4 (- y3))))
             (if (<= b 8.5e-156)
               t_1
               (if (<= b 2e+75)
                 (* c (* y2 (- (* x y0) (* t y4))))
                 (* b (* j (- (* t y4) (* x y0)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (((x * j) - (z * k)) * y1);
	double t_2 = b * (y0 * ((z * k) - (x * j)));
	double tmp;
	if (b <= -1.15e+160) {
		tmp = t_2;
	} else if (b <= -1.35e+90) {
		tmp = t * (i * ((z * c) - (j * y5)));
	} else if (b <= -5e+23) {
		tmp = t_2;
	} else if (b <= -1.4e-89) {
		tmp = t_1;
	} else if (b <= -2.1e-223) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (b <= 8.5e-156) {
		tmp = t_1;
	} else if (b <= 2e+75) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (((x * j) - (z * k)) * y1)
    t_2 = b * (y0 * ((z * k) - (x * j)))
    if (b <= (-1.15d+160)) then
        tmp = t_2
    else if (b <= (-1.35d+90)) then
        tmp = t * (i * ((z * c) - (j * y5)))
    else if (b <= (-5d+23)) then
        tmp = t_2
    else if (b <= (-1.4d-89)) then
        tmp = t_1
    else if (b <= (-2.1d-223)) then
        tmp = y1 * (j * (y4 * -y3))
    else if (b <= 8.5d-156) then
        tmp = t_1
    else if (b <= 2d+75) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (((x * j) - (z * k)) * y1);
	double t_2 = b * (y0 * ((z * k) - (x * j)));
	double tmp;
	if (b <= -1.15e+160) {
		tmp = t_2;
	} else if (b <= -1.35e+90) {
		tmp = t * (i * ((z * c) - (j * y5)));
	} else if (b <= -5e+23) {
		tmp = t_2;
	} else if (b <= -1.4e-89) {
		tmp = t_1;
	} else if (b <= -2.1e-223) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (b <= 8.5e-156) {
		tmp = t_1;
	} else if (b <= 2e+75) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (((x * j) - (z * k)) * y1)
	t_2 = b * (y0 * ((z * k) - (x * j)))
	tmp = 0
	if b <= -1.15e+160:
		tmp = t_2
	elif b <= -1.35e+90:
		tmp = t * (i * ((z * c) - (j * y5)))
	elif b <= -5e+23:
		tmp = t_2
	elif b <= -1.4e-89:
		tmp = t_1
	elif b <= -2.1e-223:
		tmp = y1 * (j * (y4 * -y3))
	elif b <= 8.5e-156:
		tmp = t_1
	elif b <= 2e+75:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(Float64(Float64(x * j) - Float64(z * k)) * y1))
	t_2 = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (b <= -1.15e+160)
		tmp = t_2;
	elseif (b <= -1.35e+90)
		tmp = Float64(t * Float64(i * Float64(Float64(z * c) - Float64(j * y5))));
	elseif (b <= -5e+23)
		tmp = t_2;
	elseif (b <= -1.4e-89)
		tmp = t_1;
	elseif (b <= -2.1e-223)
		tmp = Float64(y1 * Float64(j * Float64(y4 * Float64(-y3))));
	elseif (b <= 8.5e-156)
		tmp = t_1;
	elseif (b <= 2e+75)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (((x * j) - (z * k)) * y1);
	t_2 = b * (y0 * ((z * k) - (x * j)));
	tmp = 0.0;
	if (b <= -1.15e+160)
		tmp = t_2;
	elseif (b <= -1.35e+90)
		tmp = t * (i * ((z * c) - (j * y5)));
	elseif (b <= -5e+23)
		tmp = t_2;
	elseif (b <= -1.4e-89)
		tmp = t_1;
	elseif (b <= -2.1e-223)
		tmp = y1 * (j * (y4 * -y3));
	elseif (b <= 8.5e-156)
		tmp = t_1;
	elseif (b <= 2e+75)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+160], t$95$2, If[LessEqual[b, -1.35e+90], N[(t * N[(i * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5e+23], t$95$2, If[LessEqual[b, -1.4e-89], t$95$1, If[LessEqual[b, -2.1e-223], N[(y1 * N[(j * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-156], t$95$1, If[LessEqual[b, 2e+75], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.14999999999999994e160 or -1.35e90 < b < -4.9999999999999999e23

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 60.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y0 around inf 55.0%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 55.0%

         \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - \color{blue}{x \cdot j}\right)\right) \]

   5. Simplified 55.0%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - x \cdot j\right)\right)} \]

   if -1.14999999999999994e160 < b < -1.35e90

   1. Initial program 8.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in t around inf 33.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in i around inf 67.4%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 67.4%

         \[\leadsto t \cdot \left(i \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 67.4%

         \[\leadsto t \cdot \left(i \cdot \left(c \cdot z + \color{blue}{\left(-j \cdot y5\right)}\right)\right) \]

      3. unsub-neg 67.4%

         \[\leadsto t \cdot \left(i \cdot \color{blue}{\left(c \cdot z - j \cdot y5\right)}\right) \]

   5. Simplified 67.4%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   if -4.9999999999999999e23 < b < -1.3999999999999999e-89 or -2.09999999999999982e-223 < b < 8.5e-156

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 46.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 46.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 46.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in i around inf 42.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.0%

         \[\leadsto i \cdot \left(y1 \cdot \left(\color{blue}{x \cdot j} - k \cdot z\right)\right) \]

   7. Simplified 42.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(x \cdot j - k \cdot z\right)\right)} \]

   if -1.3999999999999999e-89 < b < -2.09999999999999982e-223

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 36.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 36.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 36.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 52.1%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 52.1%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 52.1%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 52.1%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 52.1%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 52.1%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 52.1%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around 0 46.2%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 46.2%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 46.2%

         \[\leadsto y1 \cdot \left(-j \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

      3. distribute-rgt-neg-in 46.2%

         \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-y4 \cdot y3\right)\right)} \]

      4. distribute-rgt-neg-in 46.2%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(y4 \cdot \left(-y3\right)\right)}\right) \]

   10. Simplified 46.2%

       \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)} \]

   if 8.5e-156 < b < 1.99999999999999985e75

   1. Initial program 40.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 45.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 33.6%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if 1.99999999999999985e75 < b

   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 b around inf 47.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 45.2%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 45.2%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+160}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-89}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-223}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+75}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

Alternative 22: 30.2% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{if}\;y0 \leq -7 \cdot 10^{+190}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -4.5 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -1.95 \cdot 10^{-159}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{-76}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 3.4 \cdot 10^{-66}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (- (* x j) (* z k)) y1))))
   (if (<= y0 -7e+190)
     (* b (* x (- (* y a) (* j y0))))
     (if (<= y0 -4.5e+39)
       t_1
       (if (<= y0 -1.95e-159)
         (* y1 (* a (- (* z y3) (* x y2))))
         (if (<= y0 6e-205)
           t_1
           (if (<= y0 1.4e-76)
             (* t (* y4 (- (* b j) (* c y2))))
             (if (<= y0 3.4e-66)
               (* y1 (* i (* z (- k))))
               (if (<= y0 4.8e+144)
                 (* x (* y (- (* a b) (* c i))))
                 (* b (* y0 (- (* z k) (* x j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (((x * j) - (z * k)) * y1);
	double tmp;
	if (y0 <= -7e+190) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y0 <= -4.5e+39) {
		tmp = t_1;
	} else if (y0 <= -1.95e-159) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= 6e-205) {
		tmp = t_1;
	} else if (y0 <= 1.4e-76) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y0 <= 3.4e-66) {
		tmp = y1 * (i * (z * -k));
	} else if (y0 <= 4.8e+144) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (((x * j) - (z * k)) * y1)
    if (y0 <= (-7d+190)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y0 <= (-4.5d+39)) then
        tmp = t_1
    else if (y0 <= (-1.95d-159)) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (y0 <= 6d-205) then
        tmp = t_1
    else if (y0 <= 1.4d-76) then
        tmp = t * (y4 * ((b * j) - (c * y2)))
    else if (y0 <= 3.4d-66) then
        tmp = y1 * (i * (z * -k))
    else if (y0 <= 4.8d+144) then
        tmp = x * (y * ((a * b) - (c * i)))
    else
        tmp = b * (y0 * ((z * k) - (x * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (((x * j) - (z * k)) * y1);
	double tmp;
	if (y0 <= -7e+190) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y0 <= -4.5e+39) {
		tmp = t_1;
	} else if (y0 <= -1.95e-159) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= 6e-205) {
		tmp = t_1;
	} else if (y0 <= 1.4e-76) {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	} else if (y0 <= 3.4e-66) {
		tmp = y1 * (i * (z * -k));
	} else if (y0 <= 4.8e+144) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (((x * j) - (z * k)) * y1)
	tmp = 0
	if y0 <= -7e+190:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y0 <= -4.5e+39:
		tmp = t_1
	elif y0 <= -1.95e-159:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif y0 <= 6e-205:
		tmp = t_1
	elif y0 <= 1.4e-76:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	elif y0 <= 3.4e-66:
		tmp = y1 * (i * (z * -k))
	elif y0 <= 4.8e+144:
		tmp = x * (y * ((a * b) - (c * i)))
	else:
		tmp = b * (y0 * ((z * k) - (x * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(Float64(Float64(x * j) - Float64(z * k)) * y1))
	tmp = 0.0
	if (y0 <= -7e+190)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y0 <= -4.5e+39)
		tmp = t_1;
	elseif (y0 <= -1.95e-159)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y0 <= 6e-205)
		tmp = t_1;
	elseif (y0 <= 1.4e-76)
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y0 <= 3.4e-66)
		tmp = Float64(y1 * Float64(i * Float64(z * Float64(-k))));
	elseif (y0 <= 4.8e+144)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	else
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (((x * j) - (z * k)) * y1);
	tmp = 0.0;
	if (y0 <= -7e+190)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y0 <= -4.5e+39)
		tmp = t_1;
	elseif (y0 <= -1.95e-159)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (y0 <= 6e-205)
		tmp = t_1;
	elseif (y0 <= 1.4e-76)
		tmp = t * (y4 * ((b * j) - (c * y2)));
	elseif (y0 <= 3.4e-66)
		tmp = y1 * (i * (z * -k));
	elseif (y0 <= 4.8e+144)
		tmp = x * (y * ((a * b) - (c * i)));
	else
		tmp = b * (y0 * ((z * k) - (x * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -7e+190], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4.5e+39], t$95$1, If[LessEqual[y0, -1.95e-159], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6e-205], t$95$1, If[LessEqual[y0, 1.4e-76], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.4e-66], N[(y1 * N[(i * N[(z * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.8e+144], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -6.9999999999999997e190

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 19.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in x around inf 52.4%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.4%

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{y0 \cdot j}\right)\right) \]

   5. Simplified 52.4%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   if -6.9999999999999997e190 < y0 < -4.49999999999999996e39 or -1.94999999999999988e-159 < y0 < 6e-205

   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 y1 around inf 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 39.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 39.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in i around inf 42.5%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.5%

         \[\leadsto i \cdot \left(y1 \cdot \left(\color{blue}{x \cdot j} - k \cdot z\right)\right) \]

   7. Simplified 42.5%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(x \cdot j - k \cdot z\right)\right)} \]

   if -4.49999999999999996e39 < y0 < -1.94999999999999988e-159

   1. Initial program 30.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 49.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 49.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 49.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 49.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 49.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in a around inf 42.2%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.2%

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{z \cdot y3} - x \cdot y2\right)\right) \]

   7. Simplified 42.2%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)} \]

   if 6e-205 < y0 < 1.40000000000000005e-76

   1. Initial program 52.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in t around inf 40.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in y4 around inf 40.4%

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 40.4%

         \[\leadsto t \cdot \left(y4 \cdot \left(\color{blue}{j \cdot b} - c \cdot y2\right)\right) \]

      2. *-commutative 40.4%

         \[\leadsto t \cdot \left(y4 \cdot \left(j \cdot b - \color{blue}{y2 \cdot c}\right)\right) \]

   5. Simplified 40.4%

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(j \cdot b - y2 \cdot c\right)\right)} \]

   if 1.40000000000000005e-76 < y0 < 3.39999999999999997e-66

   1. Initial program 51.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 34.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 34.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 34.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 34.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 34.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 34.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 34.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 34.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 34.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 34.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in k around inf 33.9%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 33.9%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      2. mul-1-neg 33.9%

         \[\leadsto y1 \cdot \left(k \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      3. unsub-neg 33.9%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)}\right) \]

