Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.6% → 37.1%

Time: 1.7min

Alternatives: 37

Speedup: 5.5×

• 89.0% 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: 30.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 37.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\\ t_3 := y4 \cdot \left(\left(b \cdot t_1 + t_2\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -5.5 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -2.2 \cdot 10^{+115}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -1.54 \cdot 10^{+57}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -4.9 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y1 \leq -5.2 \cdot 10^{-45}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -8 \cdot 10^{-290}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 7 \cdot 10^{-41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y1 \leq 7.2 \cdot 10^{+79}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.12 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.9 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 9.2 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (* y1 (- (* k y2) (* j y3))))
        (t_3 (* y4 (+ (+ (* b t_1) t_2) (* c (- (* y y3) (* t y2)))))))
   (if (<= y1 -5.5e+173)
     (* j (* y1 (- (* x i) (* y3 y4))))
     (if (<= y1 -2.2e+115)
       (* k (* i (- (* y y5) (* z y1))))
       (if (<= y1 -1.54e+57)
         (*
          y2
          (+
           (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= y1 -4.9e-16)
           t_3
           (if (<= y1 -5.2e-45)
             (*
              i
              (+
               (* c (- (* z t) (* x y)))
               (+ (* y1 (- (* x j) (* z k))) (* y5 (- (* y k) (* t j))))))
             (if (<= y1 -8e-290)
               (*
                b
                (+
                 (+ (* a (- (* x y) (* z t))) (* y4 t_1))
                 (* y0 (- (* z k) (* x j)))))
               (if (<= y1 7e-41)
                 t_3
                 (if (<= y1 7.2e+79)
                   (* y0 (* c (- (* x y2) (* z y3))))
                   (if (<= y1 1.12e+105)
                     (* j (* x (- (* i y1) (* b y0))))
                     (if (<= y1 1.9e+130)
                       (* y (* y3 (- (* c y4) (* a y5))))
                       (if (<= y1 9.2e+155)
                         (* j (* y0 (- (* y3 y5) (* x b))))
                         (* y4 t_2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = y1 * ((k * y2) - (j * y3));
	double t_3 = y4 * (((b * t_1) + t_2) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y1 <= -5.5e+173) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -2.2e+115) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y1 <= -1.54e+57) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y1 <= -4.9e-16) {
		tmp = t_3;
	} else if (y1 <= -5.2e-45) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	} else if (y1 <= -8e-290) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 7e-41) {
		tmp = t_3;
	} else if (y1 <= 7.2e+79) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (y1 <= 1.12e+105) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= 1.9e+130) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (y1 <= 9.2e+155) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y4 * t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = y1 * ((k * y2) - (j * y3))
    t_3 = y4 * (((b * t_1) + t_2) + (c * ((y * y3) - (t * y2))))
    if (y1 <= (-5.5d+173)) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (y1 <= (-2.2d+115)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (y1 <= (-1.54d+57)) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y1 <= (-4.9d-16)) then
        tmp = t_3
    else if (y1 <= (-5.2d-45)) then
        tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))))
    else if (y1 <= (-8d-290)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
    else if (y1 <= 7d-41) then
        tmp = t_3
    else if (y1 <= 7.2d+79) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (y1 <= 1.12d+105) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y1 <= 1.9d+130) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else if (y1 <= 9.2d+155) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = y4 * t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = y1 * ((k * y2) - (j * y3));
	double t_3 = y4 * (((b * t_1) + t_2) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y1 <= -5.5e+173) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -2.2e+115) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y1 <= -1.54e+57) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y1 <= -4.9e-16) {
		tmp = t_3;
	} else if (y1 <= -5.2e-45) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	} else if (y1 <= -8e-290) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 7e-41) {
		tmp = t_3;
	} else if (y1 <= 7.2e+79) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (y1 <= 1.12e+105) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= 1.9e+130) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (y1 <= 9.2e+155) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y4 * t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = y1 * ((k * y2) - (j * y3))
	t_3 = y4 * (((b * t_1) + t_2) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y1 <= -5.5e+173:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif y1 <= -2.2e+115:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif y1 <= -1.54e+57:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y1 <= -4.9e-16:
		tmp = t_3
	elif y1 <= -5.2e-45:
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))))
	elif y1 <= -8e-290:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
	elif y1 <= 7e-41:
		tmp = t_3
	elif y1 <= 7.2e+79:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif y1 <= 1.12e+105:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y1 <= 1.9e+130:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	elif y1 <= 9.2e+155:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = y4 * t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))
	t_3 = Float64(y4 * Float64(Float64(Float64(b * t_1) + t_2) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y1 <= -5.5e+173)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y1 <= -2.2e+115)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (y1 <= -1.54e+57)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y1 <= -4.9e-16)
		tmp = t_3;
	elseif (y1 <= -5.2e-45)
		tmp = Float64(i * Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))));
	elseif (y1 <= -8e-290)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y1 <= 7e-41)
		tmp = t_3;
	elseif (y1 <= 7.2e+79)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y1 <= 1.12e+105)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y1 <= 1.9e+130)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (y1 <= 9.2e+155)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(y4 * t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = y1 * ((k * y2) - (j * y3));
	t_3 = y4 * (((b * t_1) + t_2) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y1 <= -5.5e+173)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (y1 <= -2.2e+115)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (y1 <= -1.54e+57)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y1 <= -4.9e-16)
		tmp = t_3;
	elseif (y1 <= -5.2e-45)
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	elseif (y1 <= -8e-290)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	elseif (y1 <= 7e-41)
		tmp = t_3;
	elseif (y1 <= 7.2e+79)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (y1 <= 1.12e+105)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y1 <= 1.9e+130)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	elseif (y1 <= 9.2e+155)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = y4 * t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -5.5e+173], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.2e+115], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.54e+57], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -4.9e-16], t$95$3, If[LessEqual[y1, -5.2e-45], N[(i * N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -8e-290], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7e-41], t$95$3, If[LessEqual[y1, 7.2e+79], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.12e+105], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.9e+130], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9.2e+155], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * t$95$2), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y1 < -5.50000000000000049e173

   1. Initial program 12.2%

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

      1. +-commutative 12.2%

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

      2. fma-def 12.2%

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

      3. *-commutative 12.2%

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

      4. *-commutative 12.2%

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

   3. Simplified 16.2%

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

   4. Taylor expanded in j around inf 48.3%

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

   5. Taylor expanded in y1 around -inf 57.3%

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

      1. associate-*r* 57.3%

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

      2. neg-mul-1 57.3%

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

   7. Simplified 57.3%

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

   if -5.50000000000000049e173 < y1 < -2.2e115

   1. Initial program 7.6%

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

      1. +-commutative 7.6%

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

      2. fma-def 7.6%

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

      3. *-commutative 7.6%

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

      4. *-commutative 7.6%

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

   3. Simplified 7.6%

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

   4. Taylor expanded in k around inf 46.0%

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

   5. Taylor expanded in i around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. sub-neg 76.9%

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

      3. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -2.2e115 < y1 < -1.54e57

   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. Step-by-step derivation

      1. associate-+l- 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y2 around inf 73.9%

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

   if -1.54e57 < y1 < -4.89999999999999975e-16 or -8.0000000000000006e-290 < y1 < 6.9999999999999999e-41

   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. Step-by-step derivation

      1. associate-+l- 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in y4 around inf 61.1%

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

   if -4.89999999999999975e-16 < y1 < -5.19999999999999973e-45

   1. Initial program 51.0%

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

      1. associate-+l- 51.0%

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

   3. Simplified 51.0%

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

   4. Taylor expanded in i around -inf 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate--l+ 51.6%

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

   6. Simplified 51.6%

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

   if -5.19999999999999973e-45 < y1 < -8.0000000000000006e-290

   1. Initial program 27.7%

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

      1. associate-+l- 27.7%

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

   3. Simplified 27.7%

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

   4. Taylor expanded in b around inf 53.7%

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

   if 6.9999999999999999e-41 < y1 < 7.1999999999999999e79

   1. Initial program 17.2%

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

      1. +-commutative 17.2%

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

      2. fma-def 20.7%

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

      3. *-commutative 20.7%

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

      4. *-commutative 20.7%

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

   3. Simplified 20.7%

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

   4. Taylor expanded in y0 around inf 38.7%

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

      1. mul-1-neg 38.7%

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

   6. Simplified 38.7%

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

   7. Taylor expanded in c around inf 43.0%

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

      1. *-commutative 43.0%

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

      2. *-commutative 43.0%

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

      3. associate-*l* 42.8%

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

      4. *-commutative 42.8%

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

   9. Simplified 42.8%

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

   if 7.1999999999999999e79 < y1 < 1.12e105

   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. Step-by-step derivation

      1. +-commutative 50.0%

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

      2. fma-def 50.0%

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

      3. *-commutative 50.0%

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

      4. *-commutative 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in j around inf 83.3%

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

   5. Taylor expanded in x around inf 100.0%

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

   if 1.12e105 < y1 < 1.9000000000000001e130

   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. Step-by-step derivation

      1. associate-+l- 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in y3 around -inf 72.5%

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

   5. Taylor expanded in y around inf 72.4%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(a \cdot y5 - c \cdot y4\right) \cdot \left(y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 72.4%

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

      2. associate-*l* 85.9%

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

   7. Simplified 85.9%

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

   if 1.9000000000000001e130 < y1 < 9.19999999999999992e155

   1. Initial program 30.0%

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

      1. +-commutative 30.0%

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

      2. fma-def 30.0%

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

      3. *-commutative 30.0%

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

      4. *-commutative 30.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in j around inf 51.3%

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

   5. Taylor expanded in y0 around inf 61.1%

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

      1. *-commutative 61.1%

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

   7. Simplified 61.1%

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

   if 9.19999999999999992e155 < y1

   1. Initial program 25.0%

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

      1. associate-+l- 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in y4 around inf 55.2%

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

   5. Taylor expanded in y1 around inf 75.4%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -5.5 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -2.2 \cdot 10^{+115}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -1.54 \cdot 10^{+57}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -4.9 \cdot 10^{-16}:\\ \;\;\;\;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 -5.2 \cdot 10^{-45}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -8 \cdot 10^{-290}:\\ \;\;\;\;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}\;y1 \leq 7 \cdot 10^{-41}:\\ \;\;\;\;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 7.2 \cdot 10^{+79}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.12 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.9 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 9.2 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]

Alternative 2: 53.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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. Step-by-step derivation

      1. +-commutative 0.0%

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

      2. fma-def 1.1%

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

      3. *-commutative 1.1%

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

      4. *-commutative 1.1%

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

   3. Simplified 4.6%

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

   4. Taylor expanded in j around inf 38.9%

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

4. Final simplification 55.3%

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

Alternative 3: 34.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2\right)\right)\right)\\ t_2 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+137}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(j \cdot y1 - y \cdot c\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-232}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-211}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-186}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-183}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-157}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-32}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+48}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          a
          (+
           (* y5 (- (* t y2) (* y y3)))
           (- (* b (- (* x y) (* z t))) (* y1 (* x y2))))))
        (t_2 (* j (* x (- (* i y1) (* b y0))))))
   (if (<= x -2.9e+137)
     (* (* x i) (- (* j y1) (* y c)))
     (if (<= x -4e-253)
       t_1
       (if (<= x -9e-305)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= x 1.1e-232)
           (* c (* y4 (- (* y y3) (* t y2))))
           (if (<= x 2e-211)
             (* (* t j) (- (* b y4) (* i y5)))
             (if (<= x 1.5e-186)
               (* j (* y4 (* y1 (- y3))))
               (if (<= x 4.4e-183)
                 (* y4 (* t (- (* b j) (* c y2))))
                 (if (<= x 1.15e-157)
                   (* y0 (* c (- (* x y2) (* z y3))))
                   (if (<= x 4.4e-32)
                     (* y0 (* y3 (- (* j y5) (* z c))))
                     (if (<= x 3.1e+30)
                       t_2
                       (if (<= x 1.25e+48)
                         (* (* y y3) (- (* c y4) (* a y5)))
                         (if (<= x 4.3e+99) t_1 t_2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))));
	double t_2 = j * (x * ((i * y1) - (b * y0)));
	double tmp;
	if (x <= -2.9e+137) {
		tmp = (x * i) * ((j * y1) - (y * c));
	} else if (x <= -4e-253) {
		tmp = t_1;
	} else if (x <= -9e-305) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (x <= 1.1e-232) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (x <= 2e-211) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 1.5e-186) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (x <= 4.4e-183) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (x <= 1.15e-157) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (x <= 4.4e-32) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (x <= 3.1e+30) {
		tmp = t_2;
	} else if (x <= 1.25e+48) {
		tmp = (y * y3) * ((c * y4) - (a * y5));
	} else if (x <= 4.3e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))))
    t_2 = j * (x * ((i * y1) - (b * y0)))
    if (x <= (-2.9d+137)) then
        tmp = (x * i) * ((j * y1) - (y * c))
    else if (x <= (-4d-253)) then
        tmp = t_1
    else if (x <= (-9d-305)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (x <= 1.1d-232) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (x <= 2d-211) then
        tmp = (t * j) * ((b * y4) - (i * y5))
    else if (x <= 1.5d-186) then
        tmp = j * (y4 * (y1 * -y3))
    else if (x <= 4.4d-183) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (x <= 1.15d-157) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (x <= 4.4d-32) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (x <= 3.1d+30) then
        tmp = t_2
    else if (x <= 1.25d+48) then
        tmp = (y * y3) * ((c * y4) - (a * y5))
    else if (x <= 4.3d+99) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))));
	double t_2 = j * (x * ((i * y1) - (b * y0)));
	double tmp;
	if (x <= -2.9e+137) {
		tmp = (x * i) * ((j * y1) - (y * c));
	} else if (x <= -4e-253) {
		tmp = t_1;
	} else if (x <= -9e-305) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (x <= 1.1e-232) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (x <= 2e-211) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 1.5e-186) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (x <= 4.4e-183) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (x <= 1.15e-157) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (x <= 4.4e-32) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (x <= 3.1e+30) {
		tmp = t_2;
	} else if (x <= 1.25e+48) {
		tmp = (y * y3) * ((c * y4) - (a * y5));
	} else if (x <= 4.3e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))))
	t_2 = j * (x * ((i * y1) - (b * y0)))
	tmp = 0
	if x <= -2.9e+137:
		tmp = (x * i) * ((j * y1) - (y * c))
	elif x <= -4e-253:
		tmp = t_1
	elif x <= -9e-305:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif x <= 1.1e-232:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif x <= 2e-211:
		tmp = (t * j) * ((b * y4) - (i * y5))
	elif x <= 1.5e-186:
		tmp = j * (y4 * (y1 * -y3))
	elif x <= 4.4e-183:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif x <= 1.15e-157:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif x <= 4.4e-32:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif x <= 3.1e+30:
		tmp = t_2
	elif x <= 1.25e+48:
		tmp = (y * y3) * ((c * y4) - (a * y5))
	elif x <= 4.3e+99:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) - Float64(y1 * Float64(x * y2)))))
	t_2 = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))))
	tmp = 0.0
	if (x <= -2.9e+137)
		tmp = Float64(Float64(x * i) * Float64(Float64(j * y1) - Float64(y * c)));
	elseif (x <= -4e-253)
		tmp = t_1;
	elseif (x <= -9e-305)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (x <= 1.1e-232)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (x <= 2e-211)
		tmp = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)));
	elseif (x <= 1.5e-186)
		tmp = Float64(j * Float64(y4 * Float64(y1 * Float64(-y3))));
	elseif (x <= 4.4e-183)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (x <= 1.15e-157)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (x <= 4.4e-32)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (x <= 3.1e+30)
		tmp = t_2;
	elseif (x <= 1.25e+48)
		tmp = Float64(Float64(y * y3) * Float64(Float64(c * y4) - Float64(a * y5)));
	elseif (x <= 4.3e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))));
	t_2 = j * (x * ((i * y1) - (b * y0)));
	tmp = 0.0;
	if (x <= -2.9e+137)
		tmp = (x * i) * ((j * y1) - (y * c));
	elseif (x <= -4e-253)
		tmp = t_1;
	elseif (x <= -9e-305)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (x <= 1.1e-232)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (x <= 2e-211)
		tmp = (t * j) * ((b * y4) - (i * y5));
	elseif (x <= 1.5e-186)
		tmp = j * (y4 * (y1 * -y3));
	elseif (x <= 4.4e-183)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (x <= 1.15e-157)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (x <= 4.4e-32)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (x <= 3.1e+30)
		tmp = t_2;
	elseif (x <= 1.25e+48)
		tmp = (y * y3) * ((c * y4) - (a * y5));
	elseif (x <= 4.3e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e+137], N[(N[(x * i), $MachinePrecision] * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e-253], t$95$1, If[LessEqual[x, -9e-305], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e-232], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-211], N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-186], N[(j * N[(y4 * N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-183], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-157], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-32], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+30], t$95$2, If[LessEqual[x, 1.25e+48], N[(N[(y * y3), $MachinePrecision] * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e+99], t$95$1, t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if x < -2.89999999999999985e137

   1. Initial program 22.5%

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

      1. associate-+l- 22.5%

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

   3. Simplified 22.5%

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

   4. Taylor expanded in i around -inf 40.2%

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

      1. mul-1-neg 40.2%

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

      2. associate--l+ 40.2%

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

   6. Simplified 40.2%

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

   7. Taylor expanded in x around inf 53.2%

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

   if -2.89999999999999985e137 < x < -4.0000000000000003e-253 or 1.24999999999999993e48 < x < 4.3000000000000001e99

   1. Initial program 29.2%

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

      1. +-commutative 29.2%

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

      2. fma-def 31.5%

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

      3. *-commutative 31.5%

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

      4. *-commutative 31.5%

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

   3. Simplified 37.1%

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

   4. Taylor expanded in x around inf 43.9%

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

      1. mul-1-neg 43.9%

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

   6. Simplified 43.9%

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

   7. Taylor expanded in a around inf 50.0%

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

   if -4.0000000000000003e-253 < x < -9.0000000000000003e-305

   1. Initial program 61.5%

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

      1. associate-+l- 61.5%

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

   3. Simplified 61.5%

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

   4. Taylor expanded in y4 around inf 62.0%

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

   5. Taylor expanded in b around inf 62.1%

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

      1. associate-*r* 62.1%

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

   7. Simplified 62.1%

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

   if -9.0000000000000003e-305 < x < 1.10000000000000001e-232

   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. Step-by-step derivation

      1. associate-+l- 29.7%

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

   3. Simplified 29.7%

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

   4. Taylor expanded in y4 around inf 59.2%

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

   5. Taylor expanded in c around inf 59.2%

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

   if 1.10000000000000001e-232 < x < 2.00000000000000017e-211

   1. Initial program 59.7%

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

      1. +-commutative 59.7%

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

      2. fma-def 59.7%

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

      3. *-commutative 59.7%

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

      4. *-commutative 59.7%

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

   3. Simplified 59.7%

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

   4. Taylor expanded in j around inf 80.2%

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

   5. Taylor expanded in t around inf 79.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 79.9%

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

   7. Simplified 79.9%

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

   if 2.00000000000000017e-211 < x < 1.5000000000000001e-186

   1. Initial program 57.1%

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

      1. +-commutative 57.1%

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

      2. fma-def 57.1%

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

      3. *-commutative 57.1%

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

      4. *-commutative 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in j around inf 85.5%

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

   5. Taylor expanded in y1 around -inf 57.5%

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

      1. associate-*r* 57.5%

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

      2. neg-mul-1 57.5%

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

   7. Simplified 57.5%

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

   8. Taylor expanded in y4 around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. distribute-rgt-neg-in 71.5%

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

   10. Simplified 71.5%

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

   if 1.5000000000000001e-186 < x < 4.3999999999999999e-183

   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. Step-by-step derivation

      1. associate-+l- 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in y4 around inf 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

   if 4.3999999999999999e-183 < x < 1.14999999999999994e-157

   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. Step-by-step derivation

      1. +-commutative 16.7%

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

      2. fma-def 16.7%

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

      3. *-commutative 16.7%

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

      4. *-commutative 16.7%

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

   3. Simplified 16.7%

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

   4. Taylor expanded in y0 around inf 33.6%

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

      1. mul-1-neg 33.6%

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

   6. Simplified 33.6%

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

   7. Taylor expanded in c around inf 50.7%

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

      1. *-commutative 50.7%

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

      2. *-commutative 50.7%

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

      3. associate-*l* 50.7%

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

      4. *-commutative 50.7%

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

   9. Simplified 50.7%

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

   if 1.14999999999999994e-157 < x < 4.4e-32

   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. Step-by-step derivation

      1. +-commutative 33.3%

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

      2. fma-def 33.3%

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

      3. *-commutative 33.3%

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

      4. *-commutative 33.3%

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

   3. Simplified 38.9%

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

   4. Taylor expanded in y0 around inf 50.7%

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

      1. mul-1-neg 50.7%

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

   6. Simplified 50.7%

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

   7. Taylor expanded in y3 around inf 67.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(c \cdot z\right) - -1 \cdot \left(j \cdot y5\right)\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 67.1%

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

      2. cancel-sign-sub-inv 67.1%

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

      3. metadata-eval 67.1%

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

      4. *-lft-identity 67.1%

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

      5. +-commutative 67.1%

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

      6. mul-1-neg 67.1%

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

      7. unsub-neg 67.1%

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

      8. *-commutative 67.1%

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

   9. Simplified 67.1%

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

   if 4.4e-32 < x < 3.0999999999999998e30 or 4.3000000000000001e99 < x

   1. Initial program 19.3%

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

      1. +-commutative 19.3%

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

      2. fma-def 19.3%

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

      3. *-commutative 19.3%

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

      4. *-commutative 19.3%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in j around inf 46.8%

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

   5. Taylor expanded in x around inf 58.2%

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

   if 3.0999999999999998e30 < x < 1.24999999999999993e48

   1. Initial program 2.6%

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

      1. associate-+l- 2.6%

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

   3. Simplified 2.6%

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

   4. Taylor expanded in y3 around -inf 50.0%

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

   5. Taylor expanded in y around inf 83.6%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(a \cdot y5 - c \cdot y4\right) \cdot \left(y \cdot y3\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+137}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(j \cdot y1 - y \cdot c\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-232}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-211}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-186}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-183}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-157}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-32}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+30}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+48}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 4: 39.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot y2 - z \cdot y3\right)\\ t_2 := j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-224}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 10^{-133}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-90}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(c \cdot y2 - b \cdot j\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-74}:\\ \;\;\;\;y0 \cdot t_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+194}:\\ \;\;\;\;y0 \cdot \left(t_1 + \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \end{array} \end{array} \]

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 y2) (* z y3))))
        (t_2
         (*
          j
          (+
           (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
           (* x (- (* i y1) (* b y0)))))))
   (if (<= z -4e+113)
     (*
      z
      (+
       (* y3 (- (* a y1) (* c y0)))
       (+ (* k (- (* b y0) (* i y1))) (* t (- (* c i) (* a b))))))
     (if (<= z -5.3e-73)
       t_2
       (if (<= z -8.4e-224)
         (*
          a
          (+
           (* b (- (* x y) (* z t)))
           (+ (* y1 (- (* z y3) (* x y2))) (* y5 (- (* t y2) (* y y3))))))
         (if (<= z 2e-179)
           t_2
           (if (<= z 1e-133)
             (*
              y4
              (+
               (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
               (* c (- (* y y3) (* t y2)))))
             (if (<= z 3.6e-90)
               (* (* x y0) (- (* c y2) (* b j)))
               (if (<= z 1.45e-74)
                 (* y0 t_1)
                 (if (<= z 4.9e+41)
                   t_2
                   (if (<= z 1.4e+194)
                     (*
                      y0
                      (+
                       t_1
                       (+
                        (* y5 (- (* j y3) (* k y2)))
                        (* b (- (* z k) (* x j))))))
                     (* k (* i (- (* y y5) (* z y1)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((x * y2) - (z * y3));
	double t_2 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (z <= -4e+113) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	} else if (z <= -5.3e-73) {
		tmp = t_2;
	} else if (z <= -8.4e-224) {
		tmp = a * ((b * ((x * y) - (z * t))) + ((y1 * ((z * y3) - (x * y2))) + (y5 * ((t * y2) - (y * y3)))));
	} else if (z <= 2e-179) {
		tmp = t_2;
	} else if (z <= 1e-133) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (z <= 3.6e-90) {
		tmp = (x * y0) * ((c * y2) - (b * j));
	} else if (z <= 1.45e-74) {
		tmp = y0 * t_1;
	} else if (z <= 4.9e+41) {
		tmp = t_2;
	} else if (z <= 1.4e+194) {
		tmp = y0 * (t_1 + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	} else {
		tmp = k * (i * ((y * y5) - (z * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((x * y2) - (z * y3))
    t_2 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
    if (z <= (-4d+113)) then
        tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
    else if (z <= (-5.3d-73)) then
        tmp = t_2
    else if (z <= (-8.4d-224)) then
        tmp = a * ((b * ((x * y) - (z * t))) + ((y1 * ((z * y3) - (x * y2))) + (y5 * ((t * y2) - (y * y3)))))
    else if (z <= 2d-179) then
        tmp = t_2
    else if (z <= 1d-133) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (z <= 3.6d-90) then
        tmp = (x * y0) * ((c * y2) - (b * j))
    else if (z <= 1.45d-74) then
        tmp = y0 * t_1
    else if (z <= 4.9d+41) then
        tmp = t_2
    else if (z <= 1.4d+194) then
        tmp = y0 * (t_1 + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))))
    else
        tmp = k * (i * ((y * y5) - (z * 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 * y2) - (z * y3));
	double t_2 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (z <= -4e+113) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	} else if (z <= -5.3e-73) {
		tmp = t_2;
	} else if (z <= -8.4e-224) {
		tmp = a * ((b * ((x * y) - (z * t))) + ((y1 * ((z * y3) - (x * y2))) + (y5 * ((t * y2) - (y * y3)))));
	} else if (z <= 2e-179) {
		tmp = t_2;
	} else if (z <= 1e-133) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (z <= 3.6e-90) {
		tmp = (x * y0) * ((c * y2) - (b * j));
	} else if (z <= 1.45e-74) {
		tmp = y0 * t_1;
	} else if (z <= 4.9e+41) {
		tmp = t_2;
	} else if (z <= 1.4e+194) {
		tmp = y0 * (t_1 + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	} else {
		tmp = k * (i * ((y * y5) - (z * 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 * y2) - (z * y3))
	t_2 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
	tmp = 0
	if z <= -4e+113:
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
	elif z <= -5.3e-73:
		tmp = t_2
	elif z <= -8.4e-224:
		tmp = a * ((b * ((x * y) - (z * t))) + ((y1 * ((z * y3) - (x * y2))) + (y5 * ((t * y2) - (y * y3)))))
	elif z <= 2e-179:
		tmp = t_2
	elif z <= 1e-133:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif z <= 3.6e-90:
		tmp = (x * y0) * ((c * y2) - (b * j))
	elif z <= 1.45e-74:
		tmp = y0 * t_1
	elif z <= 4.9e+41:
		tmp = t_2
	elif z <= 1.4e+194:
		tmp = y0 * (t_1 + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))))
	else:
		tmp = k * (i * ((y * y5) - (z * 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(Float64(x * y2) - Float64(z * y3)))
	t_2 = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (z <= -4e+113)
		tmp = Float64(z * Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * Float64(Float64(c * i) - Float64(a * b))))));
	elseif (z <= -5.3e-73)
		tmp = t_2;
	elseif (z <= -8.4e-224)
		tmp = Float64(a * Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (z <= 2e-179)
		tmp = t_2;
	elseif (z <= 1e-133)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (z <= 3.6e-90)
		tmp = Float64(Float64(x * y0) * Float64(Float64(c * y2) - Float64(b * j)));
	elseif (z <= 1.45e-74)
		tmp = Float64(y0 * t_1);
	elseif (z <= 4.9e+41)
		tmp = t_2;
	elseif (z <= 1.4e+194)
		tmp = Float64(y0 * Float64(t_1 + Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(b * Float64(Float64(z * k) - Float64(x * j))))));
	else
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * 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 * y2) - (z * y3));
	t_2 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (z <= -4e+113)
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	elseif (z <= -5.3e-73)
		tmp = t_2;
	elseif (z <= -8.4e-224)
		tmp = a * ((b * ((x * y) - (z * t))) + ((y1 * ((z * y3) - (x * y2))) + (y5 * ((t * y2) - (y * y3)))));
	elseif (z <= 2e-179)
		tmp = t_2;
	elseif (z <= 1e-133)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (z <= 3.6e-90)
		tmp = (x * y0) * ((c * y2) - (b * j));
	elseif (z <= 1.45e-74)
		tmp = y0 * t_1;
	elseif (z <= 4.9e+41)
		tmp = t_2;
	elseif (z <= 1.4e+194)
		tmp = y0 * (t_1 + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	else
		tmp = k * (i * ((y * y5) - (z * 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[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+113], N[(z * N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.3e-73], t$95$2, If[LessEqual[z, -8.4e-224], N[(a * N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-179], t$95$2, If[LessEqual[z, 1e-133], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-90], N[(N[(x * y0), $MachinePrecision] * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-74], N[(y0 * t$95$1), $MachinePrecision], If[LessEqual[z, 4.9e+41], t$95$2, If[LessEqual[z, 1.4e+194], N[(y0 * N[(t$95$1 + N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if z < -4e113