   7. Simplified 33.9%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   8. Taylor expanded in y2 around 0 50.5%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(k \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 50.5%

         \[\leadsto y1 \cdot \color{blue}{\left(-i \cdot \left(k \cdot z\right)\right)} \]

      2. *-commutative 50.5%

         \[\leadsto y1 \cdot \left(-\color{blue}{\left(k \cdot z\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in 50.5%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot z\right) \cdot \left(-i\right)\right)} \]

   10. Simplified 50.5%

       \[\leadsto y1 \cdot \color{blue}{\left(\left(k \cdot z\right) \cdot \left(-i\right)\right)} \]

   if 3.39999999999999997e-66 < y0 < 4.8000000000000001e144

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 54.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if 4.8000000000000001e144 < y0

   1. Initial program 20.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 49.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y0 around inf 49.7%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.7%

         \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - \color{blue}{x \cdot j}\right)\right) \]

   5. Simplified 49.7%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - x \cdot j\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -7 \cdot 10^{+190}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -4.5 \cdot 10^{+39}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{elif}\;y0 \leq -1.95 \cdot 10^{-159}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{-205}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{-76}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 3.4 \cdot 10^{-66}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 23: 29.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{if}\;y0 \leq -1.05 \cdot 10^{+193}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.4 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -5.6 \cdot 10^{-105}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -3.2 \cdot 10^{-193}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;y0 \leq -9.5 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-138}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (- (* x j) (* z k)) y1))))
   (if (<= y0 -1.05e+193)
     (* b (* x (- (* y a) (* j y0))))
     (if (<= y0 -1.4e+28)
       t_1
       (if (<= y0 -5.6e-105)
         (* y1 (* a (- (* z y3) (* x y2))))
         (if (<= y0 -3.2e-193)
           (* b (* t (- (* j y4) (* z a))))
           (if (<= y0 -9.5e-297)
             t_1
             (if (<= y0 1.65e-138)
               (* y1 (* j (- (* x i) (* y3 y4))))
               (if (<= y0 7.5e+144)
                 (* x (* y (- (* a b) (* c i))))
                 (* b (* y0 (- (* z k) (* x j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (((x * j) - (z * k)) * y1);
	double tmp;
	if (y0 <= -1.05e+193) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y0 <= -1.4e+28) {
		tmp = t_1;
	} else if (y0 <= -5.6e-105) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= -3.2e-193) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (y0 <= -9.5e-297) {
		tmp = t_1;
	} else if (y0 <= 1.65e-138) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y0 <= 7.5e+144) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (((x * j) - (z * k)) * y1)
    if (y0 <= (-1.05d+193)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y0 <= (-1.4d+28)) then
        tmp = t_1
    else if (y0 <= (-5.6d-105)) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (y0 <= (-3.2d-193)) then
        tmp = b * (t * ((j * y4) - (z * a)))
    else if (y0 <= (-9.5d-297)) then
        tmp = t_1
    else if (y0 <= 1.65d-138) then
        tmp = y1 * (j * ((x * i) - (y3 * y4)))
    else if (y0 <= 7.5d+144) then
        tmp = x * (y * ((a * b) - (c * i)))
    else
        tmp = b * (y0 * ((z * k) - (x * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (((x * j) - (z * k)) * y1);
	double tmp;
	if (y0 <= -1.05e+193) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y0 <= -1.4e+28) {
		tmp = t_1;
	} else if (y0 <= -5.6e-105) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= -3.2e-193) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (y0 <= -9.5e-297) {
		tmp = t_1;
	} else if (y0 <= 1.65e-138) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y0 <= 7.5e+144) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else {
		tmp = b * (y0 * ((z * k) - (x * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (((x * j) - (z * k)) * y1)
	tmp = 0
	if y0 <= -1.05e+193:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y0 <= -1.4e+28:
		tmp = t_1
	elif y0 <= -5.6e-105:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif y0 <= -3.2e-193:
		tmp = b * (t * ((j * y4) - (z * a)))
	elif y0 <= -9.5e-297:
		tmp = t_1
	elif y0 <= 1.65e-138:
		tmp = y1 * (j * ((x * i) - (y3 * y4)))
	elif y0 <= 7.5e+144:
		tmp = x * (y * ((a * b) - (c * i)))
	else:
		tmp = b * (y0 * ((z * k) - (x * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(Float64(Float64(x * j) - Float64(z * k)) * y1))
	tmp = 0.0
	if (y0 <= -1.05e+193)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y0 <= -1.4e+28)
		tmp = t_1;
	elseif (y0 <= -5.6e-105)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y0 <= -3.2e-193)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (y0 <= -9.5e-297)
		tmp = t_1;
	elseif (y0 <= 1.65e-138)
		tmp = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y0 <= 7.5e+144)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	else
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (((x * j) - (z * k)) * y1);
	tmp = 0.0;
	if (y0 <= -1.05e+193)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y0 <= -1.4e+28)
		tmp = t_1;
	elseif (y0 <= -5.6e-105)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (y0 <= -3.2e-193)
		tmp = b * (t * ((j * y4) - (z * a)));
	elseif (y0 <= -9.5e-297)
		tmp = t_1;
	elseif (y0 <= 1.65e-138)
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	elseif (y0 <= 7.5e+144)
		tmp = x * (y * ((a * b) - (c * i)));
	else
		tmp = b * (y0 * ((z * k) - (x * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.05e+193], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.4e+28], t$95$1, If[LessEqual[y0, -5.6e-105], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.2e-193], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -9.5e-297], t$95$1, If[LessEqual[y0, 1.65e-138], N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7.5e+144], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -1.05e193

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 19.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in x around inf 52.4%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.4%

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{y0 \cdot j}\right)\right) \]

   5. Simplified 52.4%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   if -1.05e193 < y0 < -1.4000000000000001e28 or -3.20000000000000006e-193 < y0 < -9.5000000000000005e-297

   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 y1 around inf 41.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 41.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 41.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 41.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in i around inf 54.2%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto i \cdot \left(y1 \cdot \left(\color{blue}{x \cdot j} - k \cdot z\right)\right) \]

   7. Simplified 54.2%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(x \cdot j - k \cdot z\right)\right)} \]

   if -1.4000000000000001e28 < y0 < -5.6e-105

   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 58.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 58.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 58.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 58.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in a around inf 51.0%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{z \cdot y3} - x \cdot y2\right)\right) \]

   7. Simplified 51.0%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)} \]

   if -5.6e-105 < y0 < -3.20000000000000006e-193

   1. Initial program 39.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 27.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in t around inf 41.2%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.2%

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      2. mul-1-neg 41.2%

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right)\right) \]

      3. sub-neg 41.2%

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

   5. Simplified 41.2%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   if -9.5000000000000005e-297 < y0 < 1.64999999999999991e-138

   1. Initial program 43.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 46.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 46.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 46.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 41.9%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.9%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 41.9%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 41.9%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 41.9%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   if 1.64999999999999991e-138 < y0 < 7.5000000000000006e144

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 47.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in y around inf 39.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if 7.5000000000000006e144 < y0

   1. Initial program 20.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 49.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y0 around inf 49.7%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.7%

         \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - \color{blue}{x \cdot j}\right)\right) \]

   5. Simplified 49.7%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - x \cdot j\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.05 \cdot 10^{+193}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.4 \cdot 10^{+28}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{elif}\;y0 \leq -5.6 \cdot 10^{-105}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -3.2 \cdot 10^{-193}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;y0 \leq -9.5 \cdot 10^{-297}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-138}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 24: 29.2% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{if}\;y0 \leq -3.7 \cdot 10^{+189}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -9.2 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{-101}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.12 \cdot 10^{-192}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;y0 \leq -1.2 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 3.4 \cdot 10^{-139}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.6 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (- (* x j) (* z k)) y1))))
   (if (<= y0 -3.7e+189)
     (* b (* x (- (* y a) (* j y0))))
     (if (<= y0 -9.2e+34)
       t_1
       (if (<= y0 -1.15e-101)
         (* y1 (* a (- (* z y3) (* x y2))))
         (if (<= y0 -1.12e-192)
           (* b (* t (- (* j y4) (* z a))))
           (if (<= y0 -1.2e-296)
             t_1
             (if (<= y0 3.4e-139)
               (* y1 (* j (- (* x i) (* y3 y4))))
               (if (<= y0 4.6e+185)
                 (* x (* y (- (* a b) (* c i))))
                 (* y2 (* y0 (- (* x c) (* k 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 * (((x * j) - (z * k)) * y1);
	double tmp;
	if (y0 <= -3.7e+189) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y0 <= -9.2e+34) {
		tmp = t_1;
	} else if (y0 <= -1.15e-101) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= -1.12e-192) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (y0 <= -1.2e-296) {
		tmp = t_1;
	} else if (y0 <= 3.4e-139) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y0 <= 4.6e+185) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else {
		tmp = y2 * (y0 * ((x * c) - (k * 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 * (((x * j) - (z * k)) * y1)
    if (y0 <= (-3.7d+189)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y0 <= (-9.2d+34)) then
        tmp = t_1
    else if (y0 <= (-1.15d-101)) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (y0 <= (-1.12d-192)) then
        tmp = b * (t * ((j * y4) - (z * a)))
    else if (y0 <= (-1.2d-296)) then
        tmp = t_1
    else if (y0 <= 3.4d-139) then
        tmp = y1 * (j * ((x * i) - (y3 * y4)))
    else if (y0 <= 4.6d+185) then
        tmp = x * (y * ((a * b) - (c * i)))
    else
        tmp = y2 * (y0 * ((x * c) - (k * 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 * (((x * j) - (z * k)) * y1);
	double tmp;
	if (y0 <= -3.7e+189) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y0 <= -9.2e+34) {
		tmp = t_1;
	} else if (y0 <= -1.15e-101) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= -1.12e-192) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (y0 <= -1.2e-296) {
		tmp = t_1;
	} else if (y0 <= 3.4e-139) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y0 <= 4.6e+185) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else {
		tmp = y2 * (y0 * ((x * c) - (k * 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 * (((x * j) - (z * k)) * y1)
	tmp = 0
	if y0 <= -3.7e+189:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y0 <= -9.2e+34:
		tmp = t_1
	elif y0 <= -1.15e-101:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif y0 <= -1.12e-192:
		tmp = b * (t * ((j * y4) - (z * a)))
	elif y0 <= -1.2e-296:
		tmp = t_1
	elif y0 <= 3.4e-139:
		tmp = y1 * (j * ((x * i) - (y3 * y4)))
	elif y0 <= 4.6e+185:
		tmp = x * (y * ((a * b) - (c * i)))
	else:
		tmp = y2 * (y0 * ((x * c) - (k * 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(Float64(Float64(x * j) - Float64(z * k)) * y1))
	tmp = 0.0
	if (y0 <= -3.7e+189)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y0 <= -9.2e+34)
		tmp = t_1;
	elseif (y0 <= -1.15e-101)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y0 <= -1.12e-192)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (y0 <= -1.2e-296)
		tmp = t_1;
	elseif (y0 <= 3.4e-139)
		tmp = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y0 <= 4.6e+185)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	else
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * 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 * (((x * j) - (z * k)) * y1);
	tmp = 0.0;
	if (y0 <= -3.7e+189)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y0 <= -9.2e+34)
		tmp = t_1;
	elseif (y0 <= -1.15e-101)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (y0 <= -1.12e-192)
		tmp = b * (t * ((j * y4) - (z * a)));
	elseif (y0 <= -1.2e-296)
		tmp = t_1;
	elseif (y0 <= 3.4e-139)
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	elseif (y0 <= 4.6e+185)
		tmp = x * (y * ((a * b) - (c * i)));
	else
		tmp = y2 * (y0 * ((x * c) - (k * 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[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.7e+189], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -9.2e+34], t$95$1, If[LessEqual[y0, -1.15e-101], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.12e-192], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.2e-296], t$95$1, If[LessEqual[y0, 3.4e-139], N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.6e+185], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -3.70000000000000021e189

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 19.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in x around inf 52.4%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.4%

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{y0 \cdot j}\right)\right) \]

   5. Simplified 52.4%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   if -3.70000000000000021e189 < y0 < -9.1999999999999993e34 or -1.1200000000000001e-192 < y0 < -1.19999999999999998e-296

   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 y1 around inf 41.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 41.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 41.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 41.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in i around inf 54.2%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto i \cdot \left(y1 \cdot \left(\color{blue}{x \cdot j} - k \cdot z\right)\right) \]

   7. Simplified 54.2%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(x \cdot j - k \cdot z\right)\right)} \]

   if -9.1999999999999993e34 < y0 < -1.15e-101

   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 58.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 58.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 58.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 58.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 58.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in a around inf 51.0%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{z \cdot y3} - x \cdot y2\right)\right) \]

   7. Simplified 51.0%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)} \]

   if -1.15e-101 < y0 < -1.1200000000000001e-192

   1. Initial program 39.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 27.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in t around inf 41.2%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.2%

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      2. mul-1-neg 41.2%

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right)\right) \]

      3. sub-neg 41.2%

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

   5. Simplified 41.2%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   if -1.19999999999999998e-296 < y0 < 3.39999999999999999e-139

   1. Initial program 43.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 46.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 46.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 46.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 41.9%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.9%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 41.9%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 41.9%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 41.9%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 41.9%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   if 3.39999999999999999e-139 < y0 < 4.6000000000000003e185

   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 x around inf 44.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in y around inf 39.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if 4.6000000000000003e185 < y0

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 33.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in y0 around inf 55.9%

      \[\leadsto y2 \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.9%

         \[\leadsto y2 \cdot \left(y0 \cdot \color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 55.9%

         \[\leadsto y2 \cdot \left(y0 \cdot \left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right)\right) \]

      3. unsub-neg 55.9%

         \[\leadsto y2 \cdot \left(y0 \cdot \color{blue}{\left(c \cdot x - k \cdot y5\right)}\right) \]

      4. *-commutative 55.9%

         \[\leadsto y2 \cdot \left(y0 \cdot \left(\color{blue}{x \cdot c} - k \cdot y5\right)\right) \]

   5. Simplified 55.9%

      \[\leadsto y2 \cdot \color{blue}{\left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.7 \cdot 10^{+189}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -9.2 \cdot 10^{+34}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{-101}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.12 \cdot 10^{-192}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;y0 \leq -1.2 \cdot 10^{-296}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{elif}\;y0 \leq 3.4 \cdot 10^{-139}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.6 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \end{array} \]

Alternative 25: 30.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+17}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-97}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-224}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+78}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+199}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* k (- (* y2 y4) (* z i))))))
   (if (<= x -8.5e+17)
     (* c (* x (- (* y0 y2) (* y i))))
     (if (<= x -9.5e-97)
       (* y2 (* t (- (* a y5) (* c y4))))
       (if (<= x -4.6e-198)
         t_1
         (if (<= x -1.8e-224)
           (* (* y1 y3) (- (* z a) (* j y4)))
           (if (<= x 1.95e-134)
             t_1
             (if (<= x 3.5e+78)
               (* y1 (* y4 (- (* k y2) (* j y3))))
               (if (<= x 2.1e+199)
                 (* y2 (* y0 (- (* x c) (* k y5))))
                 (* y1 (* j (* x 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 = y1 * (k * ((y2 * y4) - (z * i)));
	double tmp;
	if (x <= -8.5e+17) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (x <= -9.5e-97) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (x <= -4.6e-198) {
		tmp = t_1;
	} else if (x <= -1.8e-224) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (x <= 1.95e-134) {
		tmp = t_1;
	} else if (x <= 3.5e+78) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 2.1e+199) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = y1 * (j * (x * 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 = y1 * (k * ((y2 * y4) - (z * i)))
    if (x <= (-8.5d+17)) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (x <= (-9.5d-97)) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (x <= (-4.6d-198)) then
        tmp = t_1
    else if (x <= (-1.8d-224)) then
        tmp = (y1 * y3) * ((z * a) - (j * y4))
    else if (x <= 1.95d-134) then
        tmp = t_1
    else if (x <= 3.5d+78) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (x <= 2.1d+199) then
        tmp = y2 * (y0 * ((x * c) - (k * y5)))
    else
        tmp = y1 * (j * (x * 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 = y1 * (k * ((y2 * y4) - (z * i)));
	double tmp;
	if (x <= -8.5e+17) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (x <= -9.5e-97) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (x <= -4.6e-198) {
		tmp = t_1;
	} else if (x <= -1.8e-224) {
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	} else if (x <= 1.95e-134) {
		tmp = t_1;
	} else if (x <= 3.5e+78) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 2.1e+199) {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	} else {
		tmp = y1 * (j * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (k * ((y2 * y4) - (z * i)))
	tmp = 0
	if x <= -8.5e+17:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif x <= -9.5e-97:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif x <= -4.6e-198:
		tmp = t_1
	elif x <= -1.8e-224:
		tmp = (y1 * y3) * ((z * a) - (j * y4))
	elif x <= 1.95e-134:
		tmp = t_1
	elif x <= 3.5e+78:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif x <= 2.1e+199:
		tmp = y2 * (y0 * ((x * c) - (k * y5)))
	else:
		tmp = y1 * (j * (x * 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(y1 * Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))))
	tmp = 0.0
	if (x <= -8.5e+17)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (x <= -9.5e-97)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= -4.6e-198)
		tmp = t_1;
	elseif (x <= -1.8e-224)
		tmp = Float64(Float64(y1 * y3) * Float64(Float64(z * a) - Float64(j * y4)));
	elseif (x <= 1.95e-134)
		tmp = t_1;
	elseif (x <= 3.5e+78)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (x <= 2.1e+199)
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(y1 * Float64(j * Float64(x * 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 = y1 * (k * ((y2 * y4) - (z * i)));
	tmp = 0.0;
	if (x <= -8.5e+17)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (x <= -9.5e-97)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (x <= -4.6e-198)
		tmp = t_1;
	elseif (x <= -1.8e-224)
		tmp = (y1 * y3) * ((z * a) - (j * y4));
	elseif (x <= 1.95e-134)
		tmp = t_1;
	elseif (x <= 3.5e+78)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (x <= 2.1e+199)
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	else
		tmp = y1 * (j * (x * 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[(y1 * N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e+17], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.5e-97], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.6e-198], t$95$1, If[LessEqual[x, -1.8e-224], N[(N[(y1 * y3), $MachinePrecision] * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e-134], t$95$1, If[LessEqual[x, 3.5e+78], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+199], N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(j * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -8.5e17

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 54.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 47.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 47.8%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 47.8%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 47.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 47.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 47.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 47.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 47.8%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   if -8.5e17 < x < -9.5000000000000001e-97

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. 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 t around inf 43.3%

      \[\leadsto y2 \cdot \color{blue}{\left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -9.5000000000000001e-97 < x < -4.60000000000000027e-198 or -1.8e-224 < x < 1.95e-134

   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 y1 around inf 45.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 45.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 45.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 45.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in k around inf 45.4%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 45.4%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      2. mul-1-neg 45.4%

         \[\leadsto y1 \cdot \left(k \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      3. unsub-neg 45.4%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)}\right) \]

   7. Simplified 45.4%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   if -4.60000000000000027e-198 < x < -1.8e-224

   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 42.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 42.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 42.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 42.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 42.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in y3 around inf 72.0%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) - -1 \cdot \left(a \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 58.7%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) - -1 \cdot \left(a \cdot z\right)\right)} \]

      2. cancel-sign-sub-inv 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + \left(--1\right) \cdot \left(a \cdot z\right)\right)} \]

      3. metadata-eval 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) + \color{blue}{1} \cdot \left(a \cdot z\right)\right) \]

      4. *-lft-identity 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(-1 \cdot \left(j \cdot y4\right) + \color{blue}{a \cdot z}\right) \]

      5. +-commutative 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(a \cdot z + -1 \cdot \left(j \cdot y4\right)\right)} \]

      6. mul-1-neg 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(a \cdot z + \color{blue}{\left(-j \cdot y4\right)}\right) \]

      7. unsub-neg 58.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(a \cdot z - j \cdot y4\right)} \]

   7. Simplified 58.7%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   if 1.95e-134 < x < 3.5000000000000001e78

   1. Initial program 48.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 34.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 34.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in y4 around inf 39.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot k} - j \cdot y3\right)\right) \]

   7. Simplified 39.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]

   if 3.5000000000000001e78 < x < 2.1e199

   1. Initial program 14.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 32.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in y0 around inf 51.1%

      \[\leadsto y2 \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto y2 \cdot \left(y0 \cdot \color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 51.1%

         \[\leadsto y2 \cdot \left(y0 \cdot \left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right)\right) \]

      3. unsub-neg 51.1%

         \[\leadsto y2 \cdot \left(y0 \cdot \color{blue}{\left(c \cdot x - k \cdot y5\right)}\right) \]

      4. *-commutative 51.1%

         \[\leadsto y2 \cdot \left(y0 \cdot \left(\color{blue}{x \cdot c} - k \cdot y5\right)\right) \]

   5. Simplified 51.1%

      \[\leadsto y2 \cdot \color{blue}{\left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)} \]

   if 2.1e199 < x

   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 y1 around inf 50.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.1%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 50.1%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 50.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 57.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 57.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 64.9%

      \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 64.9%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]

   10. Simplified 64.9%

       \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+17}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-97}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-198}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-224}:\\ \;\;\;\;\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-134}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+78}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+199}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 26: 25.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+95}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -21000000000000:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y1 \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-199}:\\ \;\;\;\;i \cdot \left(x \cdot \left(c \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+292}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0))))))
   (if (<= j -2.5e+162)
     t_1
     (if (<= j -3.2e+95)
       (* i (* j (* x y1)))
       (if (<= j -21000000000000.0)
         (* (* y3 y4) (* y1 (- j)))
         (if (<= j -3.1e-199)
           (* i (* x (* c (- y))))
           (if (<= j 5.5e-76)
             (* c (* x (* y0 y2)))
             (if (<= j 2.4e+229)
               t_1
               (if (<= j 3.9e+292)
                 (* y1 (* j (* y4 (- y3))))
                 (* i (* (* x j) 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 * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (j <= -2.5e+162) {
		tmp = t_1;
	} else if (j <= -3.2e+95) {
		tmp = i * (j * (x * y1));
	} else if (j <= -21000000000000.0) {
		tmp = (y3 * y4) * (y1 * -j);
	} else if (j <= -3.1e-199) {
		tmp = i * (x * (c * -y));
	} else if (j <= 5.5e-76) {
		tmp = c * (x * (y0 * y2));
	} else if (j <= 2.4e+229) {
		tmp = t_1;
	} else if (j <= 3.9e+292) {
		tmp = y1 * (j * (y4 * -y3));
	} else {
		tmp = i * ((x * j) * y1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (j * ((t * y4) - (x * y0)))
    if (j <= (-2.5d+162)) then
        tmp = t_1
    else if (j <= (-3.2d+95)) then
        tmp = i * (j * (x * y1))
    else if (j <= (-21000000000000.0d0)) then
        tmp = (y3 * y4) * (y1 * -j)
    else if (j <= (-3.1d-199)) then
        tmp = i * (x * (c * -y))
    else if (j <= 5.5d-76) then
        tmp = c * (x * (y0 * y2))
    else if (j <= 2.4d+229) then
        tmp = t_1
    else if (j <= 3.9d+292) then
        tmp = y1 * (j * (y4 * -y3))
    else
        tmp = i * ((x * j) * 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 * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (j <= -2.5e+162) {
		tmp = t_1;
	} else if (j <= -3.2e+95) {
		tmp = i * (j * (x * y1));
	} else if (j <= -21000000000000.0) {
		tmp = (y3 * y4) * (y1 * -j);
	} else if (j <= -3.1e-199) {
		tmp = i * (x * (c * -y));
	} else if (j <= 5.5e-76) {
		tmp = c * (x * (y0 * y2));
	} else if (j <= 2.4e+229) {
		tmp = t_1;
	} else if (j <= 3.9e+292) {
		tmp = y1 * (j * (y4 * -y3));
	} else {
		tmp = i * ((x * j) * 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 * (j * ((t * y4) - (x * y0)))
	tmp = 0
	if j <= -2.5e+162:
		tmp = t_1
	elif j <= -3.2e+95:
		tmp = i * (j * (x * y1))
	elif j <= -21000000000000.0:
		tmp = (y3 * y4) * (y1 * -j)
	elif j <= -3.1e-199:
		tmp = i * (x * (c * -y))
	elif j <= 5.5e-76:
		tmp = c * (x * (y0 * y2))
	elif j <= 2.4e+229:
		tmp = t_1
	elif j <= 3.9e+292:
		tmp = y1 * (j * (y4 * -y3))
	else:
		tmp = i * ((x * j) * y1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (j <= -2.5e+162)
		tmp = t_1;
	elseif (j <= -3.2e+95)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (j <= -21000000000000.0)
		tmp = Float64(Float64(y3 * y4) * Float64(y1 * Float64(-j)));
	elseif (j <= -3.1e-199)
		tmp = Float64(i * Float64(x * Float64(c * Float64(-y))));
	elseif (j <= 5.5e-76)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (j <= 2.4e+229)
		tmp = t_1;
	elseif (j <= 3.9e+292)
		tmp = Float64(y1 * Float64(j * Float64(y4 * Float64(-y3))));
	else
		tmp = Float64(i * Float64(Float64(x * j) * 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 * (j * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (j <= -2.5e+162)
		tmp = t_1;
	elseif (j <= -3.2e+95)
		tmp = i * (j * (x * y1));
	elseif (j <= -21000000000000.0)
		tmp = (y3 * y4) * (y1 * -j);
	elseif (j <= -3.1e-199)
		tmp = i * (x * (c * -y));
	elseif (j <= 5.5e-76)
		tmp = c * (x * (y0 * y2));
	elseif (j <= 2.4e+229)
		tmp = t_1;
	elseif (j <= 3.9e+292)
		tmp = y1 * (j * (y4 * -y3));
	else
		tmp = i * ((x * j) * y1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.5e+162], t$95$1, If[LessEqual[j, -3.2e+95], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -21000000000000.0], N[(N[(y3 * y4), $MachinePrecision] * N[(y1 * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.1e-199], N[(i * N[(x * N[(c * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.5e-76], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.4e+229], t$95$1, If[LessEqual[j, 3.9e+292], N[(y1 * N[(j * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(x * j), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -2.4999999999999998e162 or 5.50000000000000014e-76 < j < 2.4000000000000001e229