   1. Initial program 6.4%

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

      1. associate-+l- 6.4%

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

   3. Simplified 6.4%

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

   4. Taylor expanded in z around -inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. associate--l+ 64.0%

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

   6. Simplified 64.0%

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

   if -4e113 < z < -5.29999999999999972e-73 or -8.40000000000000025e-224 < z < 2e-179 or 1.45e-74 < z < 4.8999999999999999e41

   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. Step-by-step derivation

      1. +-commutative 39.6%

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

      2. fma-def 39.6%

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

      3. *-commutative 39.6%

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

      4. *-commutative 39.6%

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

   3. Simplified 40.5%

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

   4. Taylor expanded in j around inf 62.1%

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

   if -5.29999999999999972e-73 < z < -8.40000000000000025e-224

   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. Step-by-step derivation

      1. associate-+l- 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in a around inf 59.0%

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

      1. associate--l+ 59.0%

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

      2. mul-1-neg 59.0%

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

      3. mul-1-neg 59.0%

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

   6. Simplified 59.0%

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

   if 2e-179 < z < 1.0000000000000001e-133

   1. Initial program 45.5%

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

      1. associate-+l- 45.5%

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

   3. Simplified 45.5%

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

   4. Taylor expanded in y4 around inf 64.7%

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

   if 1.0000000000000001e-133 < z < 3.59999999999999981e-90

   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. Step-by-step derivation

      1. +-commutative 15.0%

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

      2. fma-def 15.0%

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

      3. *-commutative 15.0%

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

      4. *-commutative 15.0%

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

   3. Simplified 15.0%

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

   4. Taylor expanded in y0 around inf 42.6%

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

      1. mul-1-neg 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in x around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. fma-def 58.0%

         \[\leadsto y0 \cdot \left(x \cdot \color{blue}{\mathsf{fma}\left(-1, j \cdot b, c \cdot y2\right)}\right) \]

      3. *-commutative 58.0%

         \[\leadsto y0 \cdot \left(x \cdot \mathsf{fma}\left(-1, \color{blue}{b \cdot j}, c \cdot y2\right)\right) \]

      4. fma-def 58.0%

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

      5. associate-*r* 58.0%

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

      6. +-commutative 58.0%

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

      7. mul-1-neg 58.0%

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

      8. *-commutative 58.0%

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

      9. unsub-neg 58.0%

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

      10. *-commutative 58.0%

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

      11. *-commutative 58.0%

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

   9. Simplified 58.0%

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

   if 3.59999999999999981e-90 < z < 1.45e-74

   1. Initial program 2.6%

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

      1. +-commutative 2.6%

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

      2. fma-def 2.6%

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

      3. *-commutative 2.6%

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

      4. *-commutative 2.6%

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

   3. Simplified 2.6%

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

   4. Taylor expanded in y0 around inf 53.7%

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

      1. mul-1-neg 53.7%

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

   6. Simplified 53.7%

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

   7. Taylor expanded in c around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. *-commutative 68.5%

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

      3. associate-*l* 70.4%

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

      4. *-commutative 70.4%

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

   9. Simplified 70.4%

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

   if 4.8999999999999999e41 < z < 1.40000000000000005e194

   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. Step-by-step derivation

      1. +-commutative 29.0%

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

      2. fma-def 32.3%

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

      3. *-commutative 32.3%

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

      4. *-commutative 32.3%

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

   3. Simplified 38.7%

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

   4. Taylor expanded in y0 around inf 64.7%

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

      1. mul-1-neg 64.7%

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

   6. Simplified 64.7%

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

   if 1.40000000000000005e194 < z

   1. Initial program 21.4%

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

      1. +-commutative 21.4%

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

      2. fma-def 24.9%

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

      3. *-commutative 24.9%

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

      4. *-commutative 24.9%

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

   3. Simplified 24.9%

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

   4. Taylor expanded in k around inf 43.2%

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

   5. Taylor expanded in i around inf 46.9%

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

      1. mul-1-neg 46.9%

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

      2. sub-neg 46.9%

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

      3. *-commutative 46.9%

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

   7. Simplified 46.9%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-224}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 10^{-133}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-90}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(c \cdot y2 - b \cdot j\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-74}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+194}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \end{array} \]

Alternative 5: 39.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ t_2 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_3 := c \cdot y4 - a \cdot y5\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{+118}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(j \cdot y1 - y \cdot c\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+45}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-211}:\\ \;\;\;\;y3 \cdot \left(y \cdot t_3 + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-256}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-31}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot t_1 + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+154}:\\ \;\;\;\;y0 \cdot \left(c \cdot t_1 + \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot t_3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3)))
        (t_2 (* j (* x (- (* i y1) (* b y0)))))
        (t_3 (- (* c y4) (* a y5))))
   (if (<= x -1.95e+118)
     (* (* x i) (- (* j y1) (* y c)))
     (if (<= x -1.8e+45)
       (*
        y2
        (+
         (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
         (* t (- (* a y5) (* c y4)))))
       (if (<= x -5.7e-211)
         (*
          y3
          (+
           (* y t_3)
           (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))))
         (if (<= x 3.4e-256)
           (*
            y1
            (+
             (* a (- (* z y3) (* x y2)))
             (+ (* i (- (* x j) (* z k))) (* y4 (- (* k y2) (* j y3))))))
           (if (<= x 1.85e-31)
             (*
              c
              (+
               (* i (- (* z t) (* x y)))
               (+ (* y0 t_1) (* y4 (- (* y y3) (* t y2))))))
             (if (<= x 2.6e+34)
               t_2
               (if (<= x 4.2e+97)
                 (*
                  a
                  (+
                   (* y5 (- (* t y2) (* y y3)))
                   (- (* b (- (* x y) (* z t))) (* y1 (* x y2)))))
                 (if (<= x 5.2e+154)
                   (*
                    y0
                    (+
                     (* c t_1)
                     (+
                      (* y5 (- (* j y3) (* k y2)))
                      (* b (- (* z k) (* x j))))))
                   (if (<= x 2.7e+164)
                     (*
                      t
                      (+
                       (* z (- (* c i) (* a b)))
                       (- (* j (- (* b y4) (* i y5))) (* y2 t_3))))
                     t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = j * (x * ((i * y1) - (b * y0)));
	double t_3 = (c * y4) - (a * y5);
	double tmp;
	if (x <= -1.95e+118) {
		tmp = (x * i) * ((j * y1) - (y * c));
	} else if (x <= -1.8e+45) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (x <= -5.7e-211) {
		tmp = y3 * ((y * t_3) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (x <= 3.4e-256) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))));
	} else if (x <= 1.85e-31) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_1) + (y4 * ((y * y3) - (t * y2)))));
	} else if (x <= 2.6e+34) {
		tmp = t_2;
	} else if (x <= 4.2e+97) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))));
	} else if (x <= 5.2e+154) {
		tmp = y0 * ((c * t_1) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	} else if (x <= 2.7e+164) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) - (y2 * t_3)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * y2) - (z * y3)
    t_2 = j * (x * ((i * y1) - (b * y0)))
    t_3 = (c * y4) - (a * y5)
    if (x <= (-1.95d+118)) then
        tmp = (x * i) * ((j * y1) - (y * c))
    else if (x <= (-1.8d+45)) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (x <= (-5.7d-211)) then
        tmp = y3 * ((y * t_3) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (x <= 3.4d-256) then
        tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))))
    else if (x <= 1.85d-31) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_1) + (y4 * ((y * y3) - (t * y2)))))
    else if (x <= 2.6d+34) then
        tmp = t_2
    else if (x <= 4.2d+97) then
        tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))))
    else if (x <= 5.2d+154) then
        tmp = y0 * ((c * t_1) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))))
    else if (x <= 2.7d+164) then
        tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) - (y2 * t_3)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = j * (x * ((i * y1) - (b * y0)));
	double t_3 = (c * y4) - (a * y5);
	double tmp;
	if (x <= -1.95e+118) {
		tmp = (x * i) * ((j * y1) - (y * c));
	} else if (x <= -1.8e+45) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (x <= -5.7e-211) {
		tmp = y3 * ((y * t_3) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (x <= 3.4e-256) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))));
	} else if (x <= 1.85e-31) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_1) + (y4 * ((y * y3) - (t * y2)))));
	} else if (x <= 2.6e+34) {
		tmp = t_2;
	} else if (x <= 4.2e+97) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))));
	} else if (x <= 5.2e+154) {
		tmp = y0 * ((c * t_1) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	} else if (x <= 2.7e+164) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) - (y2 * t_3)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y2) - (z * y3)
	t_2 = j * (x * ((i * y1) - (b * y0)))
	t_3 = (c * y4) - (a * y5)
	tmp = 0
	if x <= -1.95e+118:
		tmp = (x * i) * ((j * y1) - (y * c))
	elif x <= -1.8e+45:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif x <= -5.7e-211:
		tmp = y3 * ((y * t_3) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif x <= 3.4e-256:
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))))
	elif x <= 1.85e-31:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_1) + (y4 * ((y * y3) - (t * y2)))))
	elif x <= 2.6e+34:
		tmp = t_2
	elif x <= 4.2e+97:
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))))
	elif x <= 5.2e+154:
		tmp = y0 * ((c * t_1) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))))
	elif x <= 2.7e+164:
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) - (y2 * t_3)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y2) - Float64(z * y3))
	t_2 = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))))
	t_3 = Float64(Float64(c * y4) - Float64(a * y5))
	tmp = 0.0
	if (x <= -1.95e+118)
		tmp = Float64(Float64(x * i) * Float64(Float64(j * y1) - Float64(y * c)));
	elseif (x <= -1.8e+45)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (x <= -5.7e-211)
		tmp = Float64(y3 * Float64(Float64(y * t_3) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (x <= 3.4e-256)
		tmp = Float64(y1 * Float64(Float64(a * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))))));
	elseif (x <= 1.85e-31)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * t_1) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))));
	elseif (x <= 2.6e+34)
		tmp = t_2;
	elseif (x <= 4.2e+97)
		tmp = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) - Float64(y1 * Float64(x * y2)))));
	elseif (x <= 5.2e+154)
		tmp = Float64(y0 * Float64(Float64(c * t_1) + Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(b * Float64(Float64(z * k) - Float64(x * j))))));
	elseif (x <= 2.7e+164)
		tmp = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(y2 * t_3))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y2) - (z * y3);
	t_2 = j * (x * ((i * y1) - (b * y0)));
	t_3 = (c * y4) - (a * y5);
	tmp = 0.0;
	if (x <= -1.95e+118)
		tmp = (x * i) * ((j * y1) - (y * c));
	elseif (x <= -1.8e+45)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (x <= -5.7e-211)
		tmp = y3 * ((y * t_3) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (x <= 3.4e-256)
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))));
	elseif (x <= 1.85e-31)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_1) + (y4 * ((y * y3) - (t * y2)))));
	elseif (x <= 2.6e+34)
		tmp = t_2;
	elseif (x <= 4.2e+97)
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))));
	elseif (x <= 5.2e+154)
		tmp = y0 * ((c * t_1) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	elseif (x <= 2.7e+164)
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) - (y2 * t_3)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.95e+118], N[(N[(x * i), $MachinePrecision] * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.8e+45], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.7e-211], N[(y3 * N[(N[(y * t$95$3), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e-256], N[(y1 * N[(N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-31], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * t$95$1), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+34], t$95$2, If[LessEqual[x, 4.2e+97], N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+154], N[(y0 * N[(N[(c * t$95$1), $MachinePrecision] + N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+164], N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -1.95e118

   1. Initial program 21.4%

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

      1. associate-+l- 21.4%

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

   3. Simplified 21.4%

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

   4. Taylor expanded in i around -inf 38.3%

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

      1. mul-1-neg 38.3%

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

      2. associate--l+ 38.3%

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

   6. Simplified 38.3%

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

   7. Taylor expanded in x around inf 53.1%

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

   if -1.95e118 < x < -1.8e45

   1. Initial program 41.5%

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

      1. associate-+l- 41.5%

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

   3. Simplified 41.5%

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

   4. Taylor expanded in y2 around inf 59.7%

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

   if -1.8e45 < x < -5.7e-211

   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. Step-by-step derivation

      1. associate-+l- 24.1%

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

   3. Simplified 24.1%

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

   4. Taylor expanded in y3 around -inf 52.6%

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

   if -5.7e-211 < x < 3.4000000000000001e-256

   1. Initial program 50.2%

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

      1. +-commutative 50.2%

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

      2. fma-def 50.2%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in y1 around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. mul-1-neg 67.5%

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

      3. sub-neg 67.5%

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

   6. Simplified 67.5%

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

   if 3.4000000000000001e-256 < x < 1.8499999999999999e-31

   1. Initial program 34.8%

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

      1. associate-+l- 34.8%

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

   3. Simplified 34.8%

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

   4. Taylor expanded in c around inf 60.7%

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

      1. associate--l+ 60.7%

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

      2. mul-1-neg 60.7%

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

   6. Simplified 60.7%

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

   if 1.8499999999999999e-31 < x < 2.59999999999999997e34 or 2.70000000000000006e164 < x

   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. Step-by-step derivation

      1. +-commutative 22.2%

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

      2. fma-def 22.2%

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

      3. *-commutative 22.2%

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

      4. *-commutative 22.2%

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

   3. Simplified 27.0%

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

   4. Taylor expanded in j around inf 52.8%

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

   5. Taylor expanded in x around inf 60.4%

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

   if 2.59999999999999997e34 < x < 4.20000000000000023e97

   1. Initial program 22.5%

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

      1. +-commutative 22.5%

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

      2. fma-def 22.5%

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

      3. *-commutative 22.5%

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

      4. *-commutative 22.5%

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

   3. Simplified 36.8%

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

   4. Taylor expanded in x around inf 51.1%

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

      1. mul-1-neg 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in a around inf 58.6%

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

   if 4.20000000000000023e97 < x < 5.19999999999999978e154

   1. Initial program 10.6%

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

      1. +-commutative 10.6%

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

      2. fma-def 10.6%

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

      3. *-commutative 10.6%

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

      4. *-commutative 10.6%

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

   3. Simplified 10.6%

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

   4. Taylor expanded in y0 around inf 72.8%

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

      1. mul-1-neg 72.8%

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

   6. Simplified 72.8%

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

   if 5.19999999999999978e154 < x < 2.70000000000000006e164

   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. Step-by-step derivation

      1. +-commutative 0.0%

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

      2. fma-def 0.0%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in t around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. sub-neg 100.0%

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

   6. Simplified 100.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(\left(a \cdot y5 - c \cdot y4\right) \cdot y2 + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+118}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(j \cdot y1 - y \cdot c\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+45}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-211}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-256}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-31}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+154}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 6: 38.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\\ t_3 := y4 \cdot \left(\left(b \cdot t_1 + t_2\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -1.05 \cdot 10^{+175}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -2.7 \cdot 10^{+110}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -1.54 \cdot 10^{+57}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -2.05 \cdot 10^{-14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y1 \leq -1.7 \cdot 10^{-45}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -2.25 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.5 \cdot 10^{-40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (* y1 (- (* k y2) (* j y3))))
        (t_3 (* y4 (+ (+ (* b t_1) t_2) (* c (- (* y y3) (* t y2)))))))
   (if (<= y1 -1.05e+175)
     (* j (* y1 (- (* x i) (* y3 y4))))
     (if (<= y1 -2.7e+110)
       (* k (* i (- (* y y5) (* z y1))))
       (if (<= y1 -1.54e+57)
         (*
          y2
          (+
           (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= y1 -2.05e-14)
           t_3
           (if (<= y1 -1.7e-45)
             (*
              i
              (+
               (* c (- (* z t) (* x y)))
               (+ (* y1 (- (* x j) (* z k))) (* y5 (- (* y k) (* t j))))))
             (if (<= y1 -2.25e-294)
               (*
                b
                (+
                 (+ (* a (- (* x y) (* z t))) (* y4 t_1))
                 (* y0 (- (* z k) (* x j)))))
               (if (<= y1 2.5e-40)
                 t_3
                 (if (<= y1 1.15e+146)
                   (*
                    z
                    (+
                     (* y3 (- (* a y1) (* c y0)))
                     (+
                      (* k (- (* b y0) (* i y1)))
                      (* t (- (* c i) (* a b))))))
                   (* y4 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = y1 * ((k * y2) - (j * y3));
	double t_3 = y4 * (((b * t_1) + t_2) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y1 <= -1.05e+175) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -2.7e+110) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y1 <= -1.54e+57) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y1 <= -2.05e-14) {
		tmp = t_3;
	} else if (y1 <= -1.7e-45) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	} else if (y1 <= -2.25e-294) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 2.5e-40) {
		tmp = t_3;
	} else if (y1 <= 1.15e+146) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	} else {
		tmp = y4 * t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = y1 * ((k * y2) - (j * y3))
    t_3 = y4 * (((b * t_1) + t_2) + (c * ((y * y3) - (t * y2))))
    if (y1 <= (-1.05d+175)) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (y1 <= (-2.7d+110)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (y1 <= (-1.54d+57)) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y1 <= (-2.05d-14)) then
        tmp = t_3
    else if (y1 <= (-1.7d-45)) then
        tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))))
    else if (y1 <= (-2.25d-294)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
    else if (y1 <= 2.5d-40) then
        tmp = t_3
    else if (y1 <= 1.15d+146) then
        tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
    else
        tmp = y4 * t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = y1 * ((k * y2) - (j * y3));
	double t_3 = y4 * (((b * t_1) + t_2) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y1 <= -1.05e+175) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -2.7e+110) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y1 <= -1.54e+57) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y1 <= -2.05e-14) {
		tmp = t_3;
	} else if (y1 <= -1.7e-45) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	} else if (y1 <= -2.25e-294) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 2.5e-40) {
		tmp = t_3;
	} else if (y1 <= 1.15e+146) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	} else {
		tmp = y4 * t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = y1 * ((k * y2) - (j * y3))
	t_3 = y4 * (((b * t_1) + t_2) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y1 <= -1.05e+175:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif y1 <= -2.7e+110:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif y1 <= -1.54e+57:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y1 <= -2.05e-14:
		tmp = t_3
	elif y1 <= -1.7e-45:
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))))
	elif y1 <= -2.25e-294:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
	elif y1 <= 2.5e-40:
		tmp = t_3
	elif y1 <= 1.15e+146:
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
	else:
		tmp = y4 * t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))
	t_3 = Float64(y4 * Float64(Float64(Float64(b * t_1) + t_2) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y1 <= -1.05e+175)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y1 <= -2.7e+110)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (y1 <= -1.54e+57)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y1 <= -2.05e-14)
		tmp = t_3;
	elseif (y1 <= -1.7e-45)
		tmp = Float64(i * Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))));
	elseif (y1 <= -2.25e-294)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y1 <= 2.5e-40)
		tmp = t_3;
	elseif (y1 <= 1.15e+146)
		tmp = Float64(z * Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * Float64(Float64(c * i) - Float64(a * b))))));
	else
		tmp = Float64(y4 * t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = y1 * ((k * y2) - (j * y3));
	t_3 = y4 * (((b * t_1) + t_2) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y1 <= -1.05e+175)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (y1 <= -2.7e+110)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (y1 <= -1.54e+57)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y1 <= -2.05e-14)
		tmp = t_3;
	elseif (y1 <= -1.7e-45)
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	elseif (y1 <= -2.25e-294)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	elseif (y1 <= 2.5e-40)
		tmp = t_3;
	elseif (y1 <= 1.15e+146)
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	else
		tmp = y4 * t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.05e+175], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.7e+110], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.54e+57], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.05e-14], t$95$3, If[LessEqual[y1, -1.7e-45], N[(i * N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.25e-294], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.5e-40], t$95$3, If[LessEqual[y1, 1.15e+146], N[(z * N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * t$95$2), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y1 < -1.05e175

   1. Initial program 12.2%

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

      1. +-commutative 12.2%

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

      2. fma-def 12.2%

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

      3. *-commutative 12.2%

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

      4. *-commutative 12.2%

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

   3. Simplified 16.2%

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

   4. Taylor expanded in j around inf 48.3%

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

   5. Taylor expanded in y1 around -inf 57.3%

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

      1. associate-*r* 57.3%

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

      2. neg-mul-1 57.3%

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

   7. Simplified 57.3%

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

   if -1.05e175 < y1 < -2.7000000000000001e110

   1. Initial program 7.6%

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

      1. +-commutative 7.6%

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

      2. fma-def 7.6%

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

      3. *-commutative 7.6%

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

      4. *-commutative 7.6%

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

   3. Simplified 7.6%

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

   4. Taylor expanded in k around inf 46.0%

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

   5. Taylor expanded in i around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. sub-neg 76.9%

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

      3. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -2.7000000000000001e110 < y1 < -1.54e57

   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. Step-by-step derivation

      1. associate-+l- 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y2 around inf 73.9%

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

   if -1.54e57 < y1 < -2.0500000000000001e-14 or -2.24999999999999991e-294 < y1 < 2.49999999999999982e-40

   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. Step-by-step derivation

      1. associate-+l- 40.8%

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

   3. Simplified 40.8%

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

   4. Taylor expanded in y4 around inf 60.3%

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

   if -2.0500000000000001e-14 < y1 < -1.70000000000000002e-45

   1. Initial program 51.0%

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

      1. associate-+l- 51.0%

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

   3. Simplified 51.0%

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

   4. Taylor expanded in i around -inf 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate--l+ 51.6%

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

   6. Simplified 51.6%

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

   if -1.70000000000000002e-45 < y1 < -2.24999999999999991e-294

   1. Initial program 27.7%

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

      1. associate-+l- 27.7%

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

   3. Simplified 27.7%

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

   4. Taylor expanded in b around inf 53.7%

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

   if 2.49999999999999982e-40 < y1 < 1.15e146

   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. Step-by-step derivation

      1. associate-+l- 19.1%

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

   3. Simplified 19.1%

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

   4. Taylor expanded in z around -inf 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate--l+ 51.6%

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

   6. Simplified 51.6%

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

   if 1.15e146 < y1

   1. Initial program 29.2%

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

      1. associate-+l- 29.2%

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

   3. Simplified 29.2%

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

   4. Taylor expanded in y4 around inf 50.1%

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

   5. Taylor expanded in y1 around inf 67.3%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.05 \cdot 10^{+175}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -2.7 \cdot 10^{+110}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -1.54 \cdot 10^{+57}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -2.05 \cdot 10^{-14}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.7 \cdot 10^{-45}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -2.25 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.5 \cdot 10^{-40}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]