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 43.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 41.8%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 41.8%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 41.8%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]

   if -2.4999999999999998e162 < j < -3.2000000000000001e95

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 28.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 28.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 28.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 28.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 28.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 28.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 28.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 28.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 28.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 28.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 44.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 44.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 44.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 44.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 44.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 44.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 44.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 62.2%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 62.2%

         \[\leadsto i \cdot \color{blue}{\left(\left(x \cdot y1\right) \cdot j\right)} \]

      2. *-commutative 62.2%

         \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot x\right)} \cdot j\right) \]

   10. Simplified 62.2%

       \[\leadsto \color{blue}{i \cdot \left(\left(y1 \cdot x\right) \cdot j\right)} \]

   if -3.2000000000000001e95 < j < -2.1e13

   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 47.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 47.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 47.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 47.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 47.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 47.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 47.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 47.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 47.7%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 47.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 48.0%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 48.0%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 48.0%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 48.0%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 48.0%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 48.0%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around 0 41.6%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 41.6%

         \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

      2. associate-*r* 47.9%

         \[\leadsto -\color{blue}{\left(j \cdot y1\right) \cdot \left(y3 \cdot y4\right)} \]

      3. *-commutative 47.9%

         \[\leadsto -\left(j \cdot y1\right) \cdot \color{blue}{\left(y4 \cdot y3\right)} \]

      4. distribute-lft-neg-in 47.9%

         \[\leadsto \color{blue}{\left(-j \cdot y1\right) \cdot \left(y4 \cdot y3\right)} \]

      5. *-commutative 47.9%

         \[\leadsto \left(-\color{blue}{y1 \cdot j}\right) \cdot \left(y4 \cdot y3\right) \]

      6. distribute-rgt-neg-in 47.9%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(-j\right)\right)} \cdot \left(y4 \cdot y3\right) \]

   10. Simplified 47.9%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(-j\right)\right) \cdot \left(y4 \cdot y3\right)} \]

   if -2.1e13 < j < -3.10000000000000012e-199

   1. Initial program 46.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 46.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 31.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 31.8%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 31.8%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 31.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 31.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 31.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 31.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 31.8%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around inf 29.9%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 29.9%

         \[\leadsto \color{blue}{-c \cdot \left(i \cdot \left(x \cdot y\right)\right)} \]

      2. *-commutative 29.9%

         \[\leadsto -\color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot c} \]

      3. distribute-rgt-neg-in 29.9%

         \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot \left(-c\right)} \]

   8. Simplified 29.9%

      \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot \left(-c\right)} \]

   9. Taylor expanded in i around 0 29.9%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 29.9%

          \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot \left(x \cdot y\right)\right) \cdot c\right)} \]

       2. neg-mul-1 29.9%

          \[\leadsto \color{blue}{-\left(i \cdot \left(x \cdot y\right)\right) \cdot c} \]

       3. distribute-rgt-neg-in 29.9%

          \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot \left(-c\right)} \]

       4. associate-*r* 32.0%

          \[\leadsto \color{blue}{i \cdot \left(\left(x \cdot y\right) \cdot \left(-c\right)\right)} \]

       5. associate-*l* 34.3%

          \[\leadsto i \cdot \color{blue}{\left(x \cdot \left(y \cdot \left(-c\right)\right)\right)} \]

   11. Simplified 34.3%

       \[\leadsto \color{blue}{i \cdot \left(x \cdot \left(y \cdot \left(-c\right)\right)\right)} \]

   if -3.10000000000000012e-199 < j < 5.50000000000000014e-76

   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 x around inf 39.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 33.2%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 33.2%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 33.2%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 33.2%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 33.2%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 33.2%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 33.2%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 33.2%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around 0 30.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.9%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   8. Simplified 30.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if 2.4000000000000001e229 < j < 3.8999999999999999e292

   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 36.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 36.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 36.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 36.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 36.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 36.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 36.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 36.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 36.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 64.4%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 64.4%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 64.4%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 64.4%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 64.4%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 64.4%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 64.4%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around 0 46.6%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 46.6%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 46.6%

         \[\leadsto y1 \cdot \left(-j \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

      3. distribute-rgt-neg-in 46.6%

         \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-y4 \cdot y3\right)\right)} \]

      4. distribute-rgt-neg-in 46.6%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(y4 \cdot \left(-y3\right)\right)}\right) \]

   10. Simplified 46.6%

       \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)} \]

   if 3.8999999999999999e292 < j

   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 y1 around inf 50.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 50.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 50.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 50.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 50.0%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 50.0%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.0%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.0%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 50.0%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 50.0%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 50.0%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

      2. *-commutative 100.0%

         \[\leadsto i \cdot \left(\color{blue}{\left(x \cdot j\right)} \cdot y1\right) \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{i \cdot \left(\left(x \cdot j\right) \cdot y1\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+162}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+95}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -21000000000000:\\ \;\;\;\;\left(y3 \cdot y4\right) \cdot \left(y1 \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-199}:\\ \;\;\;\;i \cdot \left(x \cdot \left(c \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+229}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+292}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \end{array} \]

Alternative 27: 23.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+257}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+132}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-6}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-162}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-214}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(i \cdot \left(-y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -4.8e+257)
   (* c (* i (* x (- y))))
   (if (<= y -3.8e+132)
     (* y1 (* k (* y2 y4)))
     (if (<= y -8e-6)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= y -1.1e-162)
         (* y1 (* j (* y4 (- y3))))
         (if (<= y 1.25e-214)
           (* i (* (* x j) y1))
           (if (<= y 7e+33)
             (* b (* j (- (* t y4) (* x y0))))
             (* c (* x (* i (- y)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -4.8e+257) {
		tmp = c * (i * (x * -y));
	} else if (y <= -3.8e+132) {
		tmp = y1 * (k * (y2 * y4));
	} else if (y <= -8e-6) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y <= -1.1e-162) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (y <= 1.25e-214) {
		tmp = i * ((x * j) * y1);
	} else if (y <= 7e+33) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = c * (x * (i * -y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-4.8d+257)) then
        tmp = c * (i * (x * -y))
    else if (y <= (-3.8d+132)) then
        tmp = y1 * (k * (y2 * y4))
    else if (y <= (-8d-6)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y <= (-1.1d-162)) then
        tmp = y1 * (j * (y4 * -y3))
    else if (y <= 1.25d-214) then
        tmp = i * ((x * j) * y1)
    else if (y <= 7d+33) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = c * (x * (i * -y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -4.8e+257) {
		tmp = c * (i * (x * -y));
	} else if (y <= -3.8e+132) {
		tmp = y1 * (k * (y2 * y4));
	} else if (y <= -8e-6) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y <= -1.1e-162) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (y <= 1.25e-214) {
		tmp = i * ((x * j) * y1);
	} else if (y <= 7e+33) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = c * (x * (i * -y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -4.8e+257:
		tmp = c * (i * (x * -y))
	elif y <= -3.8e+132:
		tmp = y1 * (k * (y2 * y4))
	elif y <= -8e-6:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y <= -1.1e-162:
		tmp = y1 * (j * (y4 * -y3))
	elif y <= 1.25e-214:
		tmp = i * ((x * j) * y1)
	elif y <= 7e+33:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = c * (x * (i * -y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -4.8e+257)
		tmp = Float64(c * Float64(i * Float64(x * Float64(-y))));
	elseif (y <= -3.8e+132)
		tmp = Float64(y1 * Float64(k * Float64(y2 * y4)));
	elseif (y <= -8e-6)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y <= -1.1e-162)
		tmp = Float64(y1 * Float64(j * Float64(y4 * Float64(-y3))));
	elseif (y <= 1.25e-214)
		tmp = Float64(i * Float64(Float64(x * j) * y1));
	elseif (y <= 7e+33)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(c * Float64(x * Float64(i * Float64(-y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -4.8e+257)
		tmp = c * (i * (x * -y));
	elseif (y <= -3.8e+132)
		tmp = y1 * (k * (y2 * y4));
	elseif (y <= -8e-6)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y <= -1.1e-162)
		tmp = y1 * (j * (y4 * -y3));
	elseif (y <= 1.25e-214)
		tmp = i * ((x * j) * y1);
	elseif (y <= 7e+33)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = c * (x * (i * -y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -4.8e+257], N[(c * N[(i * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e+132], N[(y1 * N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-6], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-162], N[(y1 * N[(j * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-214], N[(i * N[(N[(x * j), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+33], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(i * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -4.8000000000000001e257

   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 x around inf 51.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 52.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 52.0%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 52.0%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 52.0%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 52.0%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 52.0%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 52.0%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 52.0%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around inf 75.2%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 75.2%

         \[\leadsto \color{blue}{-c \cdot \left(i \cdot \left(x \cdot y\right)\right)} \]

      2. *-commutative 75.2%

         \[\leadsto -\color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot c} \]

      3. distribute-rgt-neg-in 75.2%

         \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot \left(-c\right)} \]

   8. Simplified 75.2%

      \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot \left(-c\right)} \]

   if -4.8000000000000001e257 < y < -3.80000000000000006e132

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 38.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 38.1%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 38.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 38.1%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 38.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 38.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 38.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 38.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 38.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 38.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in k around inf 33.3%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 33.3%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      2. mul-1-neg 33.3%

         \[\leadsto y1 \cdot \left(k \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      3. unsub-neg 33.3%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)}\right) \]

   7. Simplified 33.3%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   8. Taylor expanded in y2 around inf 33.4%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]

   if -3.80000000000000006e132 < y < -7.99999999999999964e-6

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 39.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in x around inf 36.3%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 36.3%

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{y0 \cdot j}\right)\right) \]

   5. Simplified 36.3%

      \[\leadsto b \cdot \color{blue}{\left(x \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   if -7.99999999999999964e-6 < y < -1.1e-162

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 41.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 41.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 41.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 41.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 41.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 41.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 41.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 41.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 41.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 41.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 48.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 48.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 48.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 48.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 48.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 48.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 48.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around 0 41.7%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 41.7%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 41.7%

         \[\leadsto y1 \cdot \left(-j \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

      3. distribute-rgt-neg-in 41.7%

         \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-y4 \cdot y3\right)\right)} \]

      4. distribute-rgt-neg-in 41.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(y4 \cdot \left(-y3\right)\right)}\right) \]

   10. Simplified 41.7%

       \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)} \]

   if -1.1e-162 < y < 1.2499999999999999e-214

   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 y1 around inf 40.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 40.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 40.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 33.8%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 33.8%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 33.8%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 33.8%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 33.8%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 33.8%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 33.8%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 34.2%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 37.8%

         \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

      2. *-commutative 37.8%

         \[\leadsto i \cdot \left(\color{blue}{\left(x \cdot j\right)} \cdot y1\right) \]

   10. Simplified 37.8%

       \[\leadsto \color{blue}{i \cdot \left(\left(x \cdot j\right) \cdot y1\right)} \]

   if 1.2499999999999999e-214 < y < 7.0000000000000002e33

   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 b around inf 39.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 34.6%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 34.6%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 34.6%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]

   if 7.0000000000000002e33 < y

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 40.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 42.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 42.8%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 42.8%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 42.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 42.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 42.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 42.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 42.8%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around inf 43.0%

      \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+257}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+132}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-6}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-162}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-214}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(i \cdot \left(-y\right)\right)\right)\\ \end{array} \]

Alternative 28: 30.1% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{if}\;x \leq -2.05 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-93}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-126}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+79}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (* y0 (- (* x c) (* k y5))))))
   (if (<= x -2.05e+176)
     t_1
     (if (<= x -2e+18)
       (* (* x c) (- (* y0 y2) (* y i)))
       (if (<= x -1.85e-93)
         (* y2 (* t (- (* a y5) (* c y4))))
         (if (<= x 1.25e-126)
           (* y1 (* k (- (* y2 y4) (* z i))))
           (if (<= x 1.25e+79)
             (* y1 (* y4 (- (* k y2) (* j y3))))
             (if (<= x 6.2e+196) t_1 (* y1 (* j (* x 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 = y2 * (y0 * ((x * c) - (k * y5)));
	double tmp;
	if (x <= -2.05e+176) {
		tmp = t_1;
	} else if (x <= -2e+18) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (x <= -1.85e-93) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (x <= 1.25e-126) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (x <= 1.25e+79) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 6.2e+196) {
		tmp = t_1;
	} else {
		tmp = y1 * (j * (x * 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 = y2 * (y0 * ((x * c) - (k * y5)))
    if (x <= (-2.05d+176)) then
        tmp = t_1
    else if (x <= (-2d+18)) then
        tmp = (x * c) * ((y0 * y2) - (y * i))
    else if (x <= (-1.85d-93)) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (x <= 1.25d-126) then
        tmp = y1 * (k * ((y2 * y4) - (z * i)))
    else if (x <= 1.25d+79) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (x <= 6.2d+196) then
        tmp = t_1
    else
        tmp = y1 * (j * (x * 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 = y2 * (y0 * ((x * c) - (k * y5)));
	double tmp;
	if (x <= -2.05e+176) {
		tmp = t_1;
	} else if (x <= -2e+18) {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	} else if (x <= -1.85e-93) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (x <= 1.25e-126) {
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	} else if (x <= 1.25e+79) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 6.2e+196) {
		tmp = t_1;
	} else {
		tmp = y1 * (j * (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (y0 * ((x * c) - (k * y5)))
	tmp = 0
	if x <= -2.05e+176:
		tmp = t_1
	elif x <= -2e+18:
		tmp = (x * c) * ((y0 * y2) - (y * i))
	elif x <= -1.85e-93:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif x <= 1.25e-126:
		tmp = y1 * (k * ((y2 * y4) - (z * i)))
	elif x <= 1.25e+79:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif x <= 6.2e+196:
		tmp = t_1
	else:
		tmp = y1 * (j * (x * 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(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * y5))))
	tmp = 0.0
	if (x <= -2.05e+176)
		tmp = t_1;
	elseif (x <= -2e+18)
		tmp = Float64(Float64(x * c) * Float64(Float64(y0 * y2) - Float64(y * i)));
	elseif (x <= -1.85e-93)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 1.25e-126)
		tmp = Float64(y1 * Float64(k * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (x <= 1.25e+79)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (x <= 6.2e+196)
		tmp = t_1;
	else
		tmp = Float64(y1 * Float64(j * Float64(x * 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 = y2 * (y0 * ((x * c) - (k * y5)));
	tmp = 0.0;
	if (x <= -2.05e+176)
		tmp = t_1;
	elseif (x <= -2e+18)
		tmp = (x * c) * ((y0 * y2) - (y * i));
	elseif (x <= -1.85e-93)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (x <= 1.25e-126)
		tmp = y1 * (k * ((y2 * y4) - (z * i)));
	elseif (x <= 1.25e+79)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (x <= 6.2e+196)
		tmp = t_1;
	else
		tmp = y1 * (j * (x * 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[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.05e+176], t$95$1, If[LessEqual[x, -2e+18], N[(N[(x * c), $MachinePrecision] * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.85e-93], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-126], N[(y1 * N[(k * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e+79], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+196], t$95$1, N[(y1 * N[(j * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.05e176 or 1.25e79 < x < 6.2000000000000002e196

   1. Initial program 19.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 41.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in y0 around inf 55.5%

      \[\leadsto y2 \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.5%

         \[\leadsto y2 \cdot \left(y0 \cdot \color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 55.5%

         \[\leadsto y2 \cdot \left(y0 \cdot \left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right)\right) \]

      3. unsub-neg 55.5%

         \[\leadsto y2 \cdot \left(y0 \cdot \color{blue}{\left(c \cdot x - k \cdot y5\right)}\right) \]

      4. *-commutative 55.5%

         \[\leadsto y2 \cdot \left(y0 \cdot \left(\color{blue}{x \cdot c} - k \cdot y5\right)\right) \]

   5. Simplified 55.5%

      \[\leadsto y2 \cdot \color{blue}{\left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)} \]

   if -2.05e176 < x < -2e18

   1. Initial program 21.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 50.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around inf 44.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 42.3%

         \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)} \]

      2. *-commutative 42.3%

         \[\leadsto \color{blue}{\left(x \cdot c\right)} \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \]

      3. +-commutative 42.3%

         \[\leadsto \left(x \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)} \]

      4. mul-1-neg 42.3%

         \[\leadsto \left(x \cdot c\right) \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right) \]

      5. unsub-neg 42.3%

         \[\leadsto \left(x \cdot c\right) \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)} \]

      6. *-commutative 42.3%

         \[\leadsto \left(x \cdot c\right) \cdot \left(\color{blue}{y2 \cdot y0} - i \cdot y\right) \]

   5. Simplified 42.3%

      \[\leadsto \color{blue}{\left(x \cdot c\right) \cdot \left(y2 \cdot y0 - i \cdot y\right)} \]

   if -2e18 < x < -1.85000000000000001e-93

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. 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 t around inf 43.3%

      \[\leadsto y2 \cdot \color{blue}{\left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -1.85000000000000001e-93 < x < 1.25000000000000001e-126

   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 y1 around inf 45.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 45.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 45.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 45.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 45.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 45.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 45.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 45.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 45.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in k around inf 41.4%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.4%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      2. mul-1-neg 41.4%

         \[\leadsto y1 \cdot \left(k \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      3. unsub-neg 41.4%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)}\right) \]

   7. Simplified 41.4%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   if 1.25000000000000001e-126 < x < 1.25e79

   1. Initial program 48.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 34.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 34.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 34.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in y4 around inf 39.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot k} - j \cdot y3\right)\right) \]

   7. Simplified 39.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]

   if 6.2000000000000002e196 < x

   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 y1 around inf 50.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.1%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 50.1%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 50.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 50.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 57.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 57.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 57.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 64.9%

      \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 64.9%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]

   10. Simplified 64.9%

       \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+176}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-93}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-126}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+79}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+196}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 29: 25.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+190}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-8}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-164}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-219}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(i \cdot \left(-y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -2.55e+190)
   (* c (* i (* x (- y))))
   (if (<= y -2.15e-8)
     (* b (* t (- (* j y4) (* z a))))
     (if (<= y -1.2e-164)
       (* y1 (* j (* y4 (- y3))))
       (if (<= y 2.4e-219)
         (* i (* (* x j) y1))
         (if (<= y 8.5e+33)
           (* b (* j (- (* t y4) (* x y0))))
           (* c (* x (* i (- y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -2.55e+190) {
		tmp = c * (i * (x * -y));
	} else if (y <= -2.15e-8) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (y <= -1.2e-164) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (y <= 2.4e-219) {
		tmp = i * ((x * j) * y1);
	} else if (y <= 8.5e+33) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = c * (x * (i * -y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-2.55d+190)) then
        tmp = c * (i * (x * -y))
    else if (y <= (-2.15d-8)) then
        tmp = b * (t * ((j * y4) - (z * a)))
    else if (y <= (-1.2d-164)) then
        tmp = y1 * (j * (y4 * -y3))
    else if (y <= 2.4d-219) then
        tmp = i * ((x * j) * y1)
    else if (y <= 8.5d+33) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = c * (x * (i * -y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -2.55e+190) {
		tmp = c * (i * (x * -y));
	} else if (y <= -2.15e-8) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (y <= -1.2e-164) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (y <= 2.4e-219) {
		tmp = i * ((x * j) * y1);
	} else if (y <= 8.5e+33) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = c * (x * (i * -y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -2.55e+190:
		tmp = c * (i * (x * -y))
	elif y <= -2.15e-8:
		tmp = b * (t * ((j * y4) - (z * a)))
	elif y <= -1.2e-164:
		tmp = y1 * (j * (y4 * -y3))
	elif y <= 2.4e-219:
		tmp = i * ((x * j) * y1)
	elif y <= 8.5e+33:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = c * (x * (i * -y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -2.55e+190)
		tmp = Float64(c * Float64(i * Float64(x * Float64(-y))));
	elseif (y <= -2.15e-8)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (y <= -1.2e-164)
		tmp = Float64(y1 * Float64(j * Float64(y4 * Float64(-y3))));
	elseif (y <= 2.4e-219)
		tmp = Float64(i * Float64(Float64(x * j) * y1));
	elseif (y <= 8.5e+33)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(c * Float64(x * Float64(i * Float64(-y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -2.55e+190)
		tmp = c * (i * (x * -y));
	elseif (y <= -2.15e-8)
		tmp = b * (t * ((j * y4) - (z * a)));
	elseif (y <= -1.2e-164)
		tmp = y1 * (j * (y4 * -y3));
	elseif (y <= 2.4e-219)
		tmp = i * ((x * j) * y1);
	elseif (y <= 8.5e+33)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = c * (x * (i * -y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -2.55e+190], N[(c * N[(i * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-8], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-164], N[(y1 * N[(j * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-219], N[(i * N[(N[(x * j), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+33], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(i * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.55000000000000015e190

   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 x around inf 44.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 34.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 34.8%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 34.8%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 34.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 34.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 34.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 34.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 34.8%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around inf 43.9%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.9%

         \[\leadsto \color{blue}{-c \cdot \left(i \cdot \left(x \cdot y\right)\right)} \]

      2. *-commutative 43.9%

         \[\leadsto -\color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot c} \]

      3. distribute-rgt-neg-in 43.9%

         \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot \left(-c\right)} \]

   8. Simplified 43.9%

      \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot \left(-c\right)} \]

   if -2.55000000000000015e190 < y < -2.1500000000000001e-8

   1. Initial program 39.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 42.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in t around inf 27.7%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 27.7%

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      2. mul-1-neg 27.7%

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right)\right) \]

      3. sub-neg 27.7%

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

   5. Simplified 27.7%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   if -2.1500000000000001e-8 < y < -1.19999999999999992e-164

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 42.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 42.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 42.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 42.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 42.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 42.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 42.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 42.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 42.6%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 42.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 50.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 50.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 50.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 50.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 50.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around 0 43.2%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 43.2%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 43.2%

         \[\leadsto y1 \cdot \left(-j \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

      3. distribute-rgt-neg-in 43.2%

         \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-y4 \cdot y3\right)\right)} \]

      4. distribute-rgt-neg-in 43.2%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(y4 \cdot \left(-y3\right)\right)}\right) \]

   10. Simplified 43.2%

       \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)} \]

   if -1.19999999999999992e-164 < y < 2.40000000000000014e-219

   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 y1 around inf 40.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 40.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 40.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 40.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 33.8%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 33.8%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 33.8%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 33.8%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 33.8%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 33.8%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 33.8%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 34.2%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 37.8%