Alternative 7: 37.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y1 - b \cdot y0\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := t \cdot j - y \cdot k\\ t_4 := y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\\ t_5 := y4 \cdot \left(\left(b \cdot t_3 + t_4\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -4.9 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -9.2 \cdot 10^{+111}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -3.4 \cdot 10^{+56}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -1.5 \cdot 10^{-14}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y1 \leq -2.3 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_2\right) + j \cdot t_1\right)\\ \mathbf{elif}\;y1 \leq -2.75 \cdot 10^{-291}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_3\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 4.4 \cdot 10^{-45}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y1 \leq 4 \cdot 10^{+84}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(x \cdot t_1\right)\\ \mathbf{elif}\;y1 \leq 2.05 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 1.65 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* i y1) (* b y0)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* t j) (* y k)))
        (t_4 (* y1 (- (* k y2) (* j y3))))
        (t_5 (* y4 (+ (+ (* b t_3) t_4) (* c (- (* y y3) (* t y2)))))))
   (if (<= y1 -4.9e+174)
     (* j (* y1 (- (* x i) (* y3 y4))))
     (if (<= y1 -9.2e+111)
       (* k (* i (- (* y y5) (* z y1))))
       (if (<= y1 -3.4e+56)
         (*
          y2
          (+
           (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= y1 -1.5e-14)
           t_5
           (if (<= y1 -2.3e-46)
             (* x (+ (+ (* y (- (* a b) (* c i))) (* y2 t_2)) (* j t_1)))
             (if (<= y1 -2.75e-291)
               (*
                b
                (+
                 (+ (* a (- (* x y) (* z t))) (* y4 t_3))
                 (* y0 (- (* z k) (* x j)))))
               (if (<= y1 4.4e-45)
                 t_5
                 (if (<= y1 4e+84)
                   (* y0 (* c (- (* x y2) (* z y3))))
                   (if (<= y1 2.3e+105)
                     (* j (* x t_1))
                     (if (<= y1 2.05e+130)
                       (* y (* y3 (- (* c y4) (* a y5))))
                       (if (<= y1 1.65e+156)
                         (* j (* y0 (- (* y3 y5) (* x b))))
                         (* y4 t_4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (t * j) - (y * k);
	double t_4 = y1 * ((k * y2) - (j * y3));
	double t_5 = y4 * (((b * t_3) + t_4) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y1 <= -4.9e+174) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -9.2e+111) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y1 <= -3.4e+56) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y1 <= -1.5e-14) {
		tmp = t_5;
	} else if (y1 <= -2.3e-46) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_1));
	} else if (y1 <= -2.75e-291) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 4.4e-45) {
		tmp = t_5;
	} else if (y1 <= 4e+84) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (y1 <= 2.3e+105) {
		tmp = j * (x * t_1);
	} else if (y1 <= 2.05e+130) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (y1 <= 1.65e+156) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y4 * t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (i * y1) - (b * y0)
    t_2 = (c * y0) - (a * y1)
    t_3 = (t * j) - (y * k)
    t_4 = y1 * ((k * y2) - (j * y3))
    t_5 = y4 * (((b * t_3) + t_4) + (c * ((y * y3) - (t * y2))))
    if (y1 <= (-4.9d+174)) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (y1 <= (-9.2d+111)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (y1 <= (-3.4d+56)) then
        tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y1 <= (-1.5d-14)) then
        tmp = t_5
    else if (y1 <= (-2.3d-46)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_1))
    else if (y1 <= (-2.75d-291)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
    else if (y1 <= 4.4d-45) then
        tmp = t_5
    else if (y1 <= 4d+84) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (y1 <= 2.3d+105) then
        tmp = j * (x * t_1)
    else if (y1 <= 2.05d+130) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else if (y1 <= 1.65d+156) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = y4 * t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (t * j) - (y * k);
	double t_4 = y1 * ((k * y2) - (j * y3));
	double t_5 = y4 * (((b * t_3) + t_4) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y1 <= -4.9e+174) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -9.2e+111) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y1 <= -3.4e+56) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y1 <= -1.5e-14) {
		tmp = t_5;
	} else if (y1 <= -2.3e-46) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_1));
	} else if (y1 <= -2.75e-291) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 4.4e-45) {
		tmp = t_5;
	} else if (y1 <= 4e+84) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (y1 <= 2.3e+105) {
		tmp = j * (x * t_1);
	} else if (y1 <= 2.05e+130) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (y1 <= 1.65e+156) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y4 * t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y1) - (b * y0)
	t_2 = (c * y0) - (a * y1)
	t_3 = (t * j) - (y * k)
	t_4 = y1 * ((k * y2) - (j * y3))
	t_5 = y4 * (((b * t_3) + t_4) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y1 <= -4.9e+174:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif y1 <= -9.2e+111:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif y1 <= -3.4e+56:
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y1 <= -1.5e-14:
		tmp = t_5
	elif y1 <= -2.3e-46:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_1))
	elif y1 <= -2.75e-291:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
	elif y1 <= 4.4e-45:
		tmp = t_5
	elif y1 <= 4e+84:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif y1 <= 2.3e+105:
		tmp = j * (x * t_1)
	elif y1 <= 2.05e+130:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	elif y1 <= 1.65e+156:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = y4 * t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(i * y1) - Float64(b * y0))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	t_4 = Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * t_3) + t_4) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y1 <= -4.9e+174)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y1 <= -9.2e+111)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (y1 <= -3.4e+56)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y1 <= -1.5e-14)
		tmp = t_5;
	elseif (y1 <= -2.3e-46)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * t_1)));
	elseif (y1 <= -2.75e-291)
		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 (y1 <= 4.4e-45)
		tmp = t_5;
	elseif (y1 <= 4e+84)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y1 <= 2.3e+105)
		tmp = Float64(j * Float64(x * t_1));
	elseif (y1 <= 2.05e+130)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (y1 <= 1.65e+156)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(y4 * t_4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (i * y1) - (b * y0);
	t_2 = (c * y0) - (a * y1);
	t_3 = (t * j) - (y * k);
	t_4 = y1 * ((k * y2) - (j * y3));
	t_5 = y4 * (((b * t_3) + t_4) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y1 <= -4.9e+174)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (y1 <= -9.2e+111)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (y1 <= -3.4e+56)
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y1 <= -1.5e-14)
		tmp = t_5;
	elseif (y1 <= -2.3e-46)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_1));
	elseif (y1 <= -2.75e-291)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	elseif (y1 <= 4.4e-45)
		tmp = t_5;
	elseif (y1 <= 4e+84)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (y1 <= 2.3e+105)
		tmp = j * (x * t_1);
	elseif (y1 <= 2.05e+130)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	elseif (y1 <= 1.65e+156)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = y4 * t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * t$95$3), $MachinePrecision] + t$95$4), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4.9e+174], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -9.2e+111], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.4e+56], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.5e-14], t$95$5, If[LessEqual[y1, -2.3e-46], 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$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.75e-291], 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[y1, 4.4e-45], t$95$5, If[LessEqual[y1, 4e+84], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.3e+105], N[(j * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.05e+130], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.65e+156], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * t$95$4), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y1 < -4.8999999999999997e174

   1. Initial program 12.2%

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

      1. +-commutative 12.2%

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

      2. fma-def 12.2%

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

      3. *-commutative 12.2%

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

      4. *-commutative 12.2%

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

   3. Simplified 16.2%

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

   4. Taylor expanded in j around inf 48.3%

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

   5. Taylor expanded in y1 around -inf 57.3%

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

      1. associate-*r* 57.3%

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

      2. neg-mul-1 57.3%

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

   7. Simplified 57.3%

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

   if -4.8999999999999997e174 < y1 < -9.20000000000000008e111

   1. Initial program 7.6%

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

      1. +-commutative 7.6%

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

      2. fma-def 7.6%

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

      3. *-commutative 7.6%

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

      4. *-commutative 7.6%

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

   3. Simplified 7.6%

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

   4. Taylor expanded in k around inf 46.0%

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

   5. Taylor expanded in i around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. sub-neg 76.9%

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

      3. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -9.20000000000000008e111 < y1 < -3.40000000000000001e56

   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. Step-by-step derivation

      1. associate-+l- 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y2 around inf 73.9%

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

   if -3.40000000000000001e56 < y1 < -1.4999999999999999e-14 or -2.7500000000000001e-291 < y1 < 4.39999999999999987e-45

   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. Step-by-step derivation

      1. associate-+l- 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in y4 around inf 61.1%

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

   if -1.4999999999999999e-14 < y1 < -2.2999999999999999e-46

   1. Initial program 51.0%

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

      1. associate-+l- 51.0%

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

   3. Simplified 51.0%

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

   4. Taylor expanded in x around inf 51.2%

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

   if -2.2999999999999999e-46 < y1 < -2.7500000000000001e-291

   1. Initial program 27.7%

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

      1. associate-+l- 27.7%

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

   3. Simplified 27.7%

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

   4. Taylor expanded in b around inf 53.7%

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

   if 4.39999999999999987e-45 < y1 < 4.00000000000000023e84

   1. Initial program 17.2%

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

      1. +-commutative 17.2%

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

      2. fma-def 20.7%

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

      3. *-commutative 20.7%

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

      4. *-commutative 20.7%

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

   3. Simplified 20.7%

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

   4. Taylor expanded in y0 around inf 38.7%

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

      1. mul-1-neg 38.7%

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

   6. Simplified 38.7%

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

   7. Taylor expanded in c around inf 43.0%

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

      1. *-commutative 43.0%

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

      2. *-commutative 43.0%

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

      3. associate-*l* 42.8%

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

      4. *-commutative 42.8%

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

   9. Simplified 42.8%

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

   if 4.00000000000000023e84 < y1 < 2.2999999999999998e105

   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. Step-by-step derivation

      1. +-commutative 50.0%

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

      2. fma-def 50.0%

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

      3. *-commutative 50.0%

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

      4. *-commutative 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in j around inf 83.3%

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

   5. Taylor expanded in x around inf 100.0%

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

   if 2.2999999999999998e105 < y1 < 2.04999999999999989e130

   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. Step-by-step derivation

      1. associate-+l- 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in y3 around -inf 72.5%

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

   5. Taylor expanded in y around inf 72.4%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(a \cdot y5 - c \cdot y4\right) \cdot \left(y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 72.4%

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

      2. associate-*l* 85.9%

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

   7. Simplified 85.9%

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

   if 2.04999999999999989e130 < y1 < 1.6499999999999999e156

   1. Initial program 30.0%

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

      1. +-commutative 30.0%

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

      2. fma-def 30.0%

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

      3. *-commutative 30.0%

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

      4. *-commutative 30.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in j around inf 51.3%

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

   5. Taylor expanded in y0 around inf 61.1%

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

      1. *-commutative 61.1%

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

   7. Simplified 61.1%

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

   if 1.6499999999999999e156 < y1

   1. Initial program 25.0%

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

      1. associate-+l- 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in y4 around inf 55.2%

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

   5. Taylor expanded in y1 around inf 75.4%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4.9 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -9.2 \cdot 10^{+111}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -3.4 \cdot 10^{+56}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -1.5 \cdot 10^{-14}:\\ \;\;\;\;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 -2.3 \cdot 10^{-46}:\\ \;\;\;\;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 -2.75 \cdot 10^{-291}:\\ \;\;\;\;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}\;y1 \leq 4.4 \cdot 10^{-45}:\\ \;\;\;\;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 4 \cdot 10^{+84}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 2.05 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 1.65 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]

Alternative 8: 38.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\\ t_3 := t \cdot j - y \cdot k\\ \mathbf{if}\;y1 \leq -9.2 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -2.9 \cdot 10^{+113}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -2.6 \cdot 10^{+56}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -3.4 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot t_1\right)\right)\\ \mathbf{elif}\;y1 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_3\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.05 \cdot 10^{-40}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_3 + t_2\right) + c \cdot t_1\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y y3) (* t y2)))
        (t_2 (* y1 (- (* k y2) (* j y3))))
        (t_3 (- (* t j) (* y k))))
   (if (<= y1 -9.2e+173)
     (* j (* y1 (- (* x i) (* y3 y4))))
     (if (<= y1 -2.9e+113)
       (* k (* i (- (* y y5) (* z y1))))
       (if (<= y1 -2.6e+56)
         (*
          y2
          (+
           (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= y1 -3.4e-44)
           (*
            c
            (+
             (* i (- (* z t) (* x y)))
             (+ (* y0 (- (* x y2) (* z y3))) (* y4 t_1))))
           (if (<= y1 -5e-294)
             (*
              b
              (+
               (+ (* a (- (* x y) (* z t))) (* y4 t_3))
               (* y0 (- (* z k) (* x j)))))
             (if (<= y1 3.05e-40)
               (* y4 (+ (+ (* b t_3) t_2) (* c t_1)))
               (if (<= y1 1.8e+146)
                 (*
                  z
                  (+
                   (* y3 (- (* a y1) (* c y0)))
                   (+ (* k (- (* b y0) (* i y1))) (* t (- (* c i) (* a b))))))
                 (* y4 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = y1 * ((k * y2) - (j * y3));
	double t_3 = (t * j) - (y * k);
	double tmp;
	if (y1 <= -9.2e+173) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -2.9e+113) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y1 <= -2.6e+56) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y1 <= -3.4e-44) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_1)));
	} else if (y1 <= -5e-294) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 3.05e-40) {
		tmp = y4 * (((b * t_3) + t_2) + (c * t_1));
	} else if (y1 <= 1.8e+146) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	} else {
		tmp = y4 * t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * y3) - (t * y2)
    t_2 = y1 * ((k * y2) - (j * y3))
    t_3 = (t * j) - (y * k)
    if (y1 <= (-9.2d+173)) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (y1 <= (-2.9d+113)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (y1 <= (-2.6d+56)) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y1 <= (-3.4d-44)) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_1)))
    else if (y1 <= (-5d-294)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
    else if (y1 <= 3.05d-40) then
        tmp = y4 * (((b * t_3) + t_2) + (c * t_1))
    else if (y1 <= 1.8d+146) then
        tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
    else
        tmp = y4 * t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = y1 * ((k * y2) - (j * y3));
	double t_3 = (t * j) - (y * k);
	double tmp;
	if (y1 <= -9.2e+173) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -2.9e+113) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y1 <= -2.6e+56) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y1 <= -3.4e-44) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_1)));
	} else if (y1 <= -5e-294) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 3.05e-40) {
		tmp = y4 * (((b * t_3) + t_2) + (c * t_1));
	} else if (y1 <= 1.8e+146) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	} else {
		tmp = y4 * t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * y3) - (t * y2)
	t_2 = y1 * ((k * y2) - (j * y3))
	t_3 = (t * j) - (y * k)
	tmp = 0
	if y1 <= -9.2e+173:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif y1 <= -2.9e+113:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif y1 <= -2.6e+56:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y1 <= -3.4e-44:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_1)))
	elif y1 <= -5e-294:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
	elif y1 <= 3.05e-40:
		tmp = y4 * (((b * t_3) + t_2) + (c * t_1))
	elif y1 <= 1.8e+146:
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
	else:
		tmp = y4 * t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * y3) - Float64(t * y2))
	t_2 = Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	tmp = 0.0
	if (y1 <= -9.2e+173)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y1 <= -2.9e+113)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (y1 <= -2.6e+56)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y1 <= -3.4e-44)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * t_1))));
	elseif (y1 <= -5e-294)
		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 (y1 <= 3.05e-40)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_3) + t_2) + Float64(c * t_1)));
	elseif (y1 <= 1.8e+146)
		tmp = Float64(z * Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * Float64(Float64(c * i) - Float64(a * b))))));
	else
		tmp = Float64(y4 * t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * y3) - (t * y2);
	t_2 = y1 * ((k * y2) - (j * y3));
	t_3 = (t * j) - (y * k);
	tmp = 0.0;
	if (y1 <= -9.2e+173)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (y1 <= -2.9e+113)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (y1 <= -2.6e+56)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y1 <= -3.4e-44)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_1)));
	elseif (y1 <= -5e-294)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	elseif (y1 <= 3.05e-40)
		tmp = y4 * (((b * t_3) + t_2) + (c * t_1));
	elseif (y1 <= 1.8e+146)
		tmp = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	else
		tmp = y4 * t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -9.2e+173], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.9e+113], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.6e+56], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.4e-44], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5e-294], 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[y1, 3.05e-40], N[(y4 * N[(N[(N[(b * t$95$3), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.8e+146], N[(z * N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * t$95$2), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y1 < -9.1999999999999998e173

   1. Initial program 12.2%

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

      1. +-commutative 12.2%

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

      2. fma-def 12.2%

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

      3. *-commutative 12.2%

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

      4. *-commutative 12.2%

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

   3. Simplified 16.2%

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

   4. Taylor expanded in j around inf 48.3%

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

   5. Taylor expanded in y1 around -inf 57.3%

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

      1. associate-*r* 57.3%

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

      2. neg-mul-1 57.3%

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

   7. Simplified 57.3%

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

   if -9.1999999999999998e173 < y1 < -2.89999999999999984e113

   1. Initial program 7.6%

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

      1. +-commutative 7.6%

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

      2. fma-def 7.6%

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

      3. *-commutative 7.6%

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

      4. *-commutative 7.6%

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

   3. Simplified 7.6%

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

   4. Taylor expanded in k around inf 46.0%

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

   5. Taylor expanded in i around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. sub-neg 76.9%

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

      3. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -2.89999999999999984e113 < y1 < -2.60000000000000011e56

   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. Step-by-step derivation

      1. associate-+l- 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y2 around inf 73.9%

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

   if -2.60000000000000011e56 < y1 < -3.40000000000000016e-44

   1. Initial program 58.8%

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

      1. associate-+l- 58.8%

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

   3. Simplified 58.8%

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

   4. Taylor expanded in c around inf 58.5%

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

      1. associate--l+ 58.5%

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

      2. mul-1-neg 58.5%

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

   6. Simplified 58.5%

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

   if -3.40000000000000016e-44 < y1 < -5.0000000000000003e-294

   1. Initial program 27.7%

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

      1. associate-+l- 27.7%

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

   3. Simplified 27.7%

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

   4. Taylor expanded in b around inf 53.7%

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

   if -5.0000000000000003e-294 < y1 < 3.0500000000000002e-40

   1. Initial program 35.4%

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

      1. associate-+l- 35.4%

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

   3. Simplified 35.4%

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

   4. Taylor expanded in y4 around inf 60.6%

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

   if 3.0500000000000002e-40 < y1 < 1.7999999999999999e146

   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. Step-by-step derivation

      1. associate-+l- 19.1%

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

   3. Simplified 19.1%

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

   4. Taylor expanded in z around -inf 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate--l+ 51.6%

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

   6. Simplified 51.6%

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

   if 1.7999999999999999e146 < y1

   1. Initial program 29.2%

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

      1. associate-+l- 29.2%

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

   3. Simplified 29.2%

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

   4. Taylor expanded in y4 around inf 50.1%

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

   5. Taylor expanded in y1 around inf 67.3%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -9.2 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -2.9 \cdot 10^{+113}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -2.6 \cdot 10^{+56}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -3.4 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.05 \cdot 10^{-40}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]

Alternative 9: 36.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := y1 \cdot t_1\\ t_3 := t \cdot j - y \cdot k\\ \mathbf{if}\;y1 \leq -8.2 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -2.2 \cdot 10^{+87}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y1 \leq -1.4 \cdot 10^{-44}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot t_1 - x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq -4.6 \cdot 10^{-288}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_3\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_3 + t_2\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{+76}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 9.8 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 4.4 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3))) (t_2 (* y1 t_1)) (t_3 (- (* t j) (* y k))))
   (if (<= y1 -8.2e+148)
     (* j (* y1 (- (* x i) (* y3 y4))))
     (if (<= y1 -2.2e+87)
       (* c (* i (- (* z t) (* x y))))
       (if (<= y1 -1.4e-44)
         (* y1 (- (* y4 t_1) (* x (- (* a y2) (* i j)))))
         (if (<= y1 -4.6e-288)
           (*
            b
            (+
             (+ (* a (- (* x y) (* z t))) (* y4 t_3))
             (* y0 (- (* z k) (* x j)))))
           (if (<= y1 3.5e-42)
             (* y4 (+ (+ (* b t_3) t_2) (* c (- (* y y3) (* t y2)))))
             (if (<= y1 5.2e+76)
               (* y0 (* c (- (* x y2) (* z y3))))
               (if (<= y1 9.8e+104)
                 (* j (* x (- (* i y1) (* b y0))))
                 (if (<= y1 4.4e+129)
                   (* y (* y3 (- (* c y4) (* a y5))))
                   (if (<= y1 2e+156)
                     (* j (* y0 (- (* y3 y5) (* x b))))
                     (* y4 t_2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = y1 * t_1;
	double t_3 = (t * j) - (y * k);
	double tmp;
	if (y1 <= -8.2e+148) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -2.2e+87) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y1 <= -1.4e-44) {
		tmp = y1 * ((y4 * t_1) - (x * ((a * y2) - (i * j))));
	} else if (y1 <= -4.6e-288) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 3.5e-42) {
		tmp = y4 * (((b * t_3) + t_2) + (c * ((y * y3) - (t * y2))));
	} else if (y1 <= 5.2e+76) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (y1 <= 9.8e+104) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= 4.4e+129) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (y1 <= 2e+156) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y4 * t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = y1 * t_1
    t_3 = (t * j) - (y * k)
    if (y1 <= (-8.2d+148)) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (y1 <= (-2.2d+87)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (y1 <= (-1.4d-44)) then
        tmp = y1 * ((y4 * t_1) - (x * ((a * y2) - (i * j))))
    else if (y1 <= (-4.6d-288)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
    else if (y1 <= 3.5d-42) then
        tmp = y4 * (((b * t_3) + t_2) + (c * ((y * y3) - (t * y2))))
    else if (y1 <= 5.2d+76) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (y1 <= 9.8d+104) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y1 <= 4.4d+129) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else if (y1 <= 2d+156) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = y4 * t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = y1 * t_1;
	double t_3 = (t * j) - (y * k);
	double tmp;
	if (y1 <= -8.2e+148) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y1 <= -2.2e+87) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y1 <= -1.4e-44) {
		tmp = y1 * ((y4 * t_1) - (x * ((a * y2) - (i * j))));
	} else if (y1 <= -4.6e-288) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 3.5e-42) {
		tmp = y4 * (((b * t_3) + t_2) + (c * ((y * y3) - (t * y2))));
	} else if (y1 <= 5.2e+76) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (y1 <= 9.8e+104) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= 4.4e+129) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (y1 <= 2e+156) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y4 * t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = y1 * t_1
	t_3 = (t * j) - (y * k)
	tmp = 0
	if y1 <= -8.2e+148:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif y1 <= -2.2e+87:
		tmp = c * (i * ((z * t) - (x * y)))
	elif y1 <= -1.4e-44:
		tmp = y1 * ((y4 * t_1) - (x * ((a * y2) - (i * j))))
	elif y1 <= -4.6e-288:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
	elif y1 <= 3.5e-42:
		tmp = y4 * (((b * t_3) + t_2) + (c * ((y * y3) - (t * y2))))
	elif y1 <= 5.2e+76:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif y1 <= 9.8e+104:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y1 <= 4.4e+129:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	elif y1 <= 2e+156:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = y4 * 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(k * y2) - Float64(j * y3))
	t_2 = Float64(y1 * t_1)
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	tmp = 0.0
	if (y1 <= -8.2e+148)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y1 <= -2.2e+87)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y1 <= -1.4e-44)
		tmp = Float64(y1 * Float64(Float64(y4 * t_1) - Float64(x * Float64(Float64(a * y2) - Float64(i * j)))));
	elseif (y1 <= -4.6e-288)
		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 (y1 <= 3.5e-42)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_3) + t_2) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y1 <= 5.2e+76)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y1 <= 9.8e+104)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y1 <= 4.4e+129)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (y1 <= 2e+156)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(y4 * t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y2) - (j * y3);
	t_2 = y1 * t_1;
	t_3 = (t * j) - (y * k);
	tmp = 0.0;
	if (y1 <= -8.2e+148)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (y1 <= -2.2e+87)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (y1 <= -1.4e-44)
		tmp = y1 * ((y4 * t_1) - (x * ((a * y2) - (i * j))));
	elseif (y1 <= -4.6e-288)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	elseif (y1 <= 3.5e-42)
		tmp = y4 * (((b * t_3) + t_2) + (c * ((y * y3) - (t * y2))));
	elseif (y1 <= 5.2e+76)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (y1 <= 9.8e+104)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y1 <= 4.4e+129)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	elseif (y1 <= 2e+156)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = y4 * 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[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -8.2e+148], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.2e+87], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.4e-44], N[(y1 * N[(N[(y4 * t$95$1), $MachinePrecision] - N[(x * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -4.6e-288], 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[y1, 3.5e-42], N[(y4 * N[(N[(N[(b * t$95$3), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.2e+76], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9.8e+104], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.4e+129], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2e+156], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * t$95$2), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y1 < -8.1999999999999996e148

   1. Initial program 10.2%

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

      1. +-commutative 10.2%

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

      2. fma-def 10.2%

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

      3. *-commutative 10.2%

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

      4. *-commutative 10.2%

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

   3. Simplified 13.5%

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

   4. Taylor expanded in j around inf 47.0%

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

   5. Taylor expanded in y1 around -inf 54.8%

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

      1. associate-*r* 54.8%

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

      2. neg-mul-1 54.8%

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

   7. Simplified 54.8%

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

   if -8.1999999999999996e148 < y1 < -2.2000000000000001e87

   1. Initial program 26.6%

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

      1. associate-+l- 26.6%

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

   3. Simplified 26.6%

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

   4. Taylor expanded in i around -inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. associate--l+ 53.6%

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

   6. Simplified 53.6%

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

   7. Taylor expanded in c around inf 67.3%

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

   if -2.2000000000000001e87 < y1 < -1.4e-44

   1. Initial program 50.4%

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

      1. +-commutative 50.4%

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

      2. fma-def 50.4%

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

      3. *-commutative 50.4%

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

      4. *-commutative 50.4%

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

   3. Simplified 50.4%

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

   4. Taylor expanded in x around inf 56.2%

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

      1. mul-1-neg 56.2%

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

   6. Simplified 56.2%

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

   7. Taylor expanded in y1 around -inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. *-commutative 44.9%

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

      3. distribute-rgt-neg-in 44.9%

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

      4. +-commutative 44.9%

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

      5. mul-1-neg 44.9%

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

      6. unsub-neg 44.9%

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

      7. *-commutative 44.9%

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

      8. *-commutative 44.9%

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

   9. Simplified 44.9%

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

   if -1.4e-44 < y1 < -4.6e-288

   1. Initial program 27.7%

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

      1. associate-+l- 27.7%

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

   3. Simplified 27.7%

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

   4. Taylor expanded in b around inf 53.7%

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

   if -4.6e-288 < y1 < 3.5000000000000002e-42

   1. Initial program 34.2%

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

      1. associate-+l- 34.2%

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

   3. Simplified 34.2%

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

   4. Taylor expanded in y4 around inf 61.6%

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

   if 3.5000000000000002e-42 < y1 < 5.1999999999999999e76

   1. Initial program 17.2%

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

      1. +-commutative 17.2%

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

      2. fma-def 20.7%

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

      3. *-commutative 20.7%

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

      4. *-commutative 20.7%

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

   3. Simplified 20.7%

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

   4. Taylor expanded in y0 around inf 38.7%

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

      1. mul-1-neg 38.7%

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

   6. Simplified 38.7%

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

   7. Taylor expanded in c around inf 43.0%

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

      1. *-commutative 43.0%

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

      2. *-commutative 43.0%

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

      3. associate-*l* 42.8%

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

      4. *-commutative 42.8%

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

   9. Simplified 42.8%

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

   if 5.1999999999999999e76 < y1 < 9.7999999999999997e104

   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. Step-by-step derivation

      1. +-commutative 50.0%

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

      2. fma-def 50.0%

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

      3. *-commutative 50.0%

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

      4. *-commutative 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in j around inf 83.3%

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

   5. Taylor expanded in x around inf 100.0%

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

   if 9.7999999999999997e104 < y1 < 4.3999999999999999e129

   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. Step-by-step derivation

      1. associate-+l- 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in y3 around -inf 72.5%

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

   5. Taylor expanded in y around inf 72.4%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(a \cdot y5 - c \cdot y4\right) \cdot \left(y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 72.4%

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

      2. associate-*l* 85.9%

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

   7. Simplified 85.9%

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

   if 4.3999999999999999e129 < y1 < 2e156

   1. Initial program 30.0%

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

      1. +-commutative 30.0%

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

      2. fma-def 30.0%

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

      3. *-commutative 30.0%

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

      4. *-commutative 30.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in j around inf 51.3%

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

   5. Taylor expanded in y0 around inf 61.1%

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

      1. *-commutative 61.1%

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

   7. Simplified 61.1%

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

   if 2e156 < y1

   1. Initial program 25.0%

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

      1. associate-+l- 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in y4 around inf 55.2%

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

   5. Taylor expanded in y1 around inf 75.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -8.2 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -2.2 \cdot 10^{+87}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y1 \leq -1.4 \cdot 10^{-44}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq -4.6 \cdot 10^{-288}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{+76}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 9.8 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 4.4 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]

Alternative 10: 38.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2\right)\right)\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+138}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(j \cdot y1 - y \cdot c\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-55}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+34}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          a
          (+
           (* y5 (- (* t y2) (* y y3)))
           (- (* b (- (* x y) (* z t))) (* y1 (* x y2)))))))
   (if (<= x -2.7e+138)
     (* (* x i) (- (* j y1) (* y c)))
     (if (<= x -1e-252)
       t_1
       (if (<= x 8.8e-55)
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))
         (if (<= x 3.1e+34)
           (* (* t j) (- (* b y4) (* i y5)))
           (if (<= x 4.5e+101) t_1 (* j (* x (- (* i y1) (* b y0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))));
	double tmp;
	if (x <= -2.7e+138) {
		tmp = (x * i) * ((j * y1) - (y * c));
	} else if (x <= -1e-252) {
		tmp = t_1;
	} else if (x <= 8.8e-55) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 3.1e+34) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 4.5e+101) {
		tmp = t_1;
	} else {
		tmp = j * (x * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))))
    if (x <= (-2.7d+138)) then
        tmp = (x * i) * ((j * y1) - (y * c))
    else if (x <= (-1d-252)) then
        tmp = t_1
    else if (x <= 8.8d-55) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (x <= 3.1d+34) then
        tmp = (t * j) * ((b * y4) - (i * y5))
    else if (x <= 4.5d+101) then
        tmp = t_1
    else
        tmp = j * (x * ((i * y1) - (b * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))));
	double tmp;
	if (x <= -2.7e+138) {
		tmp = (x * i) * ((j * y1) - (y * c));
	} else if (x <= -1e-252) {
		tmp = t_1;
	} else if (x <= 8.8e-55) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 3.1e+34) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 4.5e+101) {
		tmp = t_1;
	} else {
		tmp = j * (x * ((i * y1) - (b * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))))
	tmp = 0
	if x <= -2.7e+138:
		tmp = (x * i) * ((j * y1) - (y * c))
	elif x <= -1e-252:
		tmp = t_1
	elif x <= 8.8e-55:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif x <= 3.1e+34:
		tmp = (t * j) * ((b * y4) - (i * y5))
	elif x <= 4.5e+101:
		tmp = t_1
	else:
		tmp = j * (x * ((i * y1) - (b * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) - Float64(y1 * Float64(x * y2)))))
	tmp = 0.0
	if (x <= -2.7e+138)
		tmp = Float64(Float64(x * i) * Float64(Float64(j * y1) - Float64(y * c)));
	elseif (x <= -1e-252)
		tmp = t_1;
	elseif (x <= 8.8e-55)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (x <= 3.1e+34)
		tmp = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)));
	elseif (x <= 4.5e+101)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * ((y5 * ((t * y2) - (y * y3))) + ((b * ((x * y) - (z * t))) - (y1 * (x * y2))));
	tmp = 0.0;
	if (x <= -2.7e+138)
		tmp = (x * i) * ((j * y1) - (y * c));
	elseif (x <= -1e-252)
		tmp = t_1;
	elseif (x <= 8.8e-55)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (x <= 3.1e+34)
		tmp = (t * j) * ((b * y4) - (i * y5));
	elseif (x <= 4.5e+101)
		tmp = t_1;
	else
		tmp = j * (x * ((i * y1) - (b * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+138], N[(N[(x * i), $MachinePrecision] * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1e-252], t$95$1, If[LessEqual[x, 8.8e-55], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+34], N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+101], t$95$1, N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.70000000000000009e138