         \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

      2. *-commutative 37.8%

         \[\leadsto i \cdot \left(\color{blue}{\left(x \cdot j\right)} \cdot y1\right) \]

   10. Simplified 37.8%

       \[\leadsto \color{blue}{i \cdot \left(\left(x \cdot j\right) \cdot y1\right)} \]

   if 2.40000000000000014e-219 < y < 8.4999999999999998e33

   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 b around inf 39.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 34.6%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 34.6%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 34.6%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]

   if 8.4999999999999998e33 < y

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 40.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 42.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 42.8%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 42.8%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 42.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 42.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 42.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 42.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 42.8%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around inf 43.0%

      \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+190}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-8}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-164}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-219}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(i \cdot \left(-y\right)\right)\right)\\ \end{array} \]

Alternative 30: 29.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{if}\;b \leq -2.25 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-223}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+76}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (- (* x j) (* z k)) y1))))
   (if (<= b -2.25e+24)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= b -8.8e-90)
       t_1
       (if (<= b -2.15e-223)
         (* y1 (* j (* y4 (- y3))))
         (if (<= b 2.6e-146)
           t_1
           (if (<= b 1.05e+76)
             (* c (* y2 (- (* x y0) (* t y4))))
             (* b (* j (- (* t y4) (* x y0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (((x * j) - (z * k)) * y1);
	double tmp;
	if (b <= -2.25e+24) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -8.8e-90) {
		tmp = t_1;
	} else if (b <= -2.15e-223) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (b <= 2.6e-146) {
		tmp = t_1;
	} else if (b <= 1.05e+76) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (((x * j) - (z * k)) * y1)
    if (b <= (-2.25d+24)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (b <= (-8.8d-90)) then
        tmp = t_1
    else if (b <= (-2.15d-223)) then
        tmp = y1 * (j * (y4 * -y3))
    else if (b <= 2.6d-146) then
        tmp = t_1
    else if (b <= 1.05d+76) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (((x * j) - (z * k)) * y1);
	double tmp;
	if (b <= -2.25e+24) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -8.8e-90) {
		tmp = t_1;
	} else if (b <= -2.15e-223) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (b <= 2.6e-146) {
		tmp = t_1;
	} else if (b <= 1.05e+76) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (((x * j) - (z * k)) * y1)
	tmp = 0
	if b <= -2.25e+24:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif b <= -8.8e-90:
		tmp = t_1
	elif b <= -2.15e-223:
		tmp = y1 * (j * (y4 * -y3))
	elif b <= 2.6e-146:
		tmp = t_1
	elif b <= 1.05e+76:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(Float64(Float64(x * j) - Float64(z * k)) * y1))
	tmp = 0.0
	if (b <= -2.25e+24)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -8.8e-90)
		tmp = t_1;
	elseif (b <= -2.15e-223)
		tmp = Float64(y1 * Float64(j * Float64(y4 * Float64(-y3))));
	elseif (b <= 2.6e-146)
		tmp = t_1;
	elseif (b <= 1.05e+76)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (((x * j) - (z * k)) * y1);
	tmp = 0.0;
	if (b <= -2.25e+24)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (b <= -8.8e-90)
		tmp = t_1;
	elseif (b <= -2.15e-223)
		tmp = y1 * (j * (y4 * -y3));
	elseif (b <= 2.6e-146)
		tmp = t_1;
	elseif (b <= 1.05e+76)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.25e+24], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.8e-90], t$95$1, If[LessEqual[b, -2.15e-223], N[(y1 * N[(j * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e-146], t$95$1, If[LessEqual[b, 1.05e+76], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.2500000000000001e24

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 55.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y0 around inf 49.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.4%

         \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - \color{blue}{x \cdot j}\right)\right) \]

   5. Simplified 49.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - x \cdot j\right)\right)} \]

   if -2.2500000000000001e24 < b < -8.79999999999999943e-90 or -2.15e-223 < b < 2.59999999999999987e-146

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 46.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 46.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 46.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 46.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in i around inf 42.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.0%

         \[\leadsto i \cdot \left(y1 \cdot \left(\color{blue}{x \cdot j} - k \cdot z\right)\right) \]

   7. Simplified 42.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(x \cdot j - k \cdot z\right)\right)} \]

   if -8.79999999999999943e-90 < b < -2.15e-223

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 36.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 36.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 36.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 36.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 52.1%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 52.1%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 52.1%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 52.1%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 52.1%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 52.1%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 52.1%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around 0 46.2%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 46.2%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 46.2%

         \[\leadsto y1 \cdot \left(-j \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

      3. distribute-rgt-neg-in 46.2%

         \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-y4 \cdot y3\right)\right)} \]

      4. distribute-rgt-neg-in 46.2%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(y4 \cdot \left(-y3\right)\right)}\right) \]

   10. Simplified 46.2%

       \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)} \]

   if 2.59999999999999987e-146 < b < 1.05000000000000003e76

   1. Initial program 40.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 45.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 33.6%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if 1.05000000000000003e76 < b

   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 b around inf 47.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 45.2%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 45.2%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-90}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-223}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-146}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j - z \cdot k\right) \cdot y1\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+76}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

Alternative 31: 25.2% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.9 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-88}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-285}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.46 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -4.9e+22)
   (* b (* y0 (- (* z k) (* x j))))
   (if (<= b -1.35e-88)
     (* i (* (* x j) y1))
     (if (<= b -7.2e-285)
       (* y1 (* j (* y4 (- y3))))
       (if (<= b 1.46e+75)
         (* x (* (* a y1) (- y2)))
         (* b (* j (- (* t y4) (* x y0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -4.9e+22) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -1.35e-88) {
		tmp = i * ((x * j) * y1);
	} else if (b <= -7.2e-285) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (b <= 1.46e+75) {
		tmp = x * ((a * y1) * -y2);
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-4.9d+22)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (b <= (-1.35d-88)) then
        tmp = i * ((x * j) * y1)
    else if (b <= (-7.2d-285)) then
        tmp = y1 * (j * (y4 * -y3))
    else if (b <= 1.46d+75) then
        tmp = x * ((a * y1) * -y2)
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -4.9e+22) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -1.35e-88) {
		tmp = i * ((x * j) * y1);
	} else if (b <= -7.2e-285) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (b <= 1.46e+75) {
		tmp = x * ((a * y1) * -y2);
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -4.9e+22:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif b <= -1.35e-88:
		tmp = i * ((x * j) * y1)
	elif b <= -7.2e-285:
		tmp = y1 * (j * (y4 * -y3))
	elif b <= 1.46e+75:
		tmp = x * ((a * y1) * -y2)
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -4.9e+22)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -1.35e-88)
		tmp = Float64(i * Float64(Float64(x * j) * y1));
	elseif (b <= -7.2e-285)
		tmp = Float64(y1 * Float64(j * Float64(y4 * Float64(-y3))));
	elseif (b <= 1.46e+75)
		tmp = Float64(x * Float64(Float64(a * y1) * Float64(-y2)));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -4.9e+22)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (b <= -1.35e-88)
		tmp = i * ((x * j) * y1);
	elseif (b <= -7.2e-285)
		tmp = y1 * (j * (y4 * -y3));
	elseif (b <= 1.46e+75)
		tmp = x * ((a * y1) * -y2);
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -4.9e+22], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.35e-88], N[(i * N[(N[(x * j), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.2e-285], N[(y1 * N[(j * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.46e+75], N[(x * N[(N[(a * y1), $MachinePrecision] * (-y2)), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.89999999999999979e22

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 55.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y0 around inf 49.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.4%

         \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - \color{blue}{x \cdot j}\right)\right) \]

   5. Simplified 49.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - x \cdot j\right)\right)} \]

   if -4.89999999999999979e22 < b < -1.34999999999999997e-88

   1. Initial program 45.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.5%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 45.5%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 45.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 45.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 45.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 45.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 45.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 41.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 50.8%

         \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

      2. *-commutative 50.8%

         \[\leadsto i \cdot \left(\color{blue}{\left(x \cdot j\right)} \cdot y1\right) \]

   10. Simplified 50.8%

       \[\leadsto \color{blue}{i \cdot \left(\left(x \cdot j\right) \cdot y1\right)} \]

   if -1.34999999999999997e-88 < b < -7.20000000000000008e-285

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 43.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 43.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 43.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 43.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 43.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 43.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 43.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 43.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 43.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 43.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 50.6%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 50.6%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 50.6%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 50.6%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around 0 41.8%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 41.8%

         \[\leadsto y1 \cdot \left(-j \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

      3. distribute-rgt-neg-in 41.8%

         \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-y4 \cdot y3\right)\right)} \]

      4. distribute-rgt-neg-in 41.8%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(y4 \cdot \left(-y3\right)\right)}\right) \]

   10. Simplified 41.8%

       \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)} \]

   if -7.20000000000000008e-285 < b < 1.4600000000000001e75

   1. Initial program 37.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 40.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around 0 41.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   4. Taylor expanded in y1 around inf 23.1%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 23.1%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot \left(y1 \cdot y2\right)\right)} \]

      2. associate-*r* 23.1%

         \[\leadsto x \cdot \left(-\color{blue}{\left(a \cdot y1\right) \cdot y2}\right) \]

      3. distribute-rgt-neg-in 23.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   6. Simplified 23.1%

      \[\leadsto x \cdot \color{blue}{\left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)} \]

   if 1.4600000000000001e75 < b

   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 b around inf 47.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 45.2%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 45.2%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.9 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-88}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-285}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.46 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(\left(a \cdot y1\right) \cdot \left(-y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

Alternative 32: 29.4% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.04 \cdot 10^{-89}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-203}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+75}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -4.6e+22)
   (* b (* y0 (- (* z k) (* x j))))
   (if (<= b -1.04e-89)
     (* i (* (* x j) y1))
     (if (<= b -9e-203)
       (* y1 (* j (* y4 (- y3))))
       (if (<= b 5.5e+75)
         (* c (* y2 (- (* x y0) (* t y4))))
         (* b (* j (- (* t y4) (* x y0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -4.6e+22) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -1.04e-89) {
		tmp = i * ((x * j) * y1);
	} else if (b <= -9e-203) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (b <= 5.5e+75) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-4.6d+22)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (b <= (-1.04d-89)) then
        tmp = i * ((x * j) * y1)
    else if (b <= (-9d-203)) then
        tmp = y1 * (j * (y4 * -y3))
    else if (b <= 5.5d+75) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -4.6e+22) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -1.04e-89) {
		tmp = i * ((x * j) * y1);
	} else if (b <= -9e-203) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (b <= 5.5e+75) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -4.6e+22:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif b <= -1.04e-89:
		tmp = i * ((x * j) * y1)
	elif b <= -9e-203:
		tmp = y1 * (j * (y4 * -y3))
	elif b <= 5.5e+75:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -4.6e+22)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -1.04e-89)
		tmp = Float64(i * Float64(Float64(x * j) * y1));
	elseif (b <= -9e-203)
		tmp = Float64(y1 * Float64(j * Float64(y4 * Float64(-y3))));
	elseif (b <= 5.5e+75)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -4.6e+22)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (b <= -1.04e-89)
		tmp = i * ((x * j) * y1);
	elseif (b <= -9e-203)
		tmp = y1 * (j * (y4 * -y3));
	elseif (b <= 5.5e+75)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -4.6e+22], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.04e-89], N[(i * N[(N[(x * j), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9e-203], N[(y1 * N[(j * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+75], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.6000000000000004e22

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 55.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in y0 around inf 49.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.4%

         \[\leadsto b \cdot \left(y0 \cdot \left(k \cdot z - \color{blue}{x \cdot j}\right)\right) \]

   5. Simplified 49.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - x \cdot j\right)\right)} \]

   if -4.6000000000000004e22 < b < -1.04e-89

   1. Initial program 45.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.5%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 45.5%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 45.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 45.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 45.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 45.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 45.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 45.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 41.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 50.8%

         \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

      2. *-commutative 50.8%

         \[\leadsto i \cdot \left(\color{blue}{\left(x \cdot j\right)} \cdot y1\right) \]

   10. Simplified 50.8%

       \[\leadsto \color{blue}{i \cdot \left(\left(x \cdot j\right) \cdot y1\right)} \]

   if -1.04e-89 < b < -9.0000000000000003e-203

   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 y1 around inf 35.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 35.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 35.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 35.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 35.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 35.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 35.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 35.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 35.0%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 35.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 54.3%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 54.3%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 54.3%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 54.3%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 54.3%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 54.3%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 54.3%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around 0 50.5%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 50.5%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 50.5%

         \[\leadsto y1 \cdot \left(-j \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

      3. distribute-rgt-neg-in 50.5%

         \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-y4 \cdot y3\right)\right)} \]

      4. distribute-rgt-neg-in 50.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(y4 \cdot \left(-y3\right)\right)}\right) \]

   10. Simplified 50.5%

       \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)} \]

   if -9.0000000000000003e-203 < b < 5.5000000000000001e75

   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 43.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   3. Taylor expanded in c around inf 30.0%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if 5.5000000000000001e75 < b

   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 b around inf 47.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 45.2%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 45.2%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.04 \cdot 10^{-89}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-203}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+75}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

Alternative 33: 21.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-199}:\\ \;\;\;\;y1 \cdot \left(\left(z \cdot i\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-68}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (* y0 y2)))))
   (if (<= x -2.7e+72)
     t_1
     (if (<= x -4.2e-81)
       (* y1 (* j (* y4 (- y3))))
       (if (<= x -6.5e-199)
         (* y1 (* (* z i) (- k)))
         (if (<= x 1.32e-68)
           (* y1 (* k (* y2 y4)))
           (if (<= x 3e+144) t_1 (* y1 (* j (* x 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 * (x * (y0 * y2));
	double tmp;
	if (x <= -2.7e+72) {
		tmp = t_1;
	} else if (x <= -4.2e-81) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (x <= -6.5e-199) {
		tmp = y1 * ((z * i) * -k);
	} else if (x <= 1.32e-68) {
		tmp = y1 * (k * (y2 * y4));
	} else if (x <= 3e+144) {
		tmp = t_1;
	} else {
		tmp = y1 * (j * (x * 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 * (x * (y0 * y2))
    if (x <= (-2.7d+72)) then
        tmp = t_1
    else if (x <= (-4.2d-81)) then
        tmp = y1 * (j * (y4 * -y3))
    else if (x <= (-6.5d-199)) then
        tmp = y1 * ((z * i) * -k)
    else if (x <= 1.32d-68) then
        tmp = y1 * (k * (y2 * y4))
    else if (x <= 3d+144) then
        tmp = t_1
    else
        tmp = y1 * (j * (x * 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 * (x * (y0 * y2));
	double tmp;
	if (x <= -2.7e+72) {
		tmp = t_1;
	} else if (x <= -4.2e-81) {
		tmp = y1 * (j * (y4 * -y3));
	} else if (x <= -6.5e-199) {
		tmp = y1 * ((z * i) * -k);
	} else if (x <= 1.32e-68) {
		tmp = y1 * (k * (y2 * y4));
	} else if (x <= 3e+144) {
		tmp = t_1;
	} else {
		tmp = y1 * (j * (x * 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 * (x * (y0 * y2))
	tmp = 0
	if x <= -2.7e+72:
		tmp = t_1
	elif x <= -4.2e-81:
		tmp = y1 * (j * (y4 * -y3))
	elif x <= -6.5e-199:
		tmp = y1 * ((z * i) * -k)
	elif x <= 1.32e-68:
		tmp = y1 * (k * (y2 * y4))
	elif x <= 3e+144:
		tmp = t_1
	else:
		tmp = y1 * (j * (x * 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(x * Float64(y0 * y2)))
	tmp = 0.0
	if (x <= -2.7e+72)
		tmp = t_1;
	elseif (x <= -4.2e-81)
		tmp = Float64(y1 * Float64(j * Float64(y4 * Float64(-y3))));
	elseif (x <= -6.5e-199)
		tmp = Float64(y1 * Float64(Float64(z * i) * Float64(-k)));
	elseif (x <= 1.32e-68)
		tmp = Float64(y1 * Float64(k * Float64(y2 * y4)));
	elseif (x <= 3e+144)
		tmp = t_1;
	else
		tmp = Float64(y1 * Float64(j * Float64(x * 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 * (x * (y0 * y2));
	tmp = 0.0;
	if (x <= -2.7e+72)
		tmp = t_1;
	elseif (x <= -4.2e-81)
		tmp = y1 * (j * (y4 * -y3));
	elseif (x <= -6.5e-199)
		tmp = y1 * ((z * i) * -k);
	elseif (x <= 1.32e-68)
		tmp = y1 * (k * (y2 * y4));
	elseif (x <= 3e+144)
		tmp = t_1;
	else
		tmp = y1 * (j * (x * 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[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+72], t$95$1, If[LessEqual[x, -4.2e-81], N[(y1 * N[(j * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-199], N[(y1 * N[(N[(z * i), $MachinePrecision] * (-k)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.32e-68], N[(y1 * N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+144], t$95$1, N[(y1 * N[(j * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.7000000000000001e72 or 1.32e-68 < x < 2.9999999999999999e144

   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 48.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 44.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 44.8%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 44.8%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 44.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 44.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 44.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 44.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 44.8%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around 0 37.3%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   8. Simplified 37.3%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if -2.7000000000000001e72 < x < -4.1999999999999998e-81

   1. Initial program 33.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 31.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 31.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 31.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 31.4%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 31.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 31.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 31.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 31.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 31.4%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 31.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 37.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 37.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 37.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 37.7%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 37.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 37.7%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 37.7%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around 0 28.4%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 28.4%

         \[\leadsto y1 \cdot \color{blue}{\left(-j \cdot \left(y3 \cdot y4\right)\right)} \]

      2. *-commutative 28.4%

         \[\leadsto y1 \cdot \left(-j \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

      3. distribute-rgt-neg-in 28.4%

         \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-y4 \cdot y3\right)\right)} \]

      4. distribute-rgt-neg-in 28.4%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(y4 \cdot \left(-y3\right)\right)}\right) \]

   10. Simplified 28.4%

       \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)} \]

   if -4.1999999999999998e-81 < x < -6.50000000000000017e-199

   1. Initial program 42.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 42.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 42.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 42.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 42.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 42.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 42.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 42.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 42.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 42.8%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 42.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in k around inf 51.1%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      2. mul-1-neg 51.1%

         \[\leadsto y1 \cdot \left(k \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      3. unsub-neg 51.1%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)}\right) \]

   7. Simplified 51.1%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   8. Taylor expanded in y2 around 0 42.7%

      \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(-1 \cdot \left(i \cdot z\right)\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 42.7%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(-i \cdot z\right)}\right) \]

      2. distribute-rgt-neg-in 42.7%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(i \cdot \left(-z\right)\right)}\right) \]

   10. Simplified 42.7%

       \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(i \cdot \left(-z\right)\right)}\right) \]

   if -6.50000000000000017e-199 < x < 1.32e-68

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 43.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 43.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 43.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 43.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 43.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 43.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 43.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 43.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 43.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 43.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in k around inf 31.6%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 31.6%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      2. mul-1-neg 31.6%

         \[\leadsto y1 \cdot \left(k \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      3. unsub-neg 31.6%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)}\right) \]

   7. Simplified 31.6%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   8. Taylor expanded in y2 around inf 30.0%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]

   if 2.9999999999999999e144 < x

   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 y1 around inf 39.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 39.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 39.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 39.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 48.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 48.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 53.0%

      \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]

   10. Simplified 53.0%

       \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-199}:\\ \;\;\;\;y1 \cdot \left(\left(z \cdot i\right) \cdot \left(-k\right)\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-68}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+144}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 34: 21.7% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \mathbf{if}\;j \leq -3.1 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+218}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* (* x j) y1))))
   (if (<= j -3.1e+89)
     t_1
     (if (<= j 5.5e-76)
       (* c (* x (* y0 y2)))
       (if (<= j 1.2e+114)
         (* a (* (* x y) b))
         (if (<= j 1.6e+218) (* b (* t (* j y4))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * ((x * j) * y1);
	double tmp;
	if (j <= -3.1e+89) {
		tmp = t_1;
	} else if (j <= 5.5e-76) {
		tmp = c * (x * (y0 * y2));
	} else if (j <= 1.2e+114) {
		tmp = a * ((x * y) * b);
	} else if (j <= 1.6e+218) {
		tmp = b * (t * (j * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((x * j) * y1)
    if (j <= (-3.1d+89)) then
        tmp = t_1
    else if (j <= 5.5d-76) then
        tmp = c * (x * (y0 * y2))
    else if (j <= 1.2d+114) then
        tmp = a * ((x * y) * b)
    else if (j <= 1.6d+218) then
        tmp = b * (t * (j * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * ((x * j) * y1);
	double tmp;
	if (j <= -3.1e+89) {
		tmp = t_1;
	} else if (j <= 5.5e-76) {
		tmp = c * (x * (y0 * y2));
	} else if (j <= 1.2e+114) {
		tmp = a * ((x * y) * b);
	} else if (j <= 1.6e+218) {
		tmp = b * (t * (j * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * ((x * j) * y1)
	tmp = 0
	if j <= -3.1e+89:
		tmp = t_1
	elif j <= 5.5e-76:
		tmp = c * (x * (y0 * y2))
	elif j <= 1.2e+114:
		tmp = a * ((x * y) * b)
	elif j <= 1.6e+218:
		tmp = b * (t * (j * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(Float64(x * j) * y1))
	tmp = 0.0
	if (j <= -3.1e+89)
		tmp = t_1;
	elseif (j <= 5.5e-76)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (j <= 1.2e+114)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (j <= 1.6e+218)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * ((x * j) * y1);
	tmp = 0.0;
	if (j <= -3.1e+89)
		tmp = t_1;
	elseif (j <= 5.5e-76)
		tmp = c * (x * (y0 * y2));
	elseif (j <= 1.2e+114)
		tmp = a * ((x * y) * b);
	elseif (j <= 1.6e+218)
		tmp = b * (t * (j * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(N[(x * j), $MachinePrecision] * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.1e+89], t$95$1, If[LessEqual[j, 5.5e-76], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.2e+114], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.6e+218], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.1e89 or 1.59999999999999994e218 < j

   1. Initial program 20.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around inf 36.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.3%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 36.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 36.3%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 36.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 36.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 36.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 36.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 36.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 36.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 55.1%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 55.1%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 55.1%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 55.1%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 55.1%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 55.1%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 55.1%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 39.9%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 44.2%

         \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

      2. *-commutative 44.2%

         \[\leadsto i \cdot \left(\color{blue}{\left(x \cdot j\right)} \cdot y1\right) \]

   10. Simplified 44.2%

       \[\leadsto \color{blue}{i \cdot \left(\left(x \cdot j\right) \cdot y1\right)} \]

   if -3.1e89 < j < 5.50000000000000014e-76

   1. Initial program 40.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 41.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 31.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 31.8%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 31.8%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 31.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 31.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 31.8%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 31.8%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 31.8%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around 0 26.1%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 26.1%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   8. Simplified 26.1%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if 5.50000000000000014e-76 < j < 1.2e114

   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 x around inf 41.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around 0 31.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   4. Taylor expanded in b around inf 31.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if 1.2e114 < j < 1.59999999999999994e218

   1. Initial program 20.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 41.1%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 41.1%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]

   6. Taylor expanded in y4 around inf 28.3%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 28.3%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   8. Simplified 28.3%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Taylor expanded in j around 0 28.3%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 28.3%

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       2. associate-*r* 47.5%

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]

   11. Simplified 47.5%

       \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.1 \cdot 10^{+89}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+218}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(x \cdot j\right) \cdot y1\right)\\ \end{array} \]