   1. Initial program 22.5%

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

      1. associate-+l- 22.5%

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

   3. Simplified 22.5%

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

   4. Taylor expanded in i around -inf 40.2%

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

      1. mul-1-neg 40.2%

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

      2. associate--l+ 40.2%

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

   6. Simplified 40.2%

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

   7. Taylor expanded in x around inf 53.2%

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

   if -2.70000000000000009e138 < x < -9.99999999999999943e-253 or 3.09999999999999977e34 < x < 4.5000000000000002e101

   1. Initial program 28.1%

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

      1. +-commutative 28.1%

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

      2. fma-def 30.3%

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

      3. *-commutative 30.3%

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

      4. *-commutative 30.3%

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

   3. Simplified 35.7%

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

   4. Taylor expanded in x around inf 42.2%

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

      1. mul-1-neg 42.2%

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

   6. Simplified 42.2%

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

   7. Taylor expanded in a around inf 49.2%

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

   if -9.99999999999999943e-253 < x < 8.7999999999999998e-55

   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. Step-by-step derivation

      1. associate-+l- 41.3%

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

   3. Simplified 41.3%

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

   4. Taylor expanded in y4 around inf 57.5%

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

   if 8.7999999999999998e-55 < x < 3.09999999999999977e34

   1. Initial program 45.4%

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

      1. +-commutative 45.4%

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

      2. fma-def 45.4%

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

      3. *-commutative 45.4%

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

      4. *-commutative 45.4%

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

   3. Simplified 50.4%

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

   4. Taylor expanded in j around inf 55.5%

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

   5. Taylor expanded in t around inf 50.8%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 55.5%

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

   7. Simplified 55.5%

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

   if 4.5000000000000002e101 < x

   1. Initial program 7.9%

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

      1. +-commutative 7.9%

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

      2. fma-def 7.9%

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

      3. *-commutative 7.9%

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

      4. *-commutative 7.9%

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

   3. Simplified 12.9%

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

   4. Taylor expanded in j around inf 41.9%

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

   5. Taylor expanded in x around inf 59.2%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+138}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(j \cdot y1 - y \cdot c\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-252}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-55}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+34}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 11: 36.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ t_4 := y1 \cdot \left(y4 \cdot t_2 - x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{+105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-304}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-243}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-84}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-35}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(k \cdot y5 - x \cdot c\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-13}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+56}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot t_2\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* t j) (- (* b y4) (* i y5))))
        (t_2 (- (* k y2) (* j y3)))
        (t_3 (* y4 (* t (- (* b j) (* c y2)))))
        (t_4 (* y1 (- (* y4 t_2) (* x (- (* a y2) (* i j)))))))
   (if (<= t -1.5e+236)
     t_3
     (if (<= t -1.12e+195)
       t_1
       (if (<= t -1.08e+105)
         t_3
         (if (<= t -5.1e-304)
           t_4
           (if (<= t 1.25e-243)
             (* y0 (* c (- (* x y2) (* z y3))))
             (if (<= t 2.3e-84)
               t_4
               (if (<= t 2.35e-35)
                 (* (* y i) (- (* k y5) (* x c)))
                 (if (<= t 1.35e-13)
                   (* (* z y0) (- (* b k) (* c y3)))
                   (if (<= t 6e+56)
                     (* y4 (* y1 t_2))
                     (if (<= t 1.6e+111)
                       (* j (* y0 (- (* y3 y5) (* x b))))
                       t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) * ((b * y4) - (i * y5));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = y4 * (t * ((b * j) - (c * y2)));
	double t_4 = y1 * ((y4 * t_2) - (x * ((a * y2) - (i * j))));
	double tmp;
	if (t <= -1.5e+236) {
		tmp = t_3;
	} else if (t <= -1.12e+195) {
		tmp = t_1;
	} else if (t <= -1.08e+105) {
		tmp = t_3;
	} else if (t <= -5.1e-304) {
		tmp = t_4;
	} else if (t <= 1.25e-243) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (t <= 2.3e-84) {
		tmp = t_4;
	} else if (t <= 2.35e-35) {
		tmp = (y * i) * ((k * y5) - (x * c));
	} else if (t <= 1.35e-13) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (t <= 6e+56) {
		tmp = y4 * (y1 * t_2);
	} else if (t <= 1.6e+111) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (t * j) * ((b * y4) - (i * y5))
    t_2 = (k * y2) - (j * y3)
    t_3 = y4 * (t * ((b * j) - (c * y2)))
    t_4 = y1 * ((y4 * t_2) - (x * ((a * y2) - (i * j))))
    if (t <= (-1.5d+236)) then
        tmp = t_3
    else if (t <= (-1.12d+195)) then
        tmp = t_1
    else if (t <= (-1.08d+105)) then
        tmp = t_3
    else if (t <= (-5.1d-304)) then
        tmp = t_4
    else if (t <= 1.25d-243) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (t <= 2.3d-84) then
        tmp = t_4
    else if (t <= 2.35d-35) then
        tmp = (y * i) * ((k * y5) - (x * c))
    else if (t <= 1.35d-13) then
        tmp = (z * y0) * ((b * k) - (c * y3))
    else if (t <= 6d+56) then
        tmp = y4 * (y1 * t_2)
    else if (t <= 1.6d+111) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) * ((b * y4) - (i * y5));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = y4 * (t * ((b * j) - (c * y2)));
	double t_4 = y1 * ((y4 * t_2) - (x * ((a * y2) - (i * j))));
	double tmp;
	if (t <= -1.5e+236) {
		tmp = t_3;
	} else if (t <= -1.12e+195) {
		tmp = t_1;
	} else if (t <= -1.08e+105) {
		tmp = t_3;
	} else if (t <= -5.1e-304) {
		tmp = t_4;
	} else if (t <= 1.25e-243) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (t <= 2.3e-84) {
		tmp = t_4;
	} else if (t <= 2.35e-35) {
		tmp = (y * i) * ((k * y5) - (x * c));
	} else if (t <= 1.35e-13) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (t <= 6e+56) {
		tmp = y4 * (y1 * t_2);
	} else if (t <= 1.6e+111) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) * ((b * y4) - (i * y5))
	t_2 = (k * y2) - (j * y3)
	t_3 = y4 * (t * ((b * j) - (c * y2)))
	t_4 = y1 * ((y4 * t_2) - (x * ((a * y2) - (i * j))))
	tmp = 0
	if t <= -1.5e+236:
		tmp = t_3
	elif t <= -1.12e+195:
		tmp = t_1
	elif t <= -1.08e+105:
		tmp = t_3
	elif t <= -5.1e-304:
		tmp = t_4
	elif t <= 1.25e-243:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif t <= 2.3e-84:
		tmp = t_4
	elif t <= 2.35e-35:
		tmp = (y * i) * ((k * y5) - (x * c))
	elif t <= 1.35e-13:
		tmp = (z * y0) * ((b * k) - (c * y3))
	elif t <= 6e+56:
		tmp = y4 * (y1 * t_2)
	elif t <= 1.6e+111:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))))
	t_4 = Float64(y1 * Float64(Float64(y4 * t_2) - Float64(x * Float64(Float64(a * y2) - Float64(i * j)))))
	tmp = 0.0
	if (t <= -1.5e+236)
		tmp = t_3;
	elseif (t <= -1.12e+195)
		tmp = t_1;
	elseif (t <= -1.08e+105)
		tmp = t_3;
	elseif (t <= -5.1e-304)
		tmp = t_4;
	elseif (t <= 1.25e-243)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (t <= 2.3e-84)
		tmp = t_4;
	elseif (t <= 2.35e-35)
		tmp = Float64(Float64(y * i) * Float64(Float64(k * y5) - Float64(x * c)));
	elseif (t <= 1.35e-13)
		tmp = Float64(Float64(z * y0) * Float64(Float64(b * k) - Float64(c * y3)));
	elseif (t <= 6e+56)
		tmp = Float64(y4 * Float64(y1 * t_2));
	elseif (t <= 1.6e+111)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) * ((b * y4) - (i * y5));
	t_2 = (k * y2) - (j * y3);
	t_3 = y4 * (t * ((b * j) - (c * y2)));
	t_4 = y1 * ((y4 * t_2) - (x * ((a * y2) - (i * j))));
	tmp = 0.0;
	if (t <= -1.5e+236)
		tmp = t_3;
	elseif (t <= -1.12e+195)
		tmp = t_1;
	elseif (t <= -1.08e+105)
		tmp = t_3;
	elseif (t <= -5.1e-304)
		tmp = t_4;
	elseif (t <= 1.25e-243)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (t <= 2.3e-84)
		tmp = t_4;
	elseif (t <= 2.35e-35)
		tmp = (y * i) * ((k * y5) - (x * c));
	elseif (t <= 1.35e-13)
		tmp = (z * y0) * ((b * k) - (c * y3));
	elseif (t <= 6e+56)
		tmp = y4 * (y1 * t_2);
	elseif (t <= 1.6e+111)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y1 * N[(N[(y4 * t$95$2), $MachinePrecision] - N[(x * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+236], t$95$3, If[LessEqual[t, -1.12e+195], t$95$1, If[LessEqual[t, -1.08e+105], t$95$3, If[LessEqual[t, -5.1e-304], t$95$4, If[LessEqual[t, 1.25e-243], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-84], t$95$4, If[LessEqual[t, 2.35e-35], N[(N[(y * i), $MachinePrecision] * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-13], N[(N[(z * y0), $MachinePrecision] * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+56], N[(y4 * N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+111], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -1.4999999999999999e236 or -1.12000000000000004e195 < t < -1.07999999999999994e105

   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. Step-by-step derivation

      1. associate-+l- 34.4%

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

   3. Simplified 34.4%

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

   4. Taylor expanded in y4 around inf 55.8%

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

   5. Taylor expanded in t around inf 74.1%

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

   if -1.4999999999999999e236 < t < -1.12000000000000004e195 or 1.6e111 < t

   1. Initial program 15.3%

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

      1. +-commutative 15.3%

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

      2. fma-def 15.3%

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

      3. *-commutative 15.3%

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

      4. *-commutative 15.3%

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

   3. Simplified 17.5%

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

   4. Taylor expanded in j around inf 48.1%

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

   5. Taylor expanded in t around inf 52.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 56.9%

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

   7. Simplified 56.9%

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

   if -1.07999999999999994e105 < t < -5.09999999999999979e-304 or 1.25e-243 < t < 2.29999999999999981e-84

   1. Initial program 31.0%

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

      1. +-commutative 31.0%

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

      2. fma-def 31.8%

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

      3. *-commutative 31.8%

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

      4. *-commutative 31.8%

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

   3. Simplified 36.0%

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

   4. Taylor expanded in x around inf 44.4%

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

      1. mul-1-neg 44.4%

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

   6. Simplified 44.4%

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

   7. Taylor expanded in y1 around -inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. *-commutative 44.9%

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

      3. distribute-rgt-neg-in 44.9%

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

      4. +-commutative 44.9%

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

      5. mul-1-neg 44.9%

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

      6. unsub-neg 44.9%

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

      7. *-commutative 44.9%

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

      8. *-commutative 44.9%

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

   9. Simplified 44.9%

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

   if -5.09999999999999979e-304 < t < 1.25e-243

   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. Step-by-step derivation

      1. +-commutative 34.3%

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

      2. fma-def 40.9%

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

      3. *-commutative 40.9%

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

      4. *-commutative 40.9%

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

   3. Simplified 47.6%

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

   4. Taylor expanded in y0 around inf 54.4%

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

      1. mul-1-neg 54.4%

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

   6. Simplified 54.4%

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

   7. Taylor expanded in c around inf 47.5%

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

      1. *-commutative 47.5%

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

      2. *-commutative 47.5%

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

      3. associate-*l* 54.5%

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

      4. *-commutative 54.5%

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

   9. Simplified 54.5%

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

   if 2.29999999999999981e-84 < t < 2.35e-35

   1. Initial program 27.0%

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

      1. associate-+l- 27.0%

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

   3. Simplified 27.0%

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

   4. Taylor expanded in i around -inf 34.3%

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

      1. mul-1-neg 34.3%

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

      2. associate--l+ 34.3%

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

   6. Simplified 34.3%

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

   7. Taylor expanded in y around inf 41.2%

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

      1. *-commutative 41.2%

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

      2. *-commutative 41.2%

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

      3. +-commutative 41.2%

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

      4. mul-1-neg 41.2%

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

      5. sub-neg 41.2%

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

      6. *-commutative 41.2%

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

      7. *-commutative 41.2%

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

   9. Simplified 41.2%

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

   if 2.35e-35 < t < 1.35000000000000005e-13

   1. Initial program 59.7%

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

      1. +-commutative 59.7%

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

      2. fma-def 59.7%

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

      3. *-commutative 59.7%

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

      4. *-commutative 59.7%

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

   3. Simplified 59.7%

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

   4. Taylor expanded in y0 around inf 40.9%

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

      1. mul-1-neg 40.9%

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

   6. Simplified 40.9%

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

   7. Taylor expanded in z around inf 60.2%

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

      1. associate-*r* 60.2%

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

      2. +-commutative 60.2%

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

      3. mul-1-neg 60.2%

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

      4. sub-neg 60.2%

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

      5. *-commutative 60.2%

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

      6. *-commutative 60.2%

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

   9. Simplified 60.2%

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

   if 1.35000000000000005e-13 < t < 6.00000000000000012e56

   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. Step-by-step derivation

      1. associate-+l- 37.5%

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

   3. Simplified 37.5%

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

   4. Taylor expanded in y4 around inf 51.1%

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

   5. Taylor expanded in y1 around inf 50.3%

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

   if 6.00000000000000012e56 < t < 1.6e111

   1. Initial program 11.1%

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

      1. +-commutative 11.1%

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

      2. fma-def 11.1%

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

      3. *-commutative 11.1%

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

      4. *-commutative 11.1%

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

   3. Simplified 11.1%

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

   4. Taylor expanded in j around inf 33.5%

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

   5. Taylor expanded in y0 around inf 66.9%

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

      1. *-commutative 66.9%

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

   7. Simplified 66.9%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y5 \cdot y3 - b \cdot x\right)\right)} \cdot j \]
3. Recombined 8 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+236}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+195}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{+105}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-304}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-243}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-84}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-35}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(k \cdot y5 - x \cdot c\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-13}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+56}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \end{array} \]

Alternative 12: 32.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y4 - a \cdot y5\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+119}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(j \cdot y1 - y \cdot c\right)\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{-77}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \left(y3 \cdot t_1\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-287}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-32}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+30} \lor \neg \left(x \leq 7.8 \cdot 10^{+46}\right):\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y4) (* a y5))))
   (if (<= x -1.1e+119)
     (* (* x i) (- (* j y1) (* y c)))
     (if (<= x -1.28e-77)
       (* y4 (* t (- (* b j) (* c y2))))
       (if (<= x -4.8e-213)
         (* y (* y3 t_1))
         (if (<= x -5.8e-287)
           (* y1 (- (* y4 (- (* k y2) (* j y3))) (* x (- (* a y2) (* i j)))))
           (if (<= x 2.55e-225)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= x 1.25e-179)
               (* t (+ (* z (- (* c i) (* a b))) (* y2 (- (* a y5) (* c y4)))))
               (if (<= x 2.5e-32)
                 (* y0 (* y3 (- (* j y5) (* z c))))
                 (if (or (<= x 3.1e+30) (not (<= x 7.8e+46)))
                   (* j (* x (- (* i y1) (* b y0))))
                   (* (* y y3) t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) - (a * y5);
	double tmp;
	if (x <= -1.1e+119) {
		tmp = (x * i) * ((j * y1) - (y * c));
	} else if (x <= -1.28e-77) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (x <= -4.8e-213) {
		tmp = y * (y3 * t_1);
	} else if (x <= -5.8e-287) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) - (x * ((a * y2) - (i * j))));
	} else if (x <= 2.55e-225) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (x <= 1.25e-179) {
		tmp = t * ((z * ((c * i) - (a * b))) + (y2 * ((a * y5) - (c * y4))));
	} else if (x <= 2.5e-32) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if ((x <= 3.1e+30) || !(x <= 7.8e+46)) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = (y * y3) * 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 = (c * y4) - (a * y5)
    if (x <= (-1.1d+119)) then
        tmp = (x * i) * ((j * y1) - (y * c))
    else if (x <= (-1.28d-77)) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (x <= (-4.8d-213)) then
        tmp = y * (y3 * t_1)
    else if (x <= (-5.8d-287)) then
        tmp = y1 * ((y4 * ((k * y2) - (j * y3))) - (x * ((a * y2) - (i * j))))
    else if (x <= 2.55d-225) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (x <= 1.25d-179) then
        tmp = t * ((z * ((c * i) - (a * b))) + (y2 * ((a * y5) - (c * y4))))
    else if (x <= 2.5d-32) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if ((x <= 3.1d+30) .or. (.not. (x <= 7.8d+46))) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else
        tmp = (y * y3) * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) - (a * y5);
	double tmp;
	if (x <= -1.1e+119) {
		tmp = (x * i) * ((j * y1) - (y * c));
	} else if (x <= -1.28e-77) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (x <= -4.8e-213) {
		tmp = y * (y3 * t_1);
	} else if (x <= -5.8e-287) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) - (x * ((a * y2) - (i * j))));
	} else if (x <= 2.55e-225) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (x <= 1.25e-179) {
		tmp = t * ((z * ((c * i) - (a * b))) + (y2 * ((a * y5) - (c * y4))));
	} else if (x <= 2.5e-32) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if ((x <= 3.1e+30) || !(x <= 7.8e+46)) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = (y * y3) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y4) - (a * y5)
	tmp = 0
	if x <= -1.1e+119:
		tmp = (x * i) * ((j * y1) - (y * c))
	elif x <= -1.28e-77:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif x <= -4.8e-213:
		tmp = y * (y3 * t_1)
	elif x <= -5.8e-287:
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) - (x * ((a * y2) - (i * j))))
	elif x <= 2.55e-225:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif x <= 1.25e-179:
		tmp = t * ((z * ((c * i) - (a * b))) + (y2 * ((a * y5) - (c * y4))))
	elif x <= 2.5e-32:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif (x <= 3.1e+30) or not (x <= 7.8e+46):
		tmp = j * (x * ((i * y1) - (b * y0)))
	else:
		tmp = (y * y3) * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y4) - Float64(a * y5))
	tmp = 0.0
	if (x <= -1.1e+119)
		tmp = Float64(Float64(x * i) * Float64(Float64(j * y1) - Float64(y * c)));
	elseif (x <= -1.28e-77)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (x <= -4.8e-213)
		tmp = Float64(y * Float64(y3 * t_1));
	elseif (x <= -5.8e-287)
		tmp = Float64(y1 * Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(x * Float64(Float64(a * y2) - Float64(i * j)))));
	elseif (x <= 2.55e-225)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (x <= 1.25e-179)
		tmp = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (x <= 2.5e-32)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif ((x <= 3.1e+30) || !(x <= 7.8e+46))
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	else
		tmp = Float64(Float64(y * y3) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y4) - (a * y5);
	tmp = 0.0;
	if (x <= -1.1e+119)
		tmp = (x * i) * ((j * y1) - (y * c));
	elseif (x <= -1.28e-77)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (x <= -4.8e-213)
		tmp = y * (y3 * t_1);
	elseif (x <= -5.8e-287)
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) - (x * ((a * y2) - (i * j))));
	elseif (x <= 2.55e-225)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (x <= 1.25e-179)
		tmp = t * ((z * ((c * i) - (a * b))) + (y2 * ((a * y5) - (c * y4))));
	elseif (x <= 2.5e-32)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif ((x <= 3.1e+30) || ~((x <= 7.8e+46)))
		tmp = j * (x * ((i * y1) - (b * y0)));
	else
		tmp = (y * y3) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+119], N[(N[(x * i), $MachinePrecision] * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.28e-77], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e-213], N[(y * N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-287], N[(y1 * N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.55e-225], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-179], N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-32], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.1e+30], N[Not[LessEqual[x, 7.8e+46]], $MachinePrecision]], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * y3), $MachinePrecision] * t$95$1), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -1.1000000000000001e119

   1. Initial program 21.4%

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

      1. associate-+l- 21.4%

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

   3. Simplified 21.4%

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

   4. Taylor expanded in i around -inf 38.3%

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

      1. mul-1-neg 38.3%

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

      2. associate--l+ 38.3%

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

   6. Simplified 38.3%

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

   7. Taylor expanded in x around inf 53.1%

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

   if -1.1000000000000001e119 < x < -1.28e-77

   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. Step-by-step derivation

      1. associate-+l- 30.2%

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

   3. Simplified 30.2%

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

   4. Taylor expanded in y4 around inf 40.1%

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

   5. Taylor expanded in t around inf 46.3%

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

   if -1.28e-77 < x < -4.79999999999999991e-213

   1. Initial program 24.3%

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

      1. associate-+l- 24.3%

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

   3. Simplified 24.3%

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

   4. Taylor expanded in y3 around -inf 58.2%

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

   5. Taylor expanded in y around inf 40.6%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(a \cdot y5 - c \cdot y4\right) \cdot \left(y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.6%

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

      2. associate-*l* 43.5%

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

   7. Simplified 43.5%

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

   if -4.79999999999999991e-213 < x < -5.7999999999999996e-287

   1. Initial program 47.1%

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

      1. +-commutative 47.1%

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

      2. fma-def 47.1%

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

      3. *-commutative 47.1%

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

      4. *-commutative 47.1%

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

   3. Simplified 47.1%

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

   4. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in y1 around -inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. *-commutative 65.7%

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

      3. distribute-rgt-neg-in 65.7%

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

      4. +-commutative 65.7%

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

      5. mul-1-neg 65.7%

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

      6. unsub-neg 65.7%

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

      7. *-commutative 65.7%

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

      8. *-commutative 65.7%

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

   9. Simplified 65.7%

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

   if -5.7999999999999996e-287 < x < 2.5499999999999999e-225

   1. Initial program 42.5%

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

      1. associate-+l- 42.5%

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

   3. Simplified 42.5%

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

   4. Taylor expanded in y4 around inf 50.5%

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

   5. Taylor expanded in c around inf 46.9%

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

   if 2.5499999999999999e-225 < x < 1.2499999999999999e-179

   1. Initial program 53.7%

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

      1. +-commutative 53.7%

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

      2. fma-def 53.7%

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

      3. *-commutative 53.7%

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

      4. *-commutative 53.7%

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

   3. Simplified 53.7%

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

   4. Taylor expanded in x around inf 53.9%

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

      1. mul-1-neg 53.9%

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

   6. Simplified 53.9%

      \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \color{blue}{\left(\left(-\left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot x}\right)\right)\right) \]

   7. Taylor expanded in t around -inf 55.3%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   if 1.2499999999999999e-179 < x < 2.5e-32

   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. Step-by-step derivation

      1. +-commutative 30.4%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 30.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 30.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 30.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 34.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 48.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 48.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in y3 around inf 57.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(c \cdot z\right) - -1 \cdot \left(j \cdot y5\right)\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 57.1%

         \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) - -1 \cdot \left(j \cdot y5\right)\right)\right)} \]

      2. cancel-sign-sub-inv 57.1%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right) + \left(--1\right) \cdot \left(j \cdot y5\right)\right)}\right) \]

      3. metadata-eval 57.1%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + \color{blue}{1} \cdot \left(j \cdot y5\right)\right)\right) \]

      4. *-lft-identity 57.1%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + \color{blue}{j \cdot y5}\right)\right) \]

      5. +-commutative 57.1%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y5 + -1 \cdot \left(c \cdot z\right)\right)}\right) \]

      6. mul-1-neg 57.1%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(j \cdot y5 + \color{blue}{\left(-c \cdot z\right)}\right)\right) \]

      7. unsub-neg 57.1%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y5 - c \cdot z\right)}\right) \]

      8. *-commutative 57.1%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(\color{blue}{y5 \cdot j} - c \cdot z\right)\right) \]

   9. Simplified 57.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(y5 \cdot j - c \cdot z\right)\right)} \]

   if 2.5e-32 < x < 3.0999999999999998e30 or 7.7999999999999999e46 < x

   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. Step-by-step derivation

      1. +-commutative 21.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 21.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 21.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 21.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 44.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 52.6%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   if 3.0999999999999998e30 < x < 7.7999999999999999e46

   1. Initial program 2.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 2.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 2.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y3 around -inf 50.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(j \cdot \left(y4 \cdot y1 - y0 \cdot y5\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot z\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y3\right)} \]

   5. Taylor expanded in y around inf 83.6%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(a \cdot y5 - c \cdot y4\right) \cdot \left(y \cdot y3\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+119}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(j \cdot y1 - y \cdot c\right)\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{-77}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-287}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-32}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+30} \lor \neg \left(x \leq 7.8 \cdot 10^{+46}\right):\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\\ \end{array} \]

Alternative 13: 32.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ t_2 := y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{if}\;i \leq -9.5 \cdot 10^{+135}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;i \leq -2.9 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-43}:\\ \;\;\;\;y4 \cdot \left(\left(j \cdot y1\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-236}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 6.4 \cdot 10^{-69}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* t (- (* b j) (* c y2)))))
        (t_2 (* y0 (* y2 (- (* x c) (* k y5))))))
   (if (<= i -9.5e+135)
     (* k (* i (- (* y y5) (* z y1))))
     (if (<= i -5.2e+44)
       (* j (* y0 (- (* y3 y5) (* x b))))
       (if (<= i -2.9e-6)
         t_2
         (if (<= i -9e-43)
           (* y4 (* (* j y1) (- y3)))
           (if (<= i -2.2e-195)
             t_2
             (if (<= i -5.5e-283)
               t_1
               (if (<= i 3e-236)
                 (* c (* y4 (- (* y y3) (* t y2))))
                 (if (<= i 6.4e-69)
                   (* y4 (* y1 (- (* k y2) (* j y3))))
                   (if (<= i 7.5e-5)
                     t_1
                     (* c (* i (- (* z t) (* x y)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (t * ((b * j) - (c * y2)));
	double t_2 = y0 * (y2 * ((x * c) - (k * y5)));
	double tmp;
	if (i <= -9.5e+135) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (i <= -5.2e+44) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (i <= -2.9e-6) {
		tmp = t_2;
	} else if (i <= -9e-43) {
		tmp = y4 * ((j * y1) * -y3);
	} else if (i <= -2.2e-195) {
		tmp = t_2;
	} else if (i <= -5.5e-283) {
		tmp = t_1;
	} else if (i <= 3e-236) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (i <= 6.4e-69) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (i <= 7.5e-5) {
		tmp = t_1;
	} else {
		tmp = c * (i * ((z * t) - (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y4 * (t * ((b * j) - (c * y2)))
    t_2 = y0 * (y2 * ((x * c) - (k * y5)))
    if (i <= (-9.5d+135)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (i <= (-5.2d+44)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (i <= (-2.9d-6)) then
        tmp = t_2
    else if (i <= (-9d-43)) then
        tmp = y4 * ((j * y1) * -y3)
    else if (i <= (-2.2d-195)) then
        tmp = t_2
    else if (i <= (-5.5d-283)) then
        tmp = t_1
    else if (i <= 3d-236) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (i <= 6.4d-69) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (i <= 7.5d-5) then
        tmp = t_1
    else
        tmp = c * (i * ((z * t) - (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (t * ((b * j) - (c * y2)));
	double t_2 = y0 * (y2 * ((x * c) - (k * y5)));
	double tmp;
	if (i <= -9.5e+135) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (i <= -5.2e+44) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (i <= -2.9e-6) {
		tmp = t_2;
	} else if (i <= -9e-43) {
		tmp = y4 * ((j * y1) * -y3);
	} else if (i <= -2.2e-195) {
		tmp = t_2;
	} else if (i <= -5.5e-283) {
		tmp = t_1;
	} else if (i <= 3e-236) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (i <= 6.4e-69) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (i <= 7.5e-5) {
		tmp = t_1;
	} else {
		tmp = c * (i * ((z * t) - (x * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (t * ((b * j) - (c * y2)))
	t_2 = y0 * (y2 * ((x * c) - (k * y5)))
	tmp = 0
	if i <= -9.5e+135:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif i <= -5.2e+44:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif i <= -2.9e-6:
		tmp = t_2
	elif i <= -9e-43:
		tmp = y4 * ((j * y1) * -y3)
	elif i <= -2.2e-195:
		tmp = t_2
	elif i <= -5.5e-283:
		tmp = t_1
	elif i <= 3e-236:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif i <= 6.4e-69:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif i <= 7.5e-5:
		tmp = t_1
	else:
		tmp = c * (i * ((z * t) - (x * y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))))
	t_2 = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))))
	tmp = 0.0
	if (i <= -9.5e+135)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (i <= -5.2e+44)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (i <= -2.9e-6)
		tmp = t_2;
	elseif (i <= -9e-43)
		tmp = Float64(y4 * Float64(Float64(j * y1) * Float64(-y3)));
	elseif (i <= -2.2e-195)
		tmp = t_2;
	elseif (i <= -5.5e-283)
		tmp = t_1;
	elseif (i <= 3e-236)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (i <= 6.4e-69)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (i <= 7.5e-5)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (t * ((b * j) - (c * y2)));
	t_2 = y0 * (y2 * ((x * c) - (k * y5)));
	tmp = 0.0;
	if (i <= -9.5e+135)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (i <= -5.2e+44)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (i <= -2.9e-6)
		tmp = t_2;
	elseif (i <= -9e-43)
		tmp = y4 * ((j * y1) * -y3);
	elseif (i <= -2.2e-195)
		tmp = t_2;
	elseif (i <= -5.5e-283)
		tmp = t_1;
	elseif (i <= 3e-236)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (i <= 6.4e-69)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (i <= 7.5e-5)
		tmp = t_1;
	else
		tmp = c * (i * ((z * t) - (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.5e+135], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.2e+44], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.9e-6], t$95$2, If[LessEqual[i, -9e-43], N[(y4 * N[(N[(j * y1), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.2e-195], t$95$2, If[LessEqual[i, -5.5e-283], t$95$1, If[LessEqual[i, 3e-236], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.4e-69], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.5e-5], t$95$1, N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -9.50000000000000036e135

   1. Initial program 13.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 13.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 13.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 13.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 13.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 15.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in k around inf 45.2%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(y \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(y0 \cdot b - i \cdot y1\right) \cdot z + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)\right)} \]

   5. Taylor expanded in i around inf 48.2%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 48.2%

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(-y1 \cdot z\right)}\right)\right) \]

      2. sub-neg 48.2%

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      3. *-commutative 48.2%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if -9.50000000000000036e135 < i < -5.1999999999999998e44

   1. Initial program 47.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 47.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 47.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 47.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 47.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 52.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 47.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 53.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 53.6%

         \[\leadsto \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \cdot j \]

   7. Simplified 53.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y5 \cdot y3 - b \cdot x\right)\right)} \cdot j \]

   if -5.1999999999999998e44 < i < -2.9000000000000002e-6 or -9.0000000000000005e-43 < i < -2.20000000000000005e-195

   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. Step-by-step derivation

      1. +-commutative 37.5%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 37.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 37.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 37.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 42.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 38.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 38.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in y2 around inf 41.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot x - k \cdot y5\right) \cdot y2\right)} \]

   if -2.9000000000000002e-6 < i < -9.0000000000000005e-43

   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. Step-by-step derivation

      1. +-commutative 37.5%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 37.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 37.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 37.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 37.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 62.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y1 around -inf 75.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* 75.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 75.2%

         \[\leadsto \left(\color{blue}{\left(-y1\right)} \cdot \left(y4 \cdot y3 - i \cdot x\right)\right) \cdot j \]

   7. Simplified 75.2%

      \[\leadsto \color{blue}{\left(\left(-y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

   8. Taylor expanded in y4 around inf 75.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 75.3%

         \[\leadsto \color{blue}{-y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)} \]

      2. distribute-rgt-neg-in 75.3%

         \[\leadsto \color{blue}{y4 \cdot \left(-y1 \cdot \left(y3 \cdot j\right)\right)} \]

      3. associate-*r* 75.3%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(y1 \cdot y3\right) \cdot j}\right) \]

      4. *-commutative 75.3%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(y3 \cdot y1\right)} \cdot j\right) \]

      5. associate-*l* 75.3%

         \[\leadsto y4 \cdot \left(-\color{blue}{y3 \cdot \left(y1 \cdot j\right)}\right) \]

   10. Simplified 75.3%

       \[\leadsto \color{blue}{y4 \cdot \left(-y3 \cdot \left(y1 \cdot j\right)\right)} \]

   if -2.20000000000000005e-195 < i < -5.49999999999999953e-283 or 6.39999999999999997e-69 < i < 7.49999999999999934e-5

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 42.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 43.0%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]

   if -5.49999999999999953e-283 < i < 3.00000000000000014e-236

   1. Initial program 54.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 54.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 54.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 50.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 50.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 3.00000000000000014e-236 < i < 6.39999999999999997e-69

   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. Step-by-step derivation

      1. associate-+l- 37.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 37.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 56.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 53.8%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]

   if 7.49999999999999934e-5 < i

   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. Step-by-step derivation

      1. associate-+l- 14.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 14.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in i around -inf 56.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(t \cdot j - k \cdot y\right) \cdot y5\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.6%

         \[\leadsto \color{blue}{-i \cdot \left(\left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(t \cdot j - k \cdot y\right) \cdot y5\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ 56.6%

         \[\leadsto -i \cdot \color{blue}{\left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(t \cdot j - k \cdot y\right) \cdot y5 - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Simplified 56.6%

      \[\leadsto \color{blue}{-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(t \cdot j - k \cdot y\right) \cdot y5 - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   7. Taylor expanded in c around inf 55.2%

      \[\leadsto -\color{blue}{c \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.5 \cdot 10^{+135}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;i \leq -2.9 \cdot 10^{-6}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-43}:\\ \;\;\;\;y4 \cdot \left(\left(j \cdot y1\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{-195}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-283}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-236}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 6.4 \cdot 10^{-69}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-5}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \end{array} \]

Alternative 14: 31.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;c \leq -7.6 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-265}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{-304}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-291}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-223}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-76}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+68}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* c (- (* y y3) (* t y2))))))
   (if (<= c -7.6e-39)
     t_1
     (if (<= c -1.5e-265)
       (* (* t j) (- (* b y4) (* i y5)))
       (if (<= c 7.4e-304)
         (* k (* i (- (* y y5) (* z y1))))
         (if (<= c 4e-291)
           (* y4 (* y1 (- (* k y2) (* j y3))))
           (if (<= c 9e-223)
             (* j (* x (- (* i y1) (* b y0))))
             (if (<= c 6e-76)
               (* j (* y0 (- (* y3 y5) (* x b))))
               (if (<= c 5.2e+68)
                 (* y4 (* t (- (* b j) (* c y2))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (c * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -7.6e-39) {
		tmp = t_1;
	} else if (c <= -1.5e-265) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (c <= 7.4e-304) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 4e-291) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (c <= 9e-223) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (c <= 6e-76) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (c <= 5.2e+68) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y4 * (c * ((y * y3) - (t * y2)))
    if (c <= (-7.6d-39)) then
        tmp = t_1
    else if (c <= (-1.5d-265)) then
        tmp = (t * j) * ((b * y4) - (i * y5))
    else if (c <= 7.4d-304) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (c <= 4d-291) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (c <= 9d-223) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (c <= 6d-76) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (c <= 5.2d+68) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (c * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -7.6e-39) {
		tmp = t_1;
	} else if (c <= -1.5e-265) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (c <= 7.4e-304) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 4e-291) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (c <= 9e-223) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (c <= 6e-76) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (c <= 5.2e+68) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (c * ((y * y3) - (t * y2)))
	tmp = 0
	if c <= -7.6e-39:
		tmp = t_1
	elif c <= -1.5e-265:
		tmp = (t * j) * ((b * y4) - (i * y5))
	elif c <= 7.4e-304:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif c <= 4e-291:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif c <= 9e-223:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif c <= 6e-76:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif c <= 5.2e+68:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (c <= -7.6e-39)
		tmp = t_1;
	elseif (c <= -1.5e-265)
		tmp = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)));
	elseif (c <= 7.4e-304)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (c <= 4e-291)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (c <= 9e-223)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (c <= 6e-76)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (c <= 5.2e+68)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (c * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (c <= -7.6e-39)
		tmp = t_1;
	elseif (c <= -1.5e-265)
		tmp = (t * j) * ((b * y4) - (i * y5));
	elseif (c <= 7.4e-304)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (c <= 4e-291)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (c <= 9e-223)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (c <= 6e-76)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (c <= 5.2e+68)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.6e-39], t$95$1, If[LessEqual[c, -1.5e-265], N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.4e-304], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4e-291], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9e-223], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6e-76], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.2e+68], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -7.6000000000000004e-39 or 5.1999999999999996e68 < c

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 42.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around 0 33.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right) + -1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 33.3%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3\right)} + -1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right) \]

      2. mul-1-neg 33.3%

         \[\leadsto \left(c \cdot y4\right) \cdot \left(y \cdot y3\right) + \color{blue}{\left(-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]

      3. associate-*r* 27.9%

         \[\leadsto \left(c \cdot y4\right) \cdot \left(y \cdot y3\right) + \left(-\color{blue}{\left(c \cdot y4\right) \cdot \left(t \cdot y2\right)}\right) \]

      4. distribute-rgt-neg-in 27.9%

         \[\leadsto \left(c \cdot y4\right) \cdot \left(y \cdot y3\right) + \color{blue}{\left(c \cdot y4\right) \cdot \left(-t \cdot y2\right)} \]

      5. distribute-lft-in 42.2%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 + \left(-t \cdot y2\right)\right)} \]

      6. sub-neg 42.2%

         \[\leadsto \left(c \cdot y4\right) \cdot \color{blue}{\left(y \cdot y3 - t \cdot y2\right)} \]

      7. associate-*r* 42.2%

         \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

      8. *-commutative 42.2%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \cdot c} \]

      9. associate-*l* 47.3%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3 - t \cdot y2\right) \cdot c\right)} \]

   8. Simplified 47.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3 - t \cdot y2\right) \cdot c\right)} \]

   if -7.6000000000000004e-39 < c < -1.4999999999999999e-265

   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. Step-by-step derivation

      1. +-commutative 32.9%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 32.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 32.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 32.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 36.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in t around inf 38.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \]

   if -1.4999999999999999e-265 < c < 7.4000000000000006e-304

   1. Initial program 46.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 46.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 46.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 46.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 46.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 53.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in k around inf 46.7%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(y \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(y0 \cdot b - i \cdot y1\right) \cdot z + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)\right)} \]

   5. Taylor expanded in i around inf 69.8%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 69.8%

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(-y1 \cdot z\right)}\right)\right) \]

      2. sub-neg 69.8%

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      3. *-commutative 69.8%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   7. Simplified 69.8%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if 7.4000000000000006e-304 < c < 3.99999999999999985e-291

   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. Step-by-step derivation

      1. associate-+l- 28.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 29.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 58.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]

   if 3.99999999999999985e-291 < c < 8.99999999999999935e-223

   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. Step-by-step derivation

      1. +-commutative 26.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 26.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 26.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 26.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 40.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 40.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 41.2%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   if 8.99999999999999935e-223 < c < 6.00000000000000048e-76

   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. Step-by-step derivation

      1. +-commutative 32.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 32.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 32.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 32.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 42.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 39.9%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 39.9%

         \[\leadsto \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \cdot j \]

   7. Simplified 39.9%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y5 \cdot y3 - b \cdot x\right)\right)} \cdot j \]

   if 6.00000000000000048e-76 < c < 5.1999999999999996e68

   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. Step-by-step derivation

      1. associate-+l- 37.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 37.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 47.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 57.0%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.6 \cdot 10^{-39}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-265}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{-304}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-291}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-223}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-76}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+68}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 15: 31.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ t_2 := j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{if}\;i \leq -5.5 \cdot 10^{+135}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -7.8 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-6}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq -2.5 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 0.0115:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* t (- (* b j) (* c y2)))))
        (t_2 (* j (* y1 (- (* x i) (* y3 y4))))))
   (if (<= i -5.5e+135)
     (* k (* i (- (* y y5) (* z y1))))
     (if (<= i -7.8e+43)
       (* j (* y0 (- (* y3 y5) (* x b))))
       (if (<= i -4.2e-6)
         (* y0 (* y2 (- (* x c) (* k y5))))
         (if (<= i -2.5e-126)
           t_2
           (if (<= i 1.15e-127)
             t_1
             (if (<= i 1.15e-95)
               t_2
               (if (<= i 0.0115) t_1 (* c (* i (- (* z t) (* x y)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (t * ((b * j) - (c * y2)));
	double t_2 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (i <= -5.5e+135) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (i <= -7.8e+43) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (i <= -4.2e-6) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (i <= -2.5e-126) {
		tmp = t_2;
	} else if (i <= 1.15e-127) {
		tmp = t_1;
	} else if (i <= 1.15e-95) {
		tmp = t_2;
	} else if (i <= 0.0115) {
		tmp = t_1;
	} else {
		tmp = c * (i * ((z * t) - (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y4 * (t * ((b * j) - (c * y2)))
    t_2 = j * (y1 * ((x * i) - (y3 * y4)))
    if (i <= (-5.5d+135)) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (i <= (-7.8d+43)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (i <= (-4.2d-6)) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (i <= (-2.5d-126)) then
        tmp = t_2
    else if (i <= 1.15d-127) then
        tmp = t_1
    else if (i <= 1.15d-95) then
        tmp = t_2
    else if (i <= 0.0115d0) then
        tmp = t_1
    else
        tmp = c * (i * ((z * t) - (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (t * ((b * j) - (c * y2)));
	double t_2 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (i <= -5.5e+135) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (i <= -7.8e+43) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (i <= -4.2e-6) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (i <= -2.5e-126) {
		tmp = t_2;
	} else if (i <= 1.15e-127) {
		tmp = t_1;
	} else if (i <= 1.15e-95) {
		tmp = t_2;
	} else if (i <= 0.0115) {
		tmp = t_1;
	} else {
		tmp = c * (i * ((z * t) - (x * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (t * ((b * j) - (c * y2)))
	t_2 = j * (y1 * ((x * i) - (y3 * y4)))
	tmp = 0
	if i <= -5.5e+135:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif i <= -7.8e+43:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif i <= -4.2e-6:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif i <= -2.5e-126:
		tmp = t_2
	elif i <= 1.15e-127:
		tmp = t_1
	elif i <= 1.15e-95:
		tmp = t_2
	elif i <= 0.0115:
		tmp = t_1
	else:
		tmp = c * (i * ((z * t) - (x * y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))))
	t_2 = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))))
	tmp = 0.0
	if (i <= -5.5e+135)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (i <= -7.8e+43)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (i <= -4.2e-6)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (i <= -2.5e-126)
		tmp = t_2;
	elseif (i <= 1.15e-127)
		tmp = t_1;
	elseif (i <= 1.15e-95)
		tmp = t_2;
	elseif (i <= 0.0115)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (t * ((b * j) - (c * y2)));
	t_2 = j * (y1 * ((x * i) - (y3 * y4)));
	tmp = 0.0;
	if (i <= -5.5e+135)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (i <= -7.8e+43)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (i <= -4.2e-6)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (i <= -2.5e-126)
		tmp = t_2;
	elseif (i <= 1.15e-127)
		tmp = t_1;
	elseif (i <= 1.15e-95)
		tmp = t_2;
	elseif (i <= 0.0115)
		tmp = t_1;
	else
		tmp = c * (i * ((z * t) - (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.5e+135], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7.8e+43], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.2e-6], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.5e-126], t$95$2, If[LessEqual[i, 1.15e-127], t$95$1, If[LessEqual[i, 1.15e-95], t$95$2, If[LessEqual[i, 0.0115], t$95$1, N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -5.4999999999999999e135

   1. Initial program 13.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 13.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 13.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 13.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 13.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 15.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in k around inf 45.2%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(y \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(y0 \cdot b - i \cdot y1\right) \cdot z + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)\right)} \]

   5. Taylor expanded in i around inf 48.2%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 48.2%

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(-y1 \cdot z\right)}\right)\right) \]

      2. sub-neg 48.2%

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      3. *-commutative 48.2%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if -5.4999999999999999e135 < i < -7.8000000000000001e43

   1. Initial program 47.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 47.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 47.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 47.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 47.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 52.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 47.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 53.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 53.6%

         \[\leadsto \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \cdot j \]

   7. Simplified 53.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y5 \cdot y3 - b \cdot x\right)\right)} \cdot j \]

   if -7.8000000000000001e43 < i < -4.1999999999999996e-6

   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. Step-by-step derivation

      1. +-commutative 33.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 33.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 33.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 33.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 33.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 56.4%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 56.4%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in y2 around inf 56.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot x - k \cdot y5\right) \cdot y2\right)} \]

   if -4.1999999999999996e-6 < i < -2.50000000000000003e-126 or 1.15000000000000009e-127 < i < 1.15e-95

   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. Step-by-step derivation

      1. +-commutative 39.4%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 39.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 39.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 39.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 41.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 52.2%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y1 around -inf 47.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* 47.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 47.9%

         \[\leadsto \left(\color{blue}{\left(-y1\right)} \cdot \left(y4 \cdot y3 - i \cdot x\right)\right) \cdot j \]

   7. Simplified 47.9%

      \[\leadsto \color{blue}{\left(\left(-y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

   if -2.50000000000000003e-126 < i < 1.15000000000000009e-127 or 1.15e-95 < i < 0.0115

   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. Step-by-step derivation

      1. associate-+l- 36.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 44.7%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]

   if 0.0115 < i

   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. Step-by-step derivation

      1. associate-+l- 14.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 14.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in i around -inf 56.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(t \cdot j - k \cdot y\right) \cdot y5\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.6%

         \[\leadsto \color{blue}{-i \cdot \left(\left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(t \cdot j - k \cdot y\right) \cdot y5\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ 56.6%

         \[\leadsto -i \cdot \color{blue}{\left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(t \cdot j - k \cdot y\right) \cdot y5 - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Simplified 56.6%

      \[\leadsto \color{blue}{-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(t \cdot j - k \cdot y\right) \cdot y5 - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   7. Taylor expanded in c around inf 55.2%

      \[\leadsto -\color{blue}{c \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.5 \cdot 10^{+135}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq -7.8 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-6}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq -2.5 \cdot 10^{-126}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-127}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 0.0115:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \end{array} \]

Alternative 16: 22.5% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.7 \cdot 10^{+108}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-182}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-308}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-273}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-205}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-188}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-34}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(x \cdot \left(-b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -8.7e+108)
   (* i (* y1 (* x j)))
   (if (<= x -7e-182)
     (* y0 (* y3 (* j y5)))
     (if (<= x -9e-308)
       (* k (* y4 (* y1 y2)))
       (if (<= x 6.1e-273)
         (* c (* y4 (* y y3)))
         (if (<= x 4.2e-205)
           (* c (* y4 (* t (- y2))))
           (if (<= x 1.55e-188)
             (* j (* y4 (* y1 (- y3))))
             (if (<= x 5.1e-34)
               (* y0 (* c (* z (- y3))))
               (* j (* y0 (* x (- b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -8.7e+108) {
		tmp = i * (y1 * (x * j));
	} else if (x <= -7e-182) {
		tmp = y0 * (y3 * (j * y5));
	} else if (x <= -9e-308) {
		tmp = k * (y4 * (y1 * y2));
	} else if (x <= 6.1e-273) {
		tmp = c * (y4 * (y * y3));
	} else if (x <= 4.2e-205) {
		tmp = c * (y4 * (t * -y2));
	} else if (x <= 1.55e-188) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (x <= 5.1e-34) {
		tmp = y0 * (c * (z * -y3));
	} else {
		tmp = j * (y0 * (x * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-8.7d+108)) then
        tmp = i * (y1 * (x * j))
    else if (x <= (-7d-182)) then
        tmp = y0 * (y3 * (j * y5))
    else if (x <= (-9d-308)) then
        tmp = k * (y4 * (y1 * y2))
    else if (x <= 6.1d-273) then
        tmp = c * (y4 * (y * y3))
    else if (x <= 4.2d-205) then
        tmp = c * (y4 * (t * -y2))
    else if (x <= 1.55d-188) then
        tmp = j * (y4 * (y1 * -y3))
    else if (x <= 5.1d-34) then
        tmp = y0 * (c * (z * -y3))
    else
        tmp = j * (y0 * (x * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -8.7e+108) {
		tmp = i * (y1 * (x * j));
	} else if (x <= -7e-182) {
		tmp = y0 * (y3 * (j * y5));
	} else if (x <= -9e-308) {
		tmp = k * (y4 * (y1 * y2));
	} else if (x <= 6.1e-273) {
		tmp = c * (y4 * (y * y3));
	} else if (x <= 4.2e-205) {
		tmp = c * (y4 * (t * -y2));
	} else if (x <= 1.55e-188) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (x <= 5.1e-34) {
		tmp = y0 * (c * (z * -y3));
	} else {
		tmp = j * (y0 * (x * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -8.7e+108:
		tmp = i * (y1 * (x * j))
	elif x <= -7e-182:
		tmp = y0 * (y3 * (j * y5))
	elif x <= -9e-308:
		tmp = k * (y4 * (y1 * y2))
	elif x <= 6.1e-273:
		tmp = c * (y4 * (y * y3))
	elif x <= 4.2e-205:
		tmp = c * (y4 * (t * -y2))
	elif x <= 1.55e-188:
		tmp = j * (y4 * (y1 * -y3))
	elif x <= 5.1e-34:
		tmp = y0 * (c * (z * -y3))
	else:
		tmp = j * (y0 * (x * -b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -8.7e+108)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (x <= -7e-182)
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	elseif (x <= -9e-308)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (x <= 6.1e-273)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (x <= 4.2e-205)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (x <= 1.55e-188)
		tmp = Float64(j * Float64(y4 * Float64(y1 * Float64(-y3))));
	elseif (x <= 5.1e-34)
		tmp = Float64(y0 * Float64(c * Float64(z * Float64(-y3))));
	else
		tmp = Float64(j * Float64(y0 * Float64(x * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -8.7e+108)
		tmp = i * (y1 * (x * j));
	elseif (x <= -7e-182)
		tmp = y0 * (y3 * (j * y5));
	elseif (x <= -9e-308)
		tmp = k * (y4 * (y1 * y2));
	elseif (x <= 6.1e-273)
		tmp = c * (y4 * (y * y3));
	elseif (x <= 4.2e-205)
		tmp = c * (y4 * (t * -y2));
	elseif (x <= 1.55e-188)
		tmp = j * (y4 * (y1 * -y3));
	elseif (x <= 5.1e-34)
		tmp = y0 * (c * (z * -y3));
	else
		tmp = j * (y0 * (x * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -8.7e+108], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e-182], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9e-308], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.1e-273], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-205], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e-188], N[(j * N[(y4 * N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.1e-34], N[(y0 * N[(c * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -8.6999999999999997e108

   1. Initial program 20.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 20.9%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 20.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 20.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 20.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 20.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 28.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 36.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 42.8%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -8.6999999999999997e108 < x < -6.99999999999999966e-182

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 29.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 32.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 32.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 32.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 35.2%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 28.8%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot \left(j \cdot y5\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 28.8%

         \[\leadsto \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \cdot \left(j \cdot y5\right) \]

      2. unsub-neg 28.8%

         \[\leadsto \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \cdot \left(j \cdot y5\right) \]

      3. *-commutative 28.8%

         \[\leadsto \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right) \cdot \left(j \cdot y5\right) \]

      4. *-commutative 28.8%

         \[\leadsto \left(y0 \cdot y3 - t \cdot i\right) \cdot \color{blue}{\left(y5 \cdot j\right)} \]

   7. Simplified 28.8%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 - t \cdot i\right) \cdot \left(y5 \cdot j\right)} \]

   8. Taylor expanded in y0 around inf 23.7%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]

   if -6.99999999999999966e-182 < x < -9.00000000000000017e-308

   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. Step-by-step derivation

      1. associate-+l- 45.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 45.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 45.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 49.0%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.0%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)} \]

      2. +-commutative 40.0%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)} \]

      3. mul-1-neg 40.0%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right) \]

      4. unsub-neg 40.0%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)} \]

      5. *-commutative 40.0%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - \color{blue}{b \cdot y}\right) \]

   7. Simplified 40.0%

      \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - b \cdot y\right)} \]

   8. Taylor expanded in y1 around inf 36.6%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -9.00000000000000017e-308 < x < 6.09999999999999975e-273

   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. Step-by-step derivation

      1. associate-+l- 50.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 70.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 60.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 50.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if 6.09999999999999975e-273 < x < 4.19999999999999965e-205

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 46.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around 0 46.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.4%

         \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. distribute-rgt-neg-in 46.4%

         \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      3. distribute-rgt-neg-in 46.4%

         \[\leadsto c \cdot \color{blue}{\left(y4 \cdot \left(-t \cdot y2\right)\right)} \]

      4. distribute-rgt-neg-in 46.4%

         \[\leadsto c \cdot \left(y4 \cdot \color{blue}{\left(t \cdot \left(-y2\right)\right)}\right) \]

   8. Simplified 46.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)} \]

   if 4.19999999999999965e-205 < x < 1.5500000000000001e-188

   1. Initial program 66.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 66.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 66.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 66.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 83.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y1 around -inf 66.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* 66.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 66.9%

         \[\leadsto \left(\color{blue}{\left(-y1\right)} \cdot \left(y4 \cdot y3 - i \cdot x\right)\right) \cdot j \]