Alternative 35: 21.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -53000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-67}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (* y0 y2)))))
   (if (<= x -53000000000000.0)
     t_1
     (if (<= x 5.5e-67)
       (* k (* y1 (* y2 y4)))
       (if (<= x 7.6e+146) t_1 (* i (* j (* x y1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (x <= -53000000000000.0) {
		tmp = t_1;
	} else if (x <= 5.5e-67) {
		tmp = k * (y1 * (y2 * y4));
	} else if (x <= 7.6e+146) {
		tmp = t_1;
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (x * (y0 * y2))
    if (x <= (-53000000000000.0d0)) then
        tmp = t_1
    else if (x <= 5.5d-67) then
        tmp = k * (y1 * (y2 * y4))
    else if (x <= 7.6d+146) then
        tmp = t_1
    else
        tmp = i * (j * (x * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (x <= -53000000000000.0) {
		tmp = t_1;
	} else if (x <= 5.5e-67) {
		tmp = k * (y1 * (y2 * y4));
	} else if (x <= 7.6e+146) {
		tmp = t_1;
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (x * (y0 * y2))
	tmp = 0
	if x <= -53000000000000.0:
		tmp = t_1
	elif x <= 5.5e-67:
		tmp = k * (y1 * (y2 * y4))
	elif x <= 7.6e+146:
		tmp = t_1
	else:
		tmp = i * (j * (x * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(x * Float64(y0 * y2)))
	tmp = 0.0
	if (x <= -53000000000000.0)
		tmp = t_1;
	elseif (x <= 5.5e-67)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (x <= 7.6e+146)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (x * (y0 * y2));
	tmp = 0.0;
	if (x <= -53000000000000.0)
		tmp = t_1;
	elseif (x <= 5.5e-67)
		tmp = k * (y1 * (y2 * y4));
	elseif (x <= 7.6e+146)
		tmp = t_1;
	else
		tmp = i * (j * (x * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -53000000000000.0], t$95$1, If[LessEqual[x, 5.5e-67], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.6e+146], t$95$1, N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.3e13 or 5.5000000000000003e-67 < x < 7.59999999999999958e146

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 48.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 43.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 43.5%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 43.5%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 43.5%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 43.5%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 43.5%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 43.5%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around 0 34.4%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 34.4%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if -5.3e13 < x < 5.5000000000000003e-67

   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 y1 around inf 42.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 42.3%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 42.3%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 42.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in k around inf 34.0%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 34.0%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      2. mul-1-neg 34.0%

         \[\leadsto y1 \cdot \left(k \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      3. unsub-neg 34.0%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)}\right) \]

   7. Simplified 34.0%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   8. Taylor expanded in y2 around inf 25.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 7.59999999999999958e146 < x

   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 y1 around inf 39.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 39.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 39.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 39.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 48.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 48.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 48.9%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 48.9%

         \[\leadsto i \cdot \color{blue}{\left(\left(x \cdot y1\right) \cdot j\right)} \]

      2. *-commutative 48.9%

         \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot x\right)} \cdot j\right) \]

   10. Simplified 48.9%

       \[\leadsto \color{blue}{i \cdot \left(\left(y1 \cdot x\right) \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -53000000000000:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-67}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+146}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]

Alternative 36: 21.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -4150000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-67}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (* y0 y2)))))
   (if (<= x -4150000000000.0)
     t_1
     (if (<= x 1.1e-67)
       (* k (* y1 (* y2 y4)))
       (if (<= x 1.75e+147) t_1 (* y1 (* j (* x 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 * (x * (y0 * y2));
	double tmp;
	if (x <= -4150000000000.0) {
		tmp = t_1;
	} else if (x <= 1.1e-67) {
		tmp = k * (y1 * (y2 * y4));
	} else if (x <= 1.75e+147) {
		tmp = t_1;
	} else {
		tmp = y1 * (j * (x * 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 * (x * (y0 * y2))
    if (x <= (-4150000000000.0d0)) then
        tmp = t_1
    else if (x <= 1.1d-67) then
        tmp = k * (y1 * (y2 * y4))
    else if (x <= 1.75d+147) then
        tmp = t_1
    else
        tmp = y1 * (j * (x * 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 * (x * (y0 * y2));
	double tmp;
	if (x <= -4150000000000.0) {
		tmp = t_1;
	} else if (x <= 1.1e-67) {
		tmp = k * (y1 * (y2 * y4));
	} else if (x <= 1.75e+147) {
		tmp = t_1;
	} else {
		tmp = y1 * (j * (x * 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 * (x * (y0 * y2))
	tmp = 0
	if x <= -4150000000000.0:
		tmp = t_1
	elif x <= 1.1e-67:
		tmp = k * (y1 * (y2 * y4))
	elif x <= 1.75e+147:
		tmp = t_1
	else:
		tmp = y1 * (j * (x * 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(x * Float64(y0 * y2)))
	tmp = 0.0
	if (x <= -4150000000000.0)
		tmp = t_1;
	elseif (x <= 1.1e-67)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (x <= 1.75e+147)
		tmp = t_1;
	else
		tmp = Float64(y1 * Float64(j * Float64(x * 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 * (x * (y0 * y2));
	tmp = 0.0;
	if (x <= -4150000000000.0)
		tmp = t_1;
	elseif (x <= 1.1e-67)
		tmp = k * (y1 * (y2 * y4));
	elseif (x <= 1.75e+147)
		tmp = t_1;
	else
		tmp = y1 * (j * (x * 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[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4150000000000.0], t$95$1, If[LessEqual[x, 1.1e-67], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e+147], t$95$1, N[(y1 * N[(j * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.15e12 or 1.1000000000000001e-67 < x < 1.74999999999999987e147

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 48.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 43.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 43.5%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 43.5%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 43.5%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 43.5%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 43.5%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 43.5%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around 0 34.4%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 34.4%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if -4.15e12 < x < 1.1000000000000001e-67

   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 y1 around inf 42.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 42.3%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 42.3%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 42.3%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 42.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in k around inf 34.0%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 34.0%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      2. mul-1-neg 34.0%

         \[\leadsto y1 \cdot \left(k \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      3. unsub-neg 34.0%

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)}\right) \]

   7. Simplified 34.0%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   8. Taylor expanded in y2 around inf 25.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 1.74999999999999987e147 < x

   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 y1 around inf 39.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 39.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 39.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 39.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   4. Simplified 39.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   5. Taylor expanded in j around inf 48.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 48.5%

         \[\leadsto y1 \cdot \left(j \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 48.5%

      \[\leadsto y1 \cdot \color{blue}{\left(j \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 53.0%

      \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(i \cdot x\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]

   10. Simplified 53.0%

       \[\leadsto y1 \cdot \left(j \cdot \color{blue}{\left(x \cdot i\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4150000000000:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-67}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+147}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 37: 21.6% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.2 \cdot 10^{+197} \lor \neg \left(y4 \leq 5.8 \cdot 10^{+118}\right):\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y4 -1.2e+197) (not (<= y4 5.8e+118)))
   (* b (* j (* t y4)))
   (* a (* (* x y) b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y4 <= -1.2e+197) || !(y4 <= 5.8e+118)) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y4 <= (-1.2d+197)) .or. (.not. (y4 <= 5.8d+118))) then
        tmp = b * (j * (t * y4))
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y4 <= -1.2e+197) || !(y4 <= 5.8e+118)) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y4 <= -1.2e+197) or not (y4 <= 5.8e+118):
		tmp = b * (j * (t * y4))
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y4 <= -1.2e+197) || !(y4 <= 5.8e+118))
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y4 <= -1.2e+197) || ~((y4 <= 5.8e+118)))
		tmp = b * (j * (t * y4));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y4, -1.2e+197], N[Not[LessEqual[y4, 5.8e+118]], $MachinePrecision]], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y4 < -1.1999999999999999e197 or 5.80000000000000032e118 < y4

   1. Initial program 18.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 33.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 48.2%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 48.2%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]

   6. Taylor expanded in y4 around inf 36.4%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 36.4%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   8. Simplified 36.4%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   if -1.1999999999999999e197 < y4 < 5.80000000000000032e118

   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 x around inf 42.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around 0 39.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   4. Taylor expanded in b around inf 15.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 20.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.2 \cdot 10^{+197} \lor \neg \left(y4 \leq 5.8 \cdot 10^{+118}\right):\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]

Alternative 38: 21.6% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1 \cdot 10^{+197}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 1.4 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1e+197)
   (* b (* j (* t y4)))
   (if (<= y4 1.4e+121) (* a (* (* x y) b)) (* b (* t (* j y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1e+197) {
		tmp = b * (j * (t * y4));
	} else if (y4 <= 1.4e+121) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = b * (t * (j * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1d+197)) then
        tmp = b * (j * (t * y4))
    else if (y4 <= 1.4d+121) then
        tmp = a * ((x * y) * b)
    else
        tmp = b * (t * (j * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1e+197) {
		tmp = b * (j * (t * y4));
	} else if (y4 <= 1.4e+121) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = b * (t * (j * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1e+197:
		tmp = b * (j * (t * y4))
	elif y4 <= 1.4e+121:
		tmp = a * ((x * y) * b)
	else:
		tmp = b * (t * (j * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1e+197)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y4 <= 1.4e+121)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1e+197)
		tmp = b * (j * (t * y4));
	elseif (y4 <= 1.4e+121)
		tmp = a * ((x * y) * b);
	else
		tmp = b * (t * (j * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1e+197], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.4e+121], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -9.9999999999999995e196

   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 b around inf 35.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 56.9%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.9%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 56.9%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]

   6. Taylor expanded in y4 around inf 48.6%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 48.6%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   8. Simplified 48.6%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   if -9.9999999999999995e196 < y4 < 1.40000000000000003e121

   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 x around inf 42.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around 0 39.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   4. Taylor expanded in b around inf 15.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if 1.40000000000000003e121 < y4

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf 31.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 43.5%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 43.5%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]

   6. Taylor expanded in y4 around inf 29.6%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 29.6%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   8. Simplified 29.6%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Taylor expanded in j around 0 29.6%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 29.6%

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       2. associate-*r* 34.2%

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]

   11. Simplified 34.2%

       \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 21.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1 \cdot 10^{+197}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 1.4 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \]

Alternative 39: 18.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+176}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -1.5e+176)
   (* b (* t (* j y4)))
   (if (<= a 1.8e+50) (* c (* x (* y0 y2))) (* a (* (* x y) b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -1.5e+176) {
		tmp = b * (t * (j * y4));
	} else if (a <= 1.8e+50) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-1.5d+176)) then
        tmp = b * (t * (j * y4))
    else if (a <= 1.8d+50) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -1.5e+176) {
		tmp = b * (t * (j * y4));
	} else if (a <= 1.8e+50) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -1.5e+176:
		tmp = b * (t * (j * y4))
	elif a <= 1.8e+50:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (a <= -1.5e+176)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	elseif (a <= 1.8e+50)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -1.5e+176)
		tmp = b * (t * (j * y4));
	elseif (a <= 1.8e+50)
		tmp = c * (x * (y0 * y2));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -1.5e+176], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+50], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5e176

   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 b around inf 30.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. Taylor expanded in j around inf 40.9%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 40.9%

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{y4 \cdot t} - x \cdot y0\right)\right) \]

   5. Simplified 40.9%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t - x \cdot y0\right)\right)} \]

   6. Taylor expanded in y4 around inf 31.0%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 31.0%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   8. Simplified 31.0%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Taylor expanded in j around 0 31.0%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 31.0%

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       2. associate-*r* 31.3%

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]

   11. Simplified 31.3%

       \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]

   if -1.5e176 < a < 1.79999999999999993e50

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 40.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in c around -inf 32.9%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 32.9%

         \[\leadsto \color{blue}{-c \cdot \left(x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in 32.9%

         \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]

      3. +-commutative 32.9%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y + -1 \cdot \left(y0 \cdot y2\right)\right)}\right) \]

      4. mul-1-neg 32.9%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y + \color{blue}{\left(-y0 \cdot y2\right)}\right)\right) \]

      5. unsub-neg 32.9%

         \[\leadsto c \cdot \left(-x \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

      6. *-commutative 32.9%

         \[\leadsto c \cdot \left(-x \cdot \left(i \cdot y - \color{blue}{y2 \cdot y0}\right)\right) \]

   5. Simplified 32.9%

      \[\leadsto \color{blue}{c \cdot \left(-x \cdot \left(i \cdot y - y2 \cdot y0\right)\right)} \]

   6. Taylor expanded in i around 0 26.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 26.5%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   8. Simplified 26.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if 1.79999999999999993e50 < a

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf 49.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   3. Taylor expanded in j around 0 46.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   4. Taylor expanded in b around inf 25.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 26.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+176}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]

Alternative 40: 16.8% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 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 x around inf 41.3%

   \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

3. Taylor expanded in j around 0 37.3%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

4. Taylor expanded in b around inf 14.3%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

5. Final simplification 14.3%

   \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]

Developer target: 27.4% 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 2023318 
(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)))))