   7. Simplified 66.9%

      \[\leadsto \color{blue}{\left(\left(-y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

   8. Taylor expanded in y4 around inf 83.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y4 \cdot \left(y1 \cdot y3\right)\right)\right)} \cdot j \]
   9. Step-by-step derivation

      1. mul-1-neg 83.2%

         \[\leadsto \color{blue}{\left(-y4 \cdot \left(y1 \cdot y3\right)\right)} \cdot j \]

      2. distribute-rgt-neg-in 83.2%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(-y1 \cdot y3\right)\right)} \cdot j \]

   10. Simplified 83.2%

       \[\leadsto \color{blue}{\left(y4 \cdot \left(-y1 \cdot y3\right)\right)} \cdot j \]

   if 1.5500000000000001e-188 < x < 5.1000000000000001e-34

   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. Step-by-step derivation

      1. +-commutative 30.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 30.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 30.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 30.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 34.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 43.0%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.0%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 43.0%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 35.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.6%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 35.6%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 39.2%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 39.2%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 39.2%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around 0 43.6%

       \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y3 \cdot z\right)\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 43.6%

          \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(y3 \cdot z\right)\right)} \]

       2. neg-mul-1 43.6%

          \[\leadsto y0 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(y3 \cdot z\right)\right) \]

   12. Simplified 43.6%

       \[\leadsto y0 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(y3 \cdot z\right)\right)} \]

   if 5.1000000000000001e-34 < x

   1. Initial program 19.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 19.4%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 19.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 19.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 19.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 23.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 43.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 48.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in i around 0 38.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(b \cdot x\right)\right)\right)} \cdot j \]
   7. Step-by-step derivation

      1. associate-*r* 38.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(b \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 38.6%

         \[\leadsto \left(\color{blue}{\left(-y0\right)} \cdot \left(b \cdot x\right)\right) \cdot j \]

   8. Simplified 38.6%

      \[\leadsto \color{blue}{\left(\left(-y0\right) \cdot \left(b \cdot x\right)\right)} \cdot j \]
3. Recombined 8 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.7 \cdot 10^{+108}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-182}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-308}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-273}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-205}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-188}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-34}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(x \cdot \left(-b\right)\right)\right)\\ \end{array} \]

Alternative 17: 29.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;i \leq -1.5 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-236}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{+163} \lor \neg \left(i \leq 2.15 \cdot 10^{+268}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= i -1.5e+164)
     t_1
     (if (<= i 5.8e-236)
       (* c (* y4 (- (* y y3) (* t y2))))
       (if (<= i 2.4e-9)
         (* j (* y1 (* y4 (- y3))))
         (if (or (<= i 5.1e+163) (not (<= i 2.15e+268)))
           t_1
           (* j (* y1 (* 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 * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (i <= -1.5e+164) {
		tmp = t_1;
	} else if (i <= 5.8e-236) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (i <= 2.4e-9) {
		tmp = j * (y1 * (y4 * -y3));
	} else if ((i <= 5.1e+163) || !(i <= 2.15e+268)) {
		tmp = t_1;
	} else {
		tmp = j * (y1 * (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 = k * (i * ((y * y5) - (z * y1)))
    if (i <= (-1.5d+164)) then
        tmp = t_1
    else if (i <= 5.8d-236) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (i <= 2.4d-9) then
        tmp = j * (y1 * (y4 * -y3))
    else if ((i <= 5.1d+163) .or. (.not. (i <= 2.15d+268))) then
        tmp = t_1
    else
        tmp = j * (y1 * (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 * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (i <= -1.5e+164) {
		tmp = t_1;
	} else if (i <= 5.8e-236) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (i <= 2.4e-9) {
		tmp = j * (y1 * (y4 * -y3));
	} else if ((i <= 5.1e+163) || !(i <= 2.15e+268)) {
		tmp = t_1;
	} else {
		tmp = j * (y1 * (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 * (i * ((y * y5) - (z * y1)))
	tmp = 0
	if i <= -1.5e+164:
		tmp = t_1
	elif i <= 5.8e-236:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif i <= 2.4e-9:
		tmp = j * (y1 * (y4 * -y3))
	elif (i <= 5.1e+163) or not (i <= 2.15e+268):
		tmp = t_1
	else:
		tmp = j * (y1 * (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(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (i <= -1.5e+164)
		tmp = t_1;
	elseif (i <= 5.8e-236)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (i <= 2.4e-9)
		tmp = Float64(j * Float64(y1 * Float64(y4 * Float64(-y3))));
	elseif ((i <= 5.1e+163) || !(i <= 2.15e+268))
		tmp = t_1;
	else
		tmp = Float64(j * Float64(y1 * 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 * (i * ((y * y5) - (z * y1)));
	tmp = 0.0;
	if (i <= -1.5e+164)
		tmp = t_1;
	elseif (i <= 5.8e-236)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (i <= 2.4e-9)
		tmp = j * (y1 * (y4 * -y3));
	elseif ((i <= 5.1e+163) || ~((i <= 2.15e+268)))
		tmp = t_1;
	else
		tmp = j * (y1 * (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[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.5e+164], t$95$1, If[LessEqual[i, 5.8e-236], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.4e-9], N[(j * N[(y1 * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, 5.1e+163], N[Not[LessEqual[i, 2.15e+268]], $MachinePrecision]], t$95$1, N[(j * N[(y1 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.5e164 or 2.4e-9 < i < 5.1000000000000002e163 or 2.14999999999999985e268 < i

   1. Initial program 14.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 14.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 14.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 14.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 14.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 17.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in k around inf 40.9%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(y \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(y0 \cdot b - i \cdot y1\right) \cdot z + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)\right)} \]

   5. Taylor expanded in i around inf 49.8%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 49.8%

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(-y1 \cdot z\right)}\right)\right) \]

      2. sub-neg 49.8%

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      3. *-commutative 49.8%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   7. Simplified 49.8%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if -1.5e164 < i < 5.8e-236

   1. Initial program 38.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 38.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 38.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 38.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 33.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 5.8e-236 < i < 2.4e-9

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 33.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 35.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 35.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 35.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 37.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 51.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y1 around -inf 40.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* 40.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 40.6%

         \[\leadsto \left(\color{blue}{\left(-y1\right)} \cdot \left(y4 \cdot y3 - i \cdot x\right)\right) \cdot j \]

   7. Simplified 40.6%

      \[\leadsto \color{blue}{\left(\left(-y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

   8. Taylor expanded in y4 around inf 38.5%

      \[\leadsto \left(\left(-y1\right) \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \cdot j \]

   if 5.1000000000000002e163 < i < 2.14999999999999985e268

   1. Initial program 12.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 12.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 16.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 16.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 16.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 16.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 36.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 41.8%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in i around inf 57.3%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot x\right)\right)} \cdot j \]
   7. Step-by-step derivation

      1. *-commutative 57.3%

         \[\leadsto \left(y1 \cdot \color{blue}{\left(x \cdot i\right)}\right) \cdot j \]

   8. Simplified 57.3%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(x \cdot i\right)\right)} \cdot j \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.5 \cdot 10^{+164}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-236}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{+163} \lor \neg \left(i \leq 2.15 \cdot 10^{+268}\right):\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 18: 28.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;i \leq -1.95 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{-237}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+265}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= i -1.95e+167)
     t_1
     (if (<= i 1.5e-237)
       (* c (* y4 (- (* y y3) (* t y2))))
       (if (<= i 1.8e-9)
         (* j (* y1 (* y4 (- y3))))
         (if (<= i 9e+161)
           t_1
           (if (<= i 2.9e+265)
             (* j (* y1 (* x i)))
             (* y0 (* c (- (* x y2) (* z y3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (i <= -1.95e+167) {
		tmp = t_1;
	} else if (i <= 1.5e-237) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (i <= 1.8e-9) {
		tmp = j * (y1 * (y4 * -y3));
	} else if (i <= 9e+161) {
		tmp = t_1;
	} else if (i <= 2.9e+265) {
		tmp = j * (y1 * (x * i));
	} else {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (i * ((y * y5) - (z * y1)))
    if (i <= (-1.95d+167)) then
        tmp = t_1
    else if (i <= 1.5d-237) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (i <= 1.8d-9) then
        tmp = j * (y1 * (y4 * -y3))
    else if (i <= 9d+161) then
        tmp = t_1
    else if (i <= 2.9d+265) then
        tmp = j * (y1 * (x * i))
    else
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (i <= -1.95e+167) {
		tmp = t_1;
	} else if (i <= 1.5e-237) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (i <= 1.8e-9) {
		tmp = j * (y1 * (y4 * -y3));
	} else if (i <= 9e+161) {
		tmp = t_1;
	} else if (i <= 2.9e+265) {
		tmp = j * (y1 * (x * i));
	} else {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (i * ((y * y5) - (z * y1)))
	tmp = 0
	if i <= -1.95e+167:
		tmp = t_1
	elif i <= 1.5e-237:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif i <= 1.8e-9:
		tmp = j * (y1 * (y4 * -y3))
	elif i <= 9e+161:
		tmp = t_1
	elif i <= 2.9e+265:
		tmp = j * (y1 * (x * i))
	else:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (i <= -1.95e+167)
		tmp = t_1;
	elseif (i <= 1.5e-237)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (i <= 1.8e-9)
		tmp = Float64(j * Float64(y1 * Float64(y4 * Float64(-y3))));
	elseif (i <= 9e+161)
		tmp = t_1;
	elseif (i <= 2.9e+265)
		tmp = Float64(j * Float64(y1 * Float64(x * i)));
	else
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (i * ((y * y5) - (z * y1)));
	tmp = 0.0;
	if (i <= -1.95e+167)
		tmp = t_1;
	elseif (i <= 1.5e-237)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (i <= 1.8e-9)
		tmp = j * (y1 * (y4 * -y3));
	elseif (i <= 9e+161)
		tmp = t_1;
	elseif (i <= 2.9e+265)
		tmp = j * (y1 * (x * i));
	else
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.95e+167], t$95$1, If[LessEqual[i, 1.5e-237], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.8e-9], N[(j * N[(y1 * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9e+161], t$95$1, If[LessEqual[i, 2.9e+265], N[(j * N[(y1 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.9499999999999999e167 or 1.8e-9 < i < 8.99999999999999984e161

   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. Step-by-step derivation

      1. +-commutative 16.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 16.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 16.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 16.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 19.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in k around inf 41.3%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(y \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(y0 \cdot b - i \cdot y1\right) \cdot z + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)\right)} \]

   5. Taylor expanded in i around inf 48.1%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 48.1%

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(-y1 \cdot z\right)}\right)\right) \]

      2. sub-neg 48.1%

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      3. *-commutative 48.1%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   7. Simplified 48.1%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if -1.9499999999999999e167 < i < 1.50000000000000012e-237

   1. Initial program 38.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 38.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 38.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 38.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 33.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 1.50000000000000012e-237 < i < 1.8e-9

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 33.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 35.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 35.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 35.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 37.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 51.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y1 around -inf 40.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* 40.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 40.6%

         \[\leadsto \left(\color{blue}{\left(-y1\right)} \cdot \left(y4 \cdot y3 - i \cdot x\right)\right) \cdot j \]

   7. Simplified 40.6%

      \[\leadsto \color{blue}{\left(\left(-y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

   8. Taylor expanded in y4 around inf 38.5%

      \[\leadsto \left(\left(-y1\right) \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \cdot j \]

   if 8.99999999999999984e161 < i < 2.89999999999999996e265

   1. Initial program 13.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 13.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 17.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 17.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 17.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 17.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 39.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 41.1%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in i around inf 58.0%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot x\right)\right)} \cdot j \]
   7. Step-by-step derivation

      1. *-commutative 58.0%

         \[\leadsto \left(y1 \cdot \color{blue}{\left(x \cdot i\right)}\right) \cdot j \]

   8. Simplified 58.0%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(x \cdot i\right)\right)} \cdot j \]

   if 2.89999999999999996e265 < i

   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. Step-by-step derivation

      1. +-commutative 0.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 0.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 0.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 0.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 50.0%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.0%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 50.0%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 60.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 60.5%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 60.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 60.5%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 60.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.95 \cdot 10^{+167}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{-237}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{+161}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+265}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]

Alternative 19: 29.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;c \leq -1.12 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-18}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(x \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-102}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= c -1.12e+178)
     t_1
     (if (<= c -1.1e-18)
       (* y0 (* y2 (- (* x c) (* k y5))))
       (if (<= c -3.5e-176)
         (* j (* y0 (* x (- b))))
         (if (<= c 2.2e-102)
           (* k (* i (- (* y y5) (* z y1))))
           (if (<= c 1.9e+43) (* y0 (* y3 (- (* j y5) (* z c)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -1.12e+178) {
		tmp = t_1;
	} else if (c <= -1.1e-18) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (c <= -3.5e-176) {
		tmp = j * (y0 * (x * -b));
	} else if (c <= 2.2e-102) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 1.9e+43) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} 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 = c * (y4 * ((y * y3) - (t * y2)))
    if (c <= (-1.12d+178)) then
        tmp = t_1
    else if (c <= (-1.1d-18)) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (c <= (-3.5d-176)) then
        tmp = j * (y0 * (x * -b))
    else if (c <= 2.2d-102) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (c <= 1.9d+43) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -1.12e+178) {
		tmp = t_1;
	} else if (c <= -1.1e-18) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (c <= -3.5e-176) {
		tmp = j * (y0 * (x * -b));
	} else if (c <= 2.2e-102) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 1.9e+43) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if c <= -1.12e+178:
		tmp = t_1
	elif c <= -1.1e-18:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif c <= -3.5e-176:
		tmp = j * (y0 * (x * -b))
	elif c <= 2.2e-102:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif c <= 1.9e+43:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (c <= -1.12e+178)
		tmp = t_1;
	elseif (c <= -1.1e-18)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (c <= -3.5e-176)
		tmp = Float64(j * Float64(y0 * Float64(x * Float64(-b))));
	elseif (c <= 2.2e-102)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (c <= 1.9e+43)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (c <= -1.12e+178)
		tmp = t_1;
	elseif (c <= -1.1e-18)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (c <= -3.5e-176)
		tmp = j * (y0 * (x * -b));
	elseif (c <= 2.2e-102)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (c <= 1.9e+43)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.12e+178], t$95$1, If[LessEqual[c, -1.1e-18], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.5e-176], N[(j * N[(y0 * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-102], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.9e+43], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.12000000000000001e178 or 1.90000000000000004e43 < c

   1. Initial program 15.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 15.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 15.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 42.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 45.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if -1.12000000000000001e178 < c < -1.0999999999999999e-18

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 36.4%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 39.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 39.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 39.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 43.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 43.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in y2 around inf 49.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot x - k \cdot y5\right) \cdot y2\right)} \]

   if -1.0999999999999999e-18 < c < -3.5e-176

   1. Initial program 43.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 43.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 43.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 43.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 43.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 43.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 38.3%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 31.8%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in i around 0 22.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(b \cdot x\right)\right)\right)} \cdot j \]
   7. Step-by-step derivation

      1. associate-*r* 22.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(b \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 22.7%

         \[\leadsto \left(\color{blue}{\left(-y0\right)} \cdot \left(b \cdot x\right)\right) \cdot j \]

   8. Simplified 22.7%

      \[\leadsto \color{blue}{\left(\left(-y0\right) \cdot \left(b \cdot x\right)\right)} \cdot j \]

   if -3.5e-176 < c < 2.20000000000000013e-102

   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. Step-by-step derivation

      1. +-commutative 31.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 31.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 31.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 31.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in k around inf 38.1%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(y \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(y0 \cdot b - i \cdot y1\right) \cdot z + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)\right)} \]

   5. Taylor expanded in i around inf 42.0%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.0%

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(-y1 \cdot z\right)}\right)\right) \]

      2. sub-neg 42.0%

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      3. *-commutative 42.0%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   7. Simplified 42.0%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if 2.20000000000000013e-102 < c < 1.90000000000000004e43

   1. Initial program 32.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 32.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 35.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 35.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 35.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 37.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 35.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 35.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 35.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in y3 around inf 39.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(c \cdot z\right) - -1 \cdot \left(j \cdot y5\right)\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 39.3%

         \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) - -1 \cdot \left(j \cdot y5\right)\right)\right)} \]

      2. cancel-sign-sub-inv 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right) + \left(--1\right) \cdot \left(j \cdot y5\right)\right)}\right) \]

      3. metadata-eval 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + \color{blue}{1} \cdot \left(j \cdot y5\right)\right)\right) \]

      4. *-lft-identity 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + \color{blue}{j \cdot y5}\right)\right) \]

      5. +-commutative 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y5 + -1 \cdot \left(c \cdot z\right)\right)}\right) \]

      6. mul-1-neg 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(j \cdot y5 + \color{blue}{\left(-c \cdot z\right)}\right)\right) \]

      7. unsub-neg 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y5 - c \cdot z\right)}\right) \]

      8. *-commutative 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(\color{blue}{y5 \cdot j} - c \cdot z\right)\right) \]

   9. Simplified 39.3%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(y5 \cdot j - c \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{+178}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-18}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(x \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-102}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 20: 29.9% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{if}\;c \leq -2.6 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-15}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{-78}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2)))))
        (t_2 (* y4 (* t (- (* b j) (* c y2))))))
   (if (<= c -2.6e+175)
     t_1
     (if (<= c -1.05e-15)
       (* y0 (* y2 (- (* x c) (* k y5))))
       (if (<= c -1.05e-203)
         t_2
         (if (<= c 1.95e-78)
           (* k (* i (- (* y y5) (* z y1))))
           (if (<= c 2.7e+108) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = y4 * (t * ((b * j) - (c * y2)));
	double tmp;
	if (c <= -2.6e+175) {
		tmp = t_1;
	} else if (c <= -1.05e-15) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (c <= -1.05e-203) {
		tmp = t_2;
	} else if (c <= 1.95e-78) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 2.7e+108) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (y4 * ((y * y3) - (t * y2)))
    t_2 = y4 * (t * ((b * j) - (c * y2)))
    if (c <= (-2.6d+175)) then
        tmp = t_1
    else if (c <= (-1.05d-15)) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (c <= (-1.05d-203)) then
        tmp = t_2
    else if (c <= 1.95d-78) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (c <= 2.7d+108) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = y4 * (t * ((b * j) - (c * y2)));
	double tmp;
	if (c <= -2.6e+175) {
		tmp = t_1;
	} else if (c <= -1.05e-15) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (c <= -1.05e-203) {
		tmp = t_2;
	} else if (c <= 1.95e-78) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 2.7e+108) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	t_2 = y4 * (t * ((b * j) - (c * y2)))
	tmp = 0
	if c <= -2.6e+175:
		tmp = t_1
	elif c <= -1.05e-15:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif c <= -1.05e-203:
		tmp = t_2
	elif c <= 1.95e-78:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif c <= 2.7e+108:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	t_2 = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))))
	tmp = 0.0
	if (c <= -2.6e+175)
		tmp = t_1;
	elseif (c <= -1.05e-15)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (c <= -1.05e-203)
		tmp = t_2;
	elseif (c <= 1.95e-78)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (c <= 2.7e+108)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	t_2 = y4 * (t * ((b * j) - (c * y2)));
	tmp = 0.0;
	if (c <= -2.6e+175)
		tmp = t_1;
	elseif (c <= -1.05e-15)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (c <= -1.05e-203)
		tmp = t_2;
	elseif (c <= 1.95e-78)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (c <= 2.7e+108)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.6e+175], t$95$1, If[LessEqual[c, -1.05e-15], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.05e-203], t$95$2, If[LessEqual[c, 1.95e-78], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.7e+108], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.6e175 or 2.7e108 < c

   1. Initial program 11.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 47.6%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if -2.6e175 < c < -1.0499999999999999e-15

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 36.4%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 39.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 39.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 39.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 43.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 43.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in y2 around inf 49.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot x - k \cdot y5\right) \cdot y2\right)} \]

   if -1.0499999999999999e-15 < c < -1.05000000000000001e-203 or 1.9500000000000001e-78 < c < 2.7e108

   1. Initial program 36.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 42.1%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]

   if -1.05000000000000001e-203 < c < 1.9500000000000001e-78

   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. Step-by-step derivation

      1. +-commutative 32.1%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 32.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 32.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 32.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in k around inf 38.8%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(y \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(y0 \cdot b - i \cdot y1\right) \cdot z + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)\right)} \]

   5. Taylor expanded in i around inf 42.8%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.8%

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(-y1 \cdot z\right)}\right)\right) \]

      2. sub-neg 42.8%

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      3. *-commutative 42.8%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   7. Simplified 42.8%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{+175}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-15}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-203}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{-78}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+108}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 21: 21.6% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ t_2 := c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{if}\;y2 \leq -5.2 \cdot 10^{+123}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq -95:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -2.9 \cdot 10^{-286}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.3 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (* x j)))) (t_2 (* c (* y4 (* y y3)))))
   (if (<= y2 -5.2e+123)
     (* k (* y4 (* y1 y2)))
     (if (<= y2 -5e+65)
       t_2
       (if (<= y2 -95.0)
         t_1
         (if (<= y2 -2.9e-286)
           t_2
           (if (<= y2 1.35e-84)
             t_1
             (if (<= y2 1.3e-13) t_2 (* c (* y0 (* x 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 * (y1 * (x * j));
	double t_2 = c * (y4 * (y * y3));
	double tmp;
	if (y2 <= -5.2e+123) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y2 <= -5e+65) {
		tmp = t_2;
	} else if (y2 <= -95.0) {
		tmp = t_1;
	} else if (y2 <= -2.9e-286) {
		tmp = t_2;
	} else if (y2 <= 1.35e-84) {
		tmp = t_1;
	} else if (y2 <= 1.3e-13) {
		tmp = t_2;
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y1 * (x * j))
    t_2 = c * (y4 * (y * y3))
    if (y2 <= (-5.2d+123)) then
        tmp = k * (y4 * (y1 * y2))
    else if (y2 <= (-5d+65)) then
        tmp = t_2
    else if (y2 <= (-95.0d0)) then
        tmp = t_1
    else if (y2 <= (-2.9d-286)) then
        tmp = t_2
    else if (y2 <= 1.35d-84) then
        tmp = t_1
    else if (y2 <= 1.3d-13) then
        tmp = t_2
    else
        tmp = c * (y0 * (x * 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 * (y1 * (x * j));
	double t_2 = c * (y4 * (y * y3));
	double tmp;
	if (y2 <= -5.2e+123) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y2 <= -5e+65) {
		tmp = t_2;
	} else if (y2 <= -95.0) {
		tmp = t_1;
	} else if (y2 <= -2.9e-286) {
		tmp = t_2;
	} else if (y2 <= 1.35e-84) {
		tmp = t_1;
	} else if (y2 <= 1.3e-13) {
		tmp = t_2;
	} else {
		tmp = c * (y0 * (x * 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 * (y1 * (x * j))
	t_2 = c * (y4 * (y * y3))
	tmp = 0
	if y2 <= -5.2e+123:
		tmp = k * (y4 * (y1 * y2))
	elif y2 <= -5e+65:
		tmp = t_2
	elif y2 <= -95.0:
		tmp = t_1
	elif y2 <= -2.9e-286:
		tmp = t_2
	elif y2 <= 1.35e-84:
		tmp = t_1
	elif y2 <= 1.3e-13:
		tmp = t_2
	else:
		tmp = c * (y0 * (x * 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(y1 * Float64(x * j)))
	t_2 = Float64(c * Float64(y4 * Float64(y * y3)))
	tmp = 0.0
	if (y2 <= -5.2e+123)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y2 <= -5e+65)
		tmp = t_2;
	elseif (y2 <= -95.0)
		tmp = t_1;
	elseif (y2 <= -2.9e-286)
		tmp = t_2;
	elseif (y2 <= 1.35e-84)
		tmp = t_1;
	elseif (y2 <= 1.3e-13)
		tmp = t_2;
	else
		tmp = Float64(c * Float64(y0 * Float64(x * 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 * (y1 * (x * j));
	t_2 = c * (y4 * (y * y3));
	tmp = 0.0;
	if (y2 <= -5.2e+123)
		tmp = k * (y4 * (y1 * y2));
	elseif (y2 <= -5e+65)
		tmp = t_2;
	elseif (y2 <= -95.0)
		tmp = t_1;
	elseif (y2 <= -2.9e-286)
		tmp = t_2;
	elseif (y2 <= 1.35e-84)
		tmp = t_1;
	elseif (y2 <= 1.3e-13)
		tmp = t_2;
	else
		tmp = c * (y0 * (x * 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[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -5.2e+123], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5e+65], t$95$2, If[LessEqual[y2, -95.0], t$95$1, If[LessEqual[y2, -2.9e-286], t$95$2, If[LessEqual[y2, 1.35e-84], t$95$1, If[LessEqual[y2, 1.3e-13], t$95$2, N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -5.19999999999999971e123

   1. Initial program 13.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 13.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 13.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 45.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 35.0%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 24.3%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)} \]

      2. +-commutative 24.3%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)} \]

      3. mul-1-neg 24.3%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right) \]

      4. unsub-neg 24.3%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)} \]

      5. *-commutative 24.3%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - \color{blue}{b \cdot y}\right) \]

   7. Simplified 24.3%

      \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - b \cdot y\right)} \]

   8. Taylor expanded in y1 around inf 37.4%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -5.19999999999999971e123 < y2 < -4.99999999999999973e65 or -95 < y2 < -2.8999999999999998e-286 or 1.35e-84 < y2 < 1.3e-13

   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. Step-by-step derivation

      1. associate-+l- 32.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 32.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 27.5%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 25.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -4.99999999999999973e65 < y2 < -95 or -2.8999999999999998e-286 < y2 < 1.35e-84

   1. Initial program 34.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 34.9%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 37.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 37.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 37.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 40.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 48.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 27.5%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 26.4%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if 1.3e-13 < y2

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 27.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 37.3%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 37.3%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 31.3%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 31.3%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 31.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around inf 31.1%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.2 \cdot 10^{+123}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -95:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -2.9 \cdot 10^{-286}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-84}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 1.3 \cdot 10^{-13}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]

Alternative 22: 32.2% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;c \leq -1.18 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-265}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+70}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* c (- (* y y3) (* t y2))))))
   (if (<= c -1.18e-39)
     t_1
     (if (<= c -6e-265)
       (* (* t j) (- (* b y4) (* i y5)))
       (if (<= c 2.1e-78)
         (* k (* i (- (* y y5) (* z y1))))
         (if (<= c 1.85e+70) (* y4 (* t (- (* b j) (* c y2)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (c * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -1.18e-39) {
		tmp = t_1;
	} else if (c <= -6e-265) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (c <= 2.1e-78) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 1.85e+70) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y4 * (c * ((y * y3) - (t * y2)))
    if (c <= (-1.18d-39)) then
        tmp = t_1
    else if (c <= (-6d-265)) then
        tmp = (t * j) * ((b * y4) - (i * y5))
    else if (c <= 2.1d-78) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (c <= 1.85d+70) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (c * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -1.18e-39) {
		tmp = t_1;
	} else if (c <= -6e-265) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (c <= 2.1e-78) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 1.85e+70) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (c * ((y * y3) - (t * y2)))
	tmp = 0
	if c <= -1.18e-39:
		tmp = t_1
	elif c <= -6e-265:
		tmp = (t * j) * ((b * y4) - (i * y5))
	elif c <= 2.1e-78:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif c <= 1.85e+70:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (c <= -1.18e-39)
		tmp = t_1;
	elseif (c <= -6e-265)
		tmp = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)));
	elseif (c <= 2.1e-78)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (c <= 1.85e+70)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (c * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (c <= -1.18e-39)
		tmp = t_1;
	elseif (c <= -6e-265)
		tmp = (t * j) * ((b * y4) - (i * y5));
	elseif (c <= 2.1e-78)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (c <= 1.85e+70)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.18e-39], t$95$1, If[LessEqual[c, -6e-265], N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e-78], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.85e+70], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.17999999999999993e-39 or 1.84999999999999994e70 < c

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 42.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around 0 33.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right) + -1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 33.3%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3\right)} + -1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right) \]

      2. mul-1-neg 33.3%

         \[\leadsto \left(c \cdot y4\right) \cdot \left(y \cdot y3\right) + \color{blue}{\left(-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]

      3. associate-*r* 27.9%

         \[\leadsto \left(c \cdot y4\right) \cdot \left(y \cdot y3\right) + \left(-\color{blue}{\left(c \cdot y4\right) \cdot \left(t \cdot y2\right)}\right) \]

      4. distribute-rgt-neg-in 27.9%

         \[\leadsto \left(c \cdot y4\right) \cdot \left(y \cdot y3\right) + \color{blue}{\left(c \cdot y4\right) \cdot \left(-t \cdot y2\right)} \]

      5. distribute-lft-in 42.2%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 + \left(-t \cdot y2\right)\right)} \]

      6. sub-neg 42.2%

         \[\leadsto \left(c \cdot y4\right) \cdot \color{blue}{\left(y \cdot y3 - t \cdot y2\right)} \]

      7. associate-*r* 42.2%

         \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

      8. *-commutative 42.2%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \cdot c} \]

      9. associate-*l* 47.3%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3 - t \cdot y2\right) \cdot c\right)} \]

   8. Simplified 47.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3 - t \cdot y2\right) \cdot c\right)} \]

   if -1.17999999999999993e-39 < c < -5.9999999999999996e-265

   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. Step-by-step derivation

      1. +-commutative 32.9%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 32.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 32.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 32.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 36.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in t around inf 38.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \]

   if -5.9999999999999996e-265 < c < 2.1000000000000001e-78

   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. Step-by-step derivation

      1. +-commutative 33.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 33.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 33.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 33.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 34.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in k around inf 38.6%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(y \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(y0 \cdot b - i \cdot y1\right) \cdot z + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)\right)} \]

   5. Taylor expanded in i around inf 42.2%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.2%

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(-y1 \cdot z\right)}\right)\right) \]

      2. sub-neg 42.2%

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      3. *-commutative 42.2%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   7. Simplified 42.2%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if 2.1000000000000001e-78 < c < 1.84999999999999994e70

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 37.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 37.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 55.1%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.18 \cdot 10^{-39}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-265}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+70}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 23: 20.9% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+190}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{+23}:\\ \;\;\;\;k \cdot \left(y \cdot \left(y4 \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-168}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-210}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y1 \cdot y4\right) \cdot \left(j \cdot \left(-y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -3.2e+190)
   (* i (* y1 (* x j)))
   (if (<= j -6.5e+23)
     (* k (* y (* y4 (- b))))
     (if (<= j -2.8e-168)
       (* y0 (* c (* z (- y3))))
       (if (<= j -1.1e-210)
         (* c (* y0 (* x y2)))
         (if (<= j 7.2e+53)
           (* c (* y4 (* t (- y2))))
           (* (* y1 y4) (* j (- y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -3.2e+190) {
		tmp = i * (y1 * (x * j));
	} else if (j <= -6.5e+23) {
		tmp = k * (y * (y4 * -b));
	} else if (j <= -2.8e-168) {
		tmp = y0 * (c * (z * -y3));
	} else if (j <= -1.1e-210) {
		tmp = c * (y0 * (x * y2));
	} else if (j <= 7.2e+53) {
		tmp = c * (y4 * (t * -y2));
	} else {
		tmp = (y1 * y4) * (j * -y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-3.2d+190)) then
        tmp = i * (y1 * (x * j))
    else if (j <= (-6.5d+23)) then
        tmp = k * (y * (y4 * -b))
    else if (j <= (-2.8d-168)) then
        tmp = y0 * (c * (z * -y3))
    else if (j <= (-1.1d-210)) then
        tmp = c * (y0 * (x * y2))
    else if (j <= 7.2d+53) then
        tmp = c * (y4 * (t * -y2))
    else
        tmp = (y1 * y4) * (j * -y3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -3.2e+190) {
		tmp = i * (y1 * (x * j));
	} else if (j <= -6.5e+23) {
		tmp = k * (y * (y4 * -b));
	} else if (j <= -2.8e-168) {
		tmp = y0 * (c * (z * -y3));
	} else if (j <= -1.1e-210) {
		tmp = c * (y0 * (x * y2));
	} else if (j <= 7.2e+53) {
		tmp = c * (y4 * (t * -y2));
	} else {
		tmp = (y1 * y4) * (j * -y3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -3.2e+190:
		tmp = i * (y1 * (x * j))
	elif j <= -6.5e+23:
		tmp = k * (y * (y4 * -b))
	elif j <= -2.8e-168:
		tmp = y0 * (c * (z * -y3))
	elif j <= -1.1e-210:
		tmp = c * (y0 * (x * y2))
	elif j <= 7.2e+53:
		tmp = c * (y4 * (t * -y2))
	else:
		tmp = (y1 * y4) * (j * -y3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -3.2e+190)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (j <= -6.5e+23)
		tmp = Float64(k * Float64(y * Float64(y4 * Float64(-b))));
	elseif (j <= -2.8e-168)
		tmp = Float64(y0 * Float64(c * Float64(z * Float64(-y3))));
	elseif (j <= -1.1e-210)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	elseif (j <= 7.2e+53)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	else
		tmp = Float64(Float64(y1 * y4) * Float64(j * Float64(-y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -3.2e+190)
		tmp = i * (y1 * (x * j));
	elseif (j <= -6.5e+23)
		tmp = k * (y * (y4 * -b));
	elseif (j <= -2.8e-168)
		tmp = y0 * (c * (z * -y3));
	elseif (j <= -1.1e-210)
		tmp = c * (y0 * (x * y2));
	elseif (j <= 7.2e+53)
		tmp = c * (y4 * (t * -y2));
	else
		tmp = (y1 * y4) * (j * -y3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -3.2e+190], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.5e+23], N[(k * N[(y * N[(y4 * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.8e-168], N[(y0 * N[(c * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.1e-210], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.2e+53], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y1 * y4), $MachinePrecision] * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -3.2000000000000001e190

   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. Step-by-step derivation

      1. +-commutative 33.6%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 33.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 33.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 33.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 33.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 62.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 34.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 34.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -3.2000000000000001e190 < j < -6.4999999999999996e23

   1. Initial program 21.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 42.4%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 29.1%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)} \]

      2. +-commutative 29.1%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)} \]

      3. mul-1-neg 29.1%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right) \]

      4. unsub-neg 29.1%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)} \]

      5. *-commutative 29.1%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - \color{blue}{b \cdot y}\right) \]

   7. Simplified 29.1%

      \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - b \cdot y\right)} \]

   8. Taylor expanded in y1 around 0 38.1%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y4 \cdot \left(y \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 38.1%

         \[\leadsto \color{blue}{-k \cdot \left(y4 \cdot \left(y \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 38.1%

         \[\leadsto \color{blue}{k \cdot \left(-y4 \cdot \left(y \cdot b\right)\right)} \]

      3. associate-*r* 38.1%

         \[\leadsto k \cdot \left(-\color{blue}{\left(y4 \cdot y\right) \cdot b}\right) \]

      4. *-commutative 38.1%

         \[\leadsto k \cdot \left(-\color{blue}{\left(y \cdot y4\right)} \cdot b\right) \]

      5. associate-*l* 40.3%

         \[\leadsto k \cdot \left(-\color{blue}{y \cdot \left(y4 \cdot b\right)}\right) \]

   10. Simplified 40.3%

       \[\leadsto \color{blue}{k \cdot \left(-y \cdot \left(y4 \cdot b\right)\right)} \]

   if -6.4999999999999996e23 < j < -2.8000000000000002e-168

   1. Initial program 43.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 43.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 43.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 43.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 43.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 43.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 43.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 43.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 29.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.4%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 29.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 29.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 29.4%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 29.4%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around 0 33.1%

       \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y3 \cdot z\right)\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 33.1%

          \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(y3 \cdot z\right)\right)} \]

       2. neg-mul-1 33.1%

          \[\leadsto y0 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(y3 \cdot z\right)\right) \]

   12. Simplified 33.1%

       \[\leadsto y0 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(y3 \cdot z\right)\right)} \]

   if -2.8000000000000002e-168 < j < -1.09999999999999995e-210

   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. Step-by-step derivation

      1. +-commutative 33.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 33.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 33.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 33.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 41.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 59.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 59.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 51.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 51.7%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 51.7%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 59.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 59.5%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 59.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around inf 59.2%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]

   if -1.09999999999999995e-210 < j < 7.2e53

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 29.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around 0 24.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 24.8%

         \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. distribute-rgt-neg-in 24.8%

         \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      3. distribute-rgt-neg-in 24.8%

         \[\leadsto c \cdot \color{blue}{\left(y4 \cdot \left(-t \cdot y2\right)\right)} \]

      4. distribute-rgt-neg-in 24.8%

         \[\leadsto c \cdot \left(y4 \cdot \color{blue}{\left(t \cdot \left(-y2\right)\right)}\right) \]

   8. Simplified 24.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)} \]

   if 7.2e53 < j

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 23.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 23.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 23.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 30.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 55.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y1 around -inf 44.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* 44.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 44.2%

         \[\leadsto \left(\color{blue}{\left(-y1\right)} \cdot \left(y4 \cdot y3 - i \cdot x\right)\right) \cdot j \]

   7. Simplified 44.2%

      \[\leadsto \color{blue}{\left(\left(-y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

   8. Taylor expanded in y4 around inf 39.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 39.8%

         \[\leadsto \color{blue}{-y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)} \]

      2. associate-*r* 38.2%

         \[\leadsto -\color{blue}{\left(y4 \cdot y1\right) \cdot \left(y3 \cdot j\right)} \]

      3. *-commutative 38.2%

         \[\leadsto -\color{blue}{\left(y1 \cdot y4\right)} \cdot \left(y3 \cdot j\right) \]

   10. Simplified 38.2%

       \[\leadsto \color{blue}{-\left(y1 \cdot y4\right) \cdot \left(y3 \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+190}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{+23}:\\ \;\;\;\;k \cdot \left(y \cdot \left(y4 \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-168}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-210}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y1 \cdot y4\right) \cdot \left(j \cdot \left(-y3\right)\right)\\ \end{array} \]

Alternative 24: 21.7% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{+190}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;k \cdot \left(y \cdot \left(y4 \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-168}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-204}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.66 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(j \cdot y1\right) \cdot \left(-y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -3e+190)
   (* i (* y1 (* x j)))
   (if (<= j -4.2e+23)
     (* k (* y (* y4 (- b))))
     (if (<= j -3.7e-168)
       (* y0 (* c (* z (- y3))))
       (if (<= j -1e-204)
         (* c (* y0 (* x y2)))
         (if (<= j 1.66e+50)
           (* c (* y4 (* t (- y2))))
           (* y4 (* (* j y1) (- y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -3e+190) {
		tmp = i * (y1 * (x * j));
	} else if (j <= -4.2e+23) {
		tmp = k * (y * (y4 * -b));
	} else if (j <= -3.7e-168) {
		tmp = y0 * (c * (z * -y3));
	} else if (j <= -1e-204) {
		tmp = c * (y0 * (x * y2));
	} else if (j <= 1.66e+50) {
		tmp = c * (y4 * (t * -y2));
	} else {
		tmp = y4 * ((j * y1) * -y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-3d+190)) then
        tmp = i * (y1 * (x * j))
    else if (j <= (-4.2d+23)) then
        tmp = k * (y * (y4 * -b))
    else if (j <= (-3.7d-168)) then
        tmp = y0 * (c * (z * -y3))
    else if (j <= (-1d-204)) then
        tmp = c * (y0 * (x * y2))
    else if (j <= 1.66d+50) then
        tmp = c * (y4 * (t * -y2))
    else
        tmp = y4 * ((j * y1) * -y3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -3e+190) {
		tmp = i * (y1 * (x * j));
	} else if (j <= -4.2e+23) {
		tmp = k * (y * (y4 * -b));
	} else if (j <= -3.7e-168) {
		tmp = y0 * (c * (z * -y3));
	} else if (j <= -1e-204) {
		tmp = c * (y0 * (x * y2));
	} else if (j <= 1.66e+50) {
		tmp = c * (y4 * (t * -y2));
	} else {
		tmp = y4 * ((j * y1) * -y3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -3e+190:
		tmp = i * (y1 * (x * j))
	elif j <= -4.2e+23:
		tmp = k * (y * (y4 * -b))
	elif j <= -3.7e-168:
		tmp = y0 * (c * (z * -y3))
	elif j <= -1e-204:
		tmp = c * (y0 * (x * y2))
	elif j <= 1.66e+50:
		tmp = c * (y4 * (t * -y2))
	else:
		tmp = y4 * ((j * y1) * -y3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -3e+190)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (j <= -4.2e+23)
		tmp = Float64(k * Float64(y * Float64(y4 * Float64(-b))));
	elseif (j <= -3.7e-168)
		tmp = Float64(y0 * Float64(c * Float64(z * Float64(-y3))));
	elseif (j <= -1e-204)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	elseif (j <= 1.66e+50)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	else
		tmp = Float64(y4 * Float64(Float64(j * y1) * Float64(-y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -3e+190)
		tmp = i * (y1 * (x * j));
	elseif (j <= -4.2e+23)
		tmp = k * (y * (y4 * -b));
	elseif (j <= -3.7e-168)
		tmp = y0 * (c * (z * -y3));
	elseif (j <= -1e-204)
		tmp = c * (y0 * (x * y2));
	elseif (j <= 1.66e+50)
		tmp = c * (y4 * (t * -y2));
	else
		tmp = y4 * ((j * y1) * -y3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -3e+190], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.2e+23], N[(k * N[(y * N[(y4 * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.7e-168], N[(y0 * N[(c * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1e-204], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.66e+50], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(N[(j * y1), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.99999999999999982e190

   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. Step-by-step derivation

      1. +-commutative 33.6%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 33.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 33.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 33.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 33.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 62.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 34.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 34.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -2.99999999999999982e190 < j < -4.2000000000000003e23

   1. Initial program 21.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 42.4%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 29.1%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)} \]

      2. +-commutative 29.1%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)} \]

      3. mul-1-neg 29.1%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right) \]

      4. unsub-neg 29.1%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)} \]

      5. *-commutative 29.1%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - \color{blue}{b \cdot y}\right) \]

   7. Simplified 29.1%

      \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - b \cdot y\right)} \]

   8. Taylor expanded in y1 around 0 38.1%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y4 \cdot \left(y \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 38.1%

         \[\leadsto \color{blue}{-k \cdot \left(y4 \cdot \left(y \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 38.1%

         \[\leadsto \color{blue}{k \cdot \left(-y4 \cdot \left(y \cdot b\right)\right)} \]

      3. associate-*r* 38.1%

         \[\leadsto k \cdot \left(-\color{blue}{\left(y4 \cdot y\right) \cdot b}\right) \]

      4. *-commutative 38.1%

         \[\leadsto k \cdot \left(-\color{blue}{\left(y \cdot y4\right)} \cdot b\right) \]

      5. associate-*l* 40.3%

         \[\leadsto k \cdot \left(-\color{blue}{y \cdot \left(y4 \cdot b\right)}\right) \]

   10. Simplified 40.3%

       \[\leadsto \color{blue}{k \cdot \left(-y \cdot \left(y4 \cdot b\right)\right)} \]

   if -4.2000000000000003e23 < j < -3.69999999999999997e-168

   1. Initial program 43.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 43.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 43.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 43.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 43.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 43.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 43.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 43.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 29.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.4%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 29.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 29.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 29.4%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 29.4%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around 0 33.1%

       \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y3 \cdot z\right)\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 33.1%

          \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(y3 \cdot z\right)\right)} \]

       2. neg-mul-1 33.1%

          \[\leadsto y0 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(y3 \cdot z\right)\right) \]

   12. Simplified 33.1%

       \[\leadsto y0 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(y3 \cdot z\right)\right)} \]

   if -3.69999999999999997e-168 < j < -1e-204

   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. Step-by-step derivation

      1. +-commutative 33.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 33.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 33.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 33.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 41.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 59.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 59.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 51.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 51.7%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 51.7%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 59.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 59.5%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 59.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around inf 59.2%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]

   if -1e-204 < j < 1.66000000000000004e50

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 30.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around 0 25.3%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 25.3%

         \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. distribute-rgt-neg-in 25.3%

         \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      3. distribute-rgt-neg-in 25.3%

         \[\leadsto c \cdot \color{blue}{\left(y4 \cdot \left(-t \cdot y2\right)\right)} \]

      4. distribute-rgt-neg-in 25.3%

         \[\leadsto c \cdot \left(y4 \cdot \color{blue}{\left(t \cdot \left(-y2\right)\right)}\right) \]

   8. Simplified 25.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)} \]

   if 1.66000000000000004e50 < j

   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. Step-by-step derivation

      1. +-commutative 22.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 23.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 23.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 23.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 30.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 55.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y1 around -inf 44.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* 44.4%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 44.4%

         \[\leadsto \left(\color{blue}{\left(-y1\right)} \cdot \left(y4 \cdot y3 - i \cdot x\right)\right) \cdot j \]

   7. Simplified 44.4%

      \[\leadsto \color{blue}{\left(\left(-y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

   8. Taylor expanded in y4 around inf 40.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 40.2%

         \[\leadsto \color{blue}{-y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)} \]

      2. distribute-rgt-neg-in 40.2%

         \[\leadsto \color{blue}{y4 \cdot \left(-y1 \cdot \left(y3 \cdot j\right)\right)} \]

      3. associate-*r* 36.9%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(y1 \cdot y3\right) \cdot j}\right) \]

      4. *-commutative 36.9%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(y3 \cdot y1\right)} \cdot j\right) \]

      5. associate-*l* 38.6%

         \[\leadsto y4 \cdot \left(-\color{blue}{y3 \cdot \left(y1 \cdot j\right)}\right) \]

   10. Simplified 38.6%

       \[\leadsto \color{blue}{y4 \cdot \left(-y3 \cdot \left(y1 \cdot j\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{+190}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;k \cdot \left(y \cdot \left(y4 \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-168}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-204}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.66 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(j \cdot y1\right) \cdot \left(-y3\right)\right)\\ \end{array} \]

Alternative 25: 22.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+109}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-164}:\\ \;\;\;\;\left(y1 \cdot y4\right) \cdot \left(j \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+48}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y3 (* j y5)))))
   (if (<= x -1.05e+109)
     (* i (* y1 (* x j)))
     (if (<= x -5.5e-193)
       t_1
       (if (<= x 5.5e-164)
         (* (* y1 y4) (* j (- y3)))
         (if (<= x 3.1e-43)
           t_1
           (if (<= x 7.5e+48) (* c (* y0 (* x y2))) (* j (* i (* x y1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (x <= -1.05e+109) {
		tmp = i * (y1 * (x * j));
	} else if (x <= -5.5e-193) {
		tmp = t_1;
	} else if (x <= 5.5e-164) {
		tmp = (y1 * y4) * (j * -y3);
	} else if (x <= 3.1e-43) {
		tmp = t_1;
	} else if (x <= 7.5e+48) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = j * (i * (x * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y0 * (y3 * (j * y5))
    if (x <= (-1.05d+109)) then
        tmp = i * (y1 * (x * j))
    else if (x <= (-5.5d-193)) then
        tmp = t_1
    else if (x <= 5.5d-164) then
        tmp = (y1 * y4) * (j * -y3)
    else if (x <= 3.1d-43) then
        tmp = t_1
    else if (x <= 7.5d+48) then
        tmp = c * (y0 * (x * y2))
    else
        tmp = j * (i * (x * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (x <= -1.05e+109) {
		tmp = i * (y1 * (x * j));
	} else if (x <= -5.5e-193) {
		tmp = t_1;
	} else if (x <= 5.5e-164) {
		tmp = (y1 * y4) * (j * -y3);
	} else if (x <= 3.1e-43) {
		tmp = t_1;
	} else if (x <= 7.5e+48) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = j * (i * (x * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y3 * (j * y5))
	tmp = 0
	if x <= -1.05e+109:
		tmp = i * (y1 * (x * j))
	elif x <= -5.5e-193:
		tmp = t_1
	elif x <= 5.5e-164:
		tmp = (y1 * y4) * (j * -y3)
	elif x <= 3.1e-43:
		tmp = t_1
	elif x <= 7.5e+48:
		tmp = c * (y0 * (x * y2))
	else:
		tmp = j * (i * (x * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(y3 * Float64(j * y5)))
	tmp = 0.0
	if (x <= -1.05e+109)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (x <= -5.5e-193)
		tmp = t_1;
	elseif (x <= 5.5e-164)
		tmp = Float64(Float64(y1 * y4) * Float64(j * Float64(-y3)));
	elseif (x <= 3.1e-43)
		tmp = t_1;
	elseif (x <= 7.5e+48)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	else
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y3 * (j * y5));
	tmp = 0.0;
	if (x <= -1.05e+109)
		tmp = i * (y1 * (x * j));
	elseif (x <= -5.5e-193)
		tmp = t_1;
	elseif (x <= 5.5e-164)
		tmp = (y1 * y4) * (j * -y3);
	elseif (x <= 3.1e-43)
		tmp = t_1;
	elseif (x <= 7.5e+48)
		tmp = c * (y0 * (x * y2));
	else
		tmp = j * (i * (x * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e+109], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.5e-193], t$95$1, If[LessEqual[x, 5.5e-164], N[(N[(y1 * y4), $MachinePrecision] * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e-43], t$95$1, If[LessEqual[x, 7.5e+48], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.0500000000000001e109

   1. Initial program 20.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 20.9%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 20.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 20.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 20.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 20.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 28.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 36.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 42.8%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -1.0500000000000001e109 < x < -5.50000000000000014e-193 or 5.50000000000000027e-164 < x < 3.0999999999999999e-43

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 29.5%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 32.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 32.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 32.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 34.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 30.7%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot \left(j \cdot y5\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 30.7%

         \[\leadsto \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \cdot \left(j \cdot y5\right) \]

      2. unsub-neg 30.7%

         \[\leadsto \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \cdot \left(j \cdot y5\right) \]

      3. *-commutative 30.7%

         \[\leadsto \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right) \cdot \left(j \cdot y5\right) \]

      4. *-commutative 30.7%

         \[\leadsto \left(y0 \cdot y3 - t \cdot i\right) \cdot \color{blue}{\left(y5 \cdot j\right)} \]

   7. Simplified 30.7%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 - t \cdot i\right) \cdot \left(y5 \cdot j\right)} \]

   8. Taylor expanded in y0 around inf 25.7%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]

   if -5.50000000000000014e-193 < x < 5.50000000000000027e-164

   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. Step-by-step derivation

      1. +-commutative 42.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 42.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 42.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 42.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 45.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 58.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y1 around -inf 32.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* 32.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 32.6%

         \[\leadsto \left(\color{blue}{\left(-y1\right)} \cdot \left(y4 \cdot y3 - i \cdot x\right)\right) \cdot j \]

   7. Simplified 32.6%

      \[\leadsto \color{blue}{\left(\left(-y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

   8. Taylor expanded in y4 around inf 26.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 26.7%

         \[\leadsto \color{blue}{-y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)} \]

      2. associate-*r* 26.6%

         \[\leadsto -\color{blue}{\left(y4 \cdot y1\right) \cdot \left(y3 \cdot j\right)} \]

      3. *-commutative 26.6%

         \[\leadsto -\color{blue}{\left(y1 \cdot y4\right)} \cdot \left(y3 \cdot j\right) \]

   10. Simplified 26.6%

       \[\leadsto \color{blue}{-\left(y1 \cdot y4\right) \cdot \left(y3 \cdot j\right)} \]

   if 3.0999999999999999e-43 < x < 7.5000000000000006e48

   1. Initial program 40.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 40.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 40.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 40.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 40.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 40.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 31.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 31.5%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 31.5%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 19.7%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 19.7%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 19.7%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around inf 23.5%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]

   if 7.5000000000000006e48 < x

   1. Initial program 10.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 10.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 10.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 10.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 10.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 14.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 41.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 53.9%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 37.6%

      \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot x\right)\right)} \cdot j \]
3. Recombined 5 regimes into one program.

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+109}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-193}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-164}:\\ \;\;\;\;\left(y1 \cdot y4\right) \cdot \left(j \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-43}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+48}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]

Alternative 26: 29.0% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{-102}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= c -1.3e-199)
     t_1
     (if (<= c 2.25e-102)
       (* k (* i (- (* y y5) (* z y1))))
       (if (<= c 5.2e+43) (* y0 (* y3 (- (* j y5) (* z c)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -1.3e-199) {
		tmp = t_1;
	} else if (c <= 2.25e-102) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 5.2e+43) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} 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 = c * (y4 * ((y * y3) - (t * y2)))
    if (c <= (-1.3d-199)) then
        tmp = t_1
    else if (c <= 2.25d-102) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (c <= 5.2d+43) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -1.3e-199) {
		tmp = t_1;
	} else if (c <= 2.25e-102) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 5.2e+43) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if c <= -1.3e-199:
		tmp = t_1
	elif c <= 2.25e-102:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif c <= 5.2e+43:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (c <= -1.3e-199)
		tmp = t_1;
	elseif (c <= 2.25e-102)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (c <= 5.2e+43)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (c <= -1.3e-199)
		tmp = t_1;
	elseif (c <= 2.25e-102)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (c <= 5.2e+43)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.3e-199], t$95$1, If[LessEqual[c, 2.25e-102], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.2e+43], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.3e-199 or 5.20000000000000042e43 < c

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 37.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if -1.3e-199 < c < 2.25e-102

   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. Step-by-step derivation

      1. +-commutative 33.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 33.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 33.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 33.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 34.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in k around inf 37.9%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(y \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(y0 \cdot b - i \cdot y1\right) \cdot z + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)\right)} \]

   5. Taylor expanded in i around inf 43.5%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 43.5%

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(-y1 \cdot z\right)}\right)\right) \]

      2. sub-neg 43.5%

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      3. *-commutative 43.5%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   7. Simplified 43.5%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if 2.25e-102 < c < 5.20000000000000042e43

   1. Initial program 32.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 32.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 35.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 35.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 35.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 37.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 35.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 35.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 35.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in y3 around inf 39.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(c \cdot z\right) - -1 \cdot \left(j \cdot y5\right)\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 39.3%

         \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) - -1 \cdot \left(j \cdot y5\right)\right)\right)} \]

      2. cancel-sign-sub-inv 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right) + \left(--1\right) \cdot \left(j \cdot y5\right)\right)}\right) \]

      3. metadata-eval 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + \color{blue}{1} \cdot \left(j \cdot y5\right)\right)\right) \]

      4. *-lft-identity 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + \color{blue}{j \cdot y5}\right)\right) \]

      5. +-commutative 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y5 + -1 \cdot \left(c \cdot z\right)\right)}\right) \]

      6. mul-1-neg 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(j \cdot y5 + \color{blue}{\left(-c \cdot z\right)}\right)\right) \]

      7. unsub-neg 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(j \cdot y5 - c \cdot z\right)}\right) \]

      8. *-commutative 39.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \left(\color{blue}{y5 \cdot j} - c \cdot z\right)\right) \]

   9. Simplified 39.3%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(y5 \cdot j - c \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.3 \cdot 10^{-199}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{-102}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 27: 32.0% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;c \leq -6.5 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-77}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* c (- (* y y3) (* t y2))))))
   (if (<= c -6.5e-38)
     t_1
     (if (<= c 5.6e-77)
       (* k (* i (- (* y y5) (* z y1))))
       (if (<= c 4.7e+67) (* y4 (* t (- (* b j) (* c y2)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (c * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -6.5e-38) {
		tmp = t_1;
	} else if (c <= 5.6e-77) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 4.7e+67) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y4 * (c * ((y * y3) - (t * y2)))
    if (c <= (-6.5d-38)) then
        tmp = t_1
    else if (c <= 5.6d-77) then
        tmp = k * (i * ((y * y5) - (z * y1)))
    else if (c <= 4.7d+67) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (c * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -6.5e-38) {
		tmp = t_1;
	} else if (c <= 5.6e-77) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (c <= 4.7e+67) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (c * ((y * y3) - (t * y2)))
	tmp = 0
	if c <= -6.5e-38:
		tmp = t_1
	elif c <= 5.6e-77:
		tmp = k * (i * ((y * y5) - (z * y1)))
	elif c <= 4.7e+67:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (c <= -6.5e-38)
		tmp = t_1;
	elseif (c <= 5.6e-77)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (c <= 4.7e+67)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (c * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (c <= -6.5e-38)
		tmp = t_1;
	elseif (c <= 5.6e-77)
		tmp = k * (i * ((y * y5) - (z * y1)));
	elseif (c <= 4.7e+67)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.5e-38], t$95$1, If[LessEqual[c, 5.6e-77], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.7e+67], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.49999999999999949e-38 or 4.70000000000000017e67 < c

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 42.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around 0 33.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right) + -1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 33.3%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3\right)} + -1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right) \]

      2. mul-1-neg 33.3%

         \[\leadsto \left(c \cdot y4\right) \cdot \left(y \cdot y3\right) + \color{blue}{\left(-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]

      3. associate-*r* 27.9%

         \[\leadsto \left(c \cdot y4\right) \cdot \left(y \cdot y3\right) + \left(-\color{blue}{\left(c \cdot y4\right) \cdot \left(t \cdot y2\right)}\right) \]

      4. distribute-rgt-neg-in 27.9%

         \[\leadsto \left(c \cdot y4\right) \cdot \left(y \cdot y3\right) + \color{blue}{\left(c \cdot y4\right) \cdot \left(-t \cdot y2\right)} \]

      5. distribute-lft-in 42.2%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 + \left(-t \cdot y2\right)\right)} \]

      6. sub-neg 42.2%

         \[\leadsto \left(c \cdot y4\right) \cdot \color{blue}{\left(y \cdot y3 - t \cdot y2\right)} \]

      7. associate-*r* 42.2%

         \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

      8. *-commutative 42.2%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right) \cdot c} \]

      9. associate-*l* 47.3%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3 - t \cdot y2\right) \cdot c\right)} \]

   8. Simplified 47.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3 - t \cdot y2\right) \cdot c\right)} \]

   if -6.49999999999999949e-38 < c < 5.5999999999999999e-77

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 33.1%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 33.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 33.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 33.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 35.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in k around inf 38.5%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(y \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(y0 \cdot b - i \cdot y1\right) \cdot z + \left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)\right)} \]

   5. Taylor expanded in i around inf 36.7%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 36.7%

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(-y1 \cdot z\right)}\right)\right) \]

      2. sub-neg 36.7%

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      3. *-commutative 36.7%

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   7. Simplified 36.7%

      \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if 5.5999999999999999e-77 < c < 4.70000000000000017e67

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 37.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 37.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 55.1%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{-38}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-77}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 28: 21.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{-125}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3\right)\\ \mathbf{elif}\;j \leq -1.62 \cdot 10^{-211}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+54}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y1 \cdot y4\right) \cdot \left(j \cdot \left(-y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -6.2e+125)
   (* i (* y1 (* x j)))
   (if (<= j -2.05e-125)
     (* (* j y5) (* y0 y3))
     (if (<= j -1.62e-211)
       (* y0 (* c (* x y2)))
       (if (<= j 4.2e+54)
         (* c (* y4 (* t (- y2))))
         (* (* y1 y4) (* j (- y3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -6.2e+125) {
		tmp = i * (y1 * (x * j));
	} else if (j <= -2.05e-125) {
		tmp = (j * y5) * (y0 * y3);
	} else if (j <= -1.62e-211) {
		tmp = y0 * (c * (x * y2));
	} else if (j <= 4.2e+54) {
		tmp = c * (y4 * (t * -y2));
	} else {
		tmp = (y1 * y4) * (j * -y3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-6.2d+125)) then
        tmp = i * (y1 * (x * j))
    else if (j <= (-2.05d-125)) then
        tmp = (j * y5) * (y0 * y3)
    else if (j <= (-1.62d-211)) then
        tmp = y0 * (c * (x * y2))
    else if (j <= 4.2d+54) then
        tmp = c * (y4 * (t * -y2))
    else
        tmp = (y1 * y4) * (j * -y3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -6.2e+125) {
		tmp = i * (y1 * (x * j));
	} else if (j <= -2.05e-125) {
		tmp = (j * y5) * (y0 * y3);
	} else if (j <= -1.62e-211) {
		tmp = y0 * (c * (x * y2));
	} else if (j <= 4.2e+54) {
		tmp = c * (y4 * (t * -y2));
	} else {
		tmp = (y1 * y4) * (j * -y3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -6.2e+125:
		tmp = i * (y1 * (x * j))
	elif j <= -2.05e-125:
		tmp = (j * y5) * (y0 * y3)
	elif j <= -1.62e-211:
		tmp = y0 * (c * (x * y2))
	elif j <= 4.2e+54:
		tmp = c * (y4 * (t * -y2))
	else:
		tmp = (y1 * y4) * (j * -y3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -6.2e+125)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (j <= -2.05e-125)
		tmp = Float64(Float64(j * y5) * Float64(y0 * y3));
	elseif (j <= -1.62e-211)
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	elseif (j <= 4.2e+54)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	else
		tmp = Float64(Float64(y1 * y4) * Float64(j * Float64(-y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -6.2e+125)
		tmp = i * (y1 * (x * j));
	elseif (j <= -2.05e-125)
		tmp = (j * y5) * (y0 * y3);
	elseif (j <= -1.62e-211)
		tmp = y0 * (c * (x * y2));
	elseif (j <= 4.2e+54)
		tmp = c * (y4 * (t * -y2));
	else
		tmp = (y1 * y4) * (j * -y3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -6.2e+125], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.05e-125], N[(N[(j * y5), $MachinePrecision] * N[(y0 * y3), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.62e-211], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.2e+54], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y1 * y4), $MachinePrecision] * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -6.2e125

   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. Step-by-step derivation

      1. +-commutative 27.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 55.2%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 36.3%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 38.7%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -6.2e125 < j < -2.0499999999999999e-125

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 35.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 37.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 37.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 37.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 37.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 33.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 36.0%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot \left(j \cdot y5\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 36.0%

         \[\leadsto \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \cdot \left(j \cdot y5\right) \]

      2. unsub-neg 36.0%

         \[\leadsto \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \cdot \left(j \cdot y5\right) \]

      3. *-commutative 36.0%

         \[\leadsto \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right) \cdot \left(j \cdot y5\right) \]

      4. *-commutative 36.0%

         \[\leadsto \left(y0 \cdot y3 - t \cdot i\right) \cdot \color{blue}{\left(y5 \cdot j\right)} \]

   7. Simplified 36.0%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 - t \cdot i\right) \cdot \left(y5 \cdot j\right)} \]

   8. Taylor expanded in y0 around inf 26.3%

      \[\leadsto \color{blue}{\left(y0 \cdot y3\right)} \cdot \left(y5 \cdot j\right) \]

   if -2.0499999999999999e-125 < j < -1.61999999999999999e-211

   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. Step-by-step derivation

      1. +-commutative 27.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 62.0%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 62.0%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 62.0%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 45.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 45.7%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 45.7%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 51.0%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 51.0%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 51.0%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around inf 45.7%

       \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(y2 \cdot x\right)}\right) \]

   if -1.61999999999999999e-211 < j < 4.19999999999999972e54

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 29.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around 0 24.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 24.8%

         \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. distribute-rgt-neg-in 24.8%

         \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      3. distribute-rgt-neg-in 24.8%

         \[\leadsto c \cdot \color{blue}{\left(y4 \cdot \left(-t \cdot y2\right)\right)} \]

      4. distribute-rgt-neg-in 24.8%

         \[\leadsto c \cdot \left(y4 \cdot \color{blue}{\left(t \cdot \left(-y2\right)\right)}\right) \]

   8. Simplified 24.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)} \]

   if 4.19999999999999972e54 < j

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 23.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 23.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 23.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 30.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 55.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y1 around -inf 44.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* 44.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 44.2%

         \[\leadsto \left(\color{blue}{\left(-y1\right)} \cdot \left(y4 \cdot y3 - i \cdot x\right)\right) \cdot j \]

   7. Simplified 44.2%

      \[\leadsto \color{blue}{\left(\left(-y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

   8. Taylor expanded in y4 around inf 39.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 39.8%

         \[\leadsto \color{blue}{-y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)} \]

      2. associate-*r* 38.2%

         \[\leadsto -\color{blue}{\left(y4 \cdot y1\right) \cdot \left(y3 \cdot j\right)} \]

      3. *-commutative 38.2%

         \[\leadsto -\color{blue}{\left(y1 \cdot y4\right)} \cdot \left(y3 \cdot j\right) \]

   10. Simplified 38.2%

       \[\leadsto \color{blue}{-\left(y1 \cdot y4\right) \cdot \left(y3 \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{-125}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3\right)\\ \mathbf{elif}\;j \leq -1.62 \cdot 10^{-211}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+54}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y1 \cdot y4\right) \cdot \left(j \cdot \left(-y3\right)\right)\\ \end{array} \]

Alternative 29: 22.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+107}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-176}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-191}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-32}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(x \cdot \left(-b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -2.2e+107)
   (* i (* y1 (* x j)))
   (if (<= x -5.5e-176)
     (* y0 (* y3 (* j y5)))
     (if (<= x 1.5e-191)
       (* j (* y1 (* y4 (- y3))))
       (if (<= x 2.25e-32)
         (* y0 (* c (* z (- y3))))
         (* j (* y0 (* x (- b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.2e+107) {
		tmp = i * (y1 * (x * j));
	} else if (x <= -5.5e-176) {
		tmp = y0 * (y3 * (j * y5));
	} else if (x <= 1.5e-191) {
		tmp = j * (y1 * (y4 * -y3));
	} else if (x <= 2.25e-32) {
		tmp = y0 * (c * (z * -y3));
	} else {
		tmp = j * (y0 * (x * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-2.2d+107)) then
        tmp = i * (y1 * (x * j))
    else if (x <= (-5.5d-176)) then
        tmp = y0 * (y3 * (j * y5))
    else if (x <= 1.5d-191) then
        tmp = j * (y1 * (y4 * -y3))
    else if (x <= 2.25d-32) then
        tmp = y0 * (c * (z * -y3))
    else
        tmp = j * (y0 * (x * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.2e+107) {
		tmp = i * (y1 * (x * j));
	} else if (x <= -5.5e-176) {
		tmp = y0 * (y3 * (j * y5));
	} else if (x <= 1.5e-191) {
		tmp = j * (y1 * (y4 * -y3));
	} else if (x <= 2.25e-32) {
		tmp = y0 * (c * (z * -y3));
	} else {
		tmp = j * (y0 * (x * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -2.2e+107:
		tmp = i * (y1 * (x * j))
	elif x <= -5.5e-176:
		tmp = y0 * (y3 * (j * y5))
	elif x <= 1.5e-191:
		tmp = j * (y1 * (y4 * -y3))
	elif x <= 2.25e-32:
		tmp = y0 * (c * (z * -y3))
	else:
		tmp = j * (y0 * (x * -b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -2.2e+107)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (x <= -5.5e-176)
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	elseif (x <= 1.5e-191)
		tmp = Float64(j * Float64(y1 * Float64(y4 * Float64(-y3))));
	elseif (x <= 2.25e-32)
		tmp = Float64(y0 * Float64(c * Float64(z * Float64(-y3))));
	else
		tmp = Float64(j * Float64(y0 * Float64(x * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -2.2e+107)
		tmp = i * (y1 * (x * j));
	elseif (x <= -5.5e-176)
		tmp = y0 * (y3 * (j * y5));
	elseif (x <= 1.5e-191)
		tmp = j * (y1 * (y4 * -y3));
	elseif (x <= 2.25e-32)
		tmp = y0 * (c * (z * -y3));
	else
		tmp = j * (y0 * (x * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -2.2e+107], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.5e-176], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-191], N[(j * N[(y1 * N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e-32], N[(y0 * N[(c * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.2e107

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 22.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 22.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 22.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 22.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 22.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 27.8%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 35.2%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 41.9%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -2.2e107 < x < -5.5e-176

   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. Step-by-step derivation

      1. +-commutative 28.6%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 32.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 32.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 32.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 33.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 34.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 29.7%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot \left(j \cdot y5\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 29.7%

         \[\leadsto \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \cdot \left(j \cdot y5\right) \]

      2. unsub-neg 29.7%

         \[\leadsto \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \cdot \left(j \cdot y5\right) \]

      3. *-commutative 29.7%

         \[\leadsto \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right) \cdot \left(j \cdot y5\right) \]

      4. *-commutative 29.7%

         \[\leadsto \left(y0 \cdot y3 - t \cdot i\right) \cdot \color{blue}{\left(y5 \cdot j\right)} \]

   7. Simplified 29.7%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 - t \cdot i\right) \cdot \left(y5 \cdot j\right)} \]

   8. Taylor expanded in y0 around inf 24.5%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]

   if -5.5e-176 < x < 1.5e-191

   1. Initial program 42.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 42.4%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 42.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 42.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 42.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 45.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 58.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y1 around -inf 35.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* 35.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 35.2%

         \[\leadsto \left(\color{blue}{\left(-y1\right)} \cdot \left(y4 \cdot y3 - i \cdot x\right)\right) \cdot j \]

   7. Simplified 35.2%

      \[\leadsto \color{blue}{\left(\left(-y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

   8. Taylor expanded in y4 around inf 33.6%

      \[\leadsto \left(\left(-y1\right) \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \cdot j \]

   if 1.5e-191 < x < 2.25000000000000002e-32

   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. Step-by-step derivation

      1. +-commutative 32.1%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 32.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 32.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 32.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 35.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 39.9%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.9%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 39.9%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 33.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.1%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 33.1%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 36.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 36.4%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 36.4%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around 0 44.1%

       \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y3 \cdot z\right)\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 44.1%

          \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(y3 \cdot z\right)\right)} \]

       2. neg-mul-1 44.1%

          \[\leadsto y0 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(y3 \cdot z\right)\right) \]

   12. Simplified 44.1%

       \[\leadsto y0 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(y3 \cdot z\right)\right)} \]

   if 2.25000000000000002e-32 < x

   1. Initial program 19.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 19.4%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 19.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 19.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 19.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 23.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 43.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 48.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in i around 0 38.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(b \cdot x\right)\right)\right)} \cdot j \]
   7. Step-by-step derivation

      1. associate-*r* 38.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(b \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 38.6%

         \[\leadsto \left(\color{blue}{\left(-y0\right)} \cdot \left(b \cdot x\right)\right) \cdot j \]

   8. Simplified 38.6%

      \[\leadsto \color{blue}{\left(\left(-y0\right) \cdot \left(b \cdot x\right)\right)} \cdot j \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+107}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-176}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-191}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-32}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(x \cdot \left(-b\right)\right)\right)\\ \end{array} \]

Alternative 30: 19.8% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{if}\;y1 \leq -3.5 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq -1.05 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.35 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 6.6 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (* x j)))))
   (if (<= y1 -3.5e+167)
     t_1
     (if (<= y1 -1.05e-30)
       (* c (* y0 (* x y2)))
       (if (<= y1 -1.35e-231)
         t_1
         (if (<= y1 6.6e-6) (* c (* y4 (* y y3))) (* k (* y2 (* y1 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 = i * (y1 * (x * j));
	double tmp;
	if (y1 <= -3.5e+167) {
		tmp = t_1;
	} else if (y1 <= -1.05e-30) {
		tmp = c * (y0 * (x * y2));
	} else if (y1 <= -1.35e-231) {
		tmp = t_1;
	} else if (y1 <= 6.6e-6) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = k * (y2 * (y1 * 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 = i * (y1 * (x * j))
    if (y1 <= (-3.5d+167)) then
        tmp = t_1
    else if (y1 <= (-1.05d-30)) then
        tmp = c * (y0 * (x * y2))
    else if (y1 <= (-1.35d-231)) then
        tmp = t_1
    else if (y1 <= 6.6d-6) then
        tmp = c * (y4 * (y * y3))
    else
        tmp = k * (y2 * (y1 * 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 = i * (y1 * (x * j));
	double tmp;
	if (y1 <= -3.5e+167) {
		tmp = t_1;
	} else if (y1 <= -1.05e-30) {
		tmp = c * (y0 * (x * y2));
	} else if (y1 <= -1.35e-231) {
		tmp = t_1;
	} else if (y1 <= 6.6e-6) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = k * (y2 * (y1 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * (x * j))
	tmp = 0
	if y1 <= -3.5e+167:
		tmp = t_1
	elif y1 <= -1.05e-30:
		tmp = c * (y0 * (x * y2))
	elif y1 <= -1.35e-231:
		tmp = t_1
	elif y1 <= 6.6e-6:
		tmp = c * (y4 * (y * y3))
	else:
		tmp = k * (y2 * (y1 * 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(i * Float64(y1 * Float64(x * j)))
	tmp = 0.0
	if (y1 <= -3.5e+167)
		tmp = t_1;
	elseif (y1 <= -1.05e-30)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	elseif (y1 <= -1.35e-231)
		tmp = t_1;
	elseif (y1 <= 6.6e-6)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	else
		tmp = Float64(k * Float64(y2 * Float64(y1 * 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 = i * (y1 * (x * j));
	tmp = 0.0;
	if (y1 <= -3.5e+167)
		tmp = t_1;
	elseif (y1 <= -1.05e-30)
		tmp = c * (y0 * (x * y2));
	elseif (y1 <= -1.35e-231)
		tmp = t_1;
	elseif (y1 <= 6.6e-6)
		tmp = c * (y4 * (y * y3));
	else
		tmp = k * (y2 * (y1 * 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[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -3.5e+167], t$95$1, If[LessEqual[y1, -1.05e-30], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.35e-231], t$95$1, If[LessEqual[y1, 6.6e-6], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -3.49999999999999987e167 or -1.0500000000000001e-30 < y1 < -1.35000000000000011e-231

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 22.6%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 23.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 23.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 23.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 25.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 49.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 31.9%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 25.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -3.49999999999999987e167 < y1 < -1.0500000000000001e-30

   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. Step-by-step derivation

      1. +-commutative 36.9%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 36.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 36.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 36.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 36.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 37.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 37.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 37.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 29.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.1%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 29.1%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 29.1%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 29.1%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 29.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around inf 27.2%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]

   if -1.35000000000000011e-231 < y1 < 6.60000000000000034e-6

   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. Step-by-step derivation

      1. associate-+l- 34.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 34.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 51.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 39.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 20.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if 6.60000000000000034e-6 < y1

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 32.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 35.1%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 23.4%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)} \]

      2. +-commutative 23.4%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)} \]

      3. mul-1-neg 23.4%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right) \]

      4. unsub-neg 23.4%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)} \]

      5. *-commutative 23.4%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - \color{blue}{b \cdot y}\right) \]

   7. Simplified 23.4%

      \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - b \cdot y\right)} \]

   8. Taylor expanded in y1 around inf 28.9%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.9%

         \[\leadsto k \cdot \color{blue}{\left(\left(y4 \cdot y1\right) \cdot y2\right)} \]

      2. *-commutative 31.9%

         \[\leadsto k \cdot \left(\color{blue}{\left(y1 \cdot y4\right)} \cdot y2\right) \]

   10. Simplified 31.9%

       \[\leadsto \color{blue}{k \cdot \left(\left(y1 \cdot y4\right) \cdot y2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 26.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.5 \cdot 10^{+167}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq -1.05 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.35 \cdot 10^{-231}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 6.6 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \]

Alternative 31: 19.9% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{if}\;y1 \leq -3.9 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq -1.02 \cdot 10^{-75}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -5.9 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 3.7 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (* x j)))))
   (if (<= y1 -3.9e+164)
     t_1
     (if (<= y1 -1.02e-75)
       (* y0 (* c (* x y2)))
       (if (<= y1 -5.9e-236)
         t_1
         (if (<= y1 3.7e-6) (* c (* y4 (* y y3))) (* k (* y2 (* y1 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 = i * (y1 * (x * j));
	double tmp;
	if (y1 <= -3.9e+164) {
		tmp = t_1;
	} else if (y1 <= -1.02e-75) {
		tmp = y0 * (c * (x * y2));
	} else if (y1 <= -5.9e-236) {
		tmp = t_1;
	} else if (y1 <= 3.7e-6) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = k * (y2 * (y1 * 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 = i * (y1 * (x * j))
    if (y1 <= (-3.9d+164)) then
        tmp = t_1
    else if (y1 <= (-1.02d-75)) then
        tmp = y0 * (c * (x * y2))
    else if (y1 <= (-5.9d-236)) then
        tmp = t_1
    else if (y1 <= 3.7d-6) then
        tmp = c * (y4 * (y * y3))
    else
        tmp = k * (y2 * (y1 * 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 = i * (y1 * (x * j));
	double tmp;
	if (y1 <= -3.9e+164) {
		tmp = t_1;
	} else if (y1 <= -1.02e-75) {
		tmp = y0 * (c * (x * y2));
	} else if (y1 <= -5.9e-236) {
		tmp = t_1;
	} else if (y1 <= 3.7e-6) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = k * (y2 * (y1 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * (x * j))
	tmp = 0
	if y1 <= -3.9e+164:
		tmp = t_1
	elif y1 <= -1.02e-75:
		tmp = y0 * (c * (x * y2))
	elif y1 <= -5.9e-236:
		tmp = t_1
	elif y1 <= 3.7e-6:
		tmp = c * (y4 * (y * y3))
	else:
		tmp = k * (y2 * (y1 * 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(i * Float64(y1 * Float64(x * j)))
	tmp = 0.0
	if (y1 <= -3.9e+164)
		tmp = t_1;
	elseif (y1 <= -1.02e-75)
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	elseif (y1 <= -5.9e-236)
		tmp = t_1;
	elseif (y1 <= 3.7e-6)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	else
		tmp = Float64(k * Float64(y2 * Float64(y1 * 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 = i * (y1 * (x * j));
	tmp = 0.0;
	if (y1 <= -3.9e+164)
		tmp = t_1;
	elseif (y1 <= -1.02e-75)
		tmp = y0 * (c * (x * y2));
	elseif (y1 <= -5.9e-236)
		tmp = t_1;
	elseif (y1 <= 3.7e-6)
		tmp = c * (y4 * (y * y3));
	else
		tmp = k * (y2 * (y1 * 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[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -3.9e+164], t$95$1, If[LessEqual[y1, -1.02e-75], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5.9e-236], t$95$1, If[LessEqual[y1, 3.7e-6], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -3.89999999999999985e164 or -1.01999999999999997e-75 < y1 < -5.90000000000000014e-236

   1. Initial program 17.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 17.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 17.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 17.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 17.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 18.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 54.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 38.3%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 30.2%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -3.89999999999999985e164 < y1 < -1.01999999999999997e-75

   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. Step-by-step derivation

      1. +-commutative 39.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 41.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 41.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 41.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 41.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 37.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 37.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 37.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 24.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 24.7%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 24.7%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 26.2%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 26.2%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 26.2%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around inf 23.1%

       \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(y2 \cdot x\right)}\right) \]

   if -5.90000000000000014e-236 < y1 < 3.7000000000000002e-6

   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. Step-by-step derivation

      1. associate-+l- 34.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 34.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 51.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 39.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 20.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if 3.7000000000000002e-6 < y1

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 32.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 35.1%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 23.4%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)} \]

      2. +-commutative 23.4%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)} \]

      3. mul-1-neg 23.4%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right) \]

      4. unsub-neg 23.4%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)} \]

      5. *-commutative 23.4%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - \color{blue}{b \cdot y}\right) \]

   7. Simplified 23.4%

      \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - b \cdot y\right)} \]

   8. Taylor expanded in y1 around inf 28.9%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.9%

         \[\leadsto k \cdot \color{blue}{\left(\left(y4 \cdot y1\right) \cdot y2\right)} \]

      2. *-commutative 31.9%

         \[\leadsto k \cdot \left(\color{blue}{\left(y1 \cdot y4\right)} \cdot y2\right) \]

   10. Simplified 31.9%

       \[\leadsto \color{blue}{k \cdot \left(\left(y1 \cdot y4\right) \cdot y2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 26.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.9 \cdot 10^{+164}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq -1.02 \cdot 10^{-75}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -5.9 \cdot 10^{-236}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.7 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \]

Alternative 32: 22.1% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ t_2 := y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;x \leq -3.35 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-165}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (* x j)))) (t_2 (* y0 (* y3 (* j y5)))))
   (if (<= x -3.35e+109)
     t_1
     (if (<= x -4.4e-182)
       t_2
       (if (<= x 1.3e-165)
         (* k (* y4 (* y1 y2)))
         (if (<= x 4.4e-43) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * (x * j));
	double t_2 = y0 * (y3 * (j * y5));
	double tmp;
	if (x <= -3.35e+109) {
		tmp = t_1;
	} else if (x <= -4.4e-182) {
		tmp = t_2;
	} else if (x <= 1.3e-165) {
		tmp = k * (y4 * (y1 * y2));
	} else if (x <= 4.4e-43) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y1 * (x * j))
    t_2 = y0 * (y3 * (j * y5))
    if (x <= (-3.35d+109)) then
        tmp = t_1
    else if (x <= (-4.4d-182)) then
        tmp = t_2
    else if (x <= 1.3d-165) then
        tmp = k * (y4 * (y1 * y2))
    else if (x <= 4.4d-43) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * (x * j));
	double t_2 = y0 * (y3 * (j * y5));
	double tmp;
	if (x <= -3.35e+109) {
		tmp = t_1;
	} else if (x <= -4.4e-182) {
		tmp = t_2;
	} else if (x <= 1.3e-165) {
		tmp = k * (y4 * (y1 * y2));
	} else if (x <= 4.4e-43) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * (x * j))
	t_2 = y0 * (y3 * (j * y5))
	tmp = 0
	if x <= -3.35e+109:
		tmp = t_1
	elif x <= -4.4e-182:
		tmp = t_2
	elif x <= 1.3e-165:
		tmp = k * (y4 * (y1 * y2))
	elif x <= 4.4e-43:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y1 * Float64(x * j)))
	t_2 = Float64(y0 * Float64(y3 * Float64(j * y5)))
	tmp = 0.0
	if (x <= -3.35e+109)
		tmp = t_1;
	elseif (x <= -4.4e-182)
		tmp = t_2;
	elseif (x <= 1.3e-165)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (x <= 4.4e-43)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y1 * (x * j));
	t_2 = y0 * (y3 * (j * y5));
	tmp = 0.0;
	if (x <= -3.35e+109)
		tmp = t_1;
	elseif (x <= -4.4e-182)
		tmp = t_2;
	elseif (x <= 1.3e-165)
		tmp = k * (y4 * (y1 * y2));
	elseif (x <= 4.4e-43)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.35e+109], t$95$1, If[LessEqual[x, -4.4e-182], t$95$2, If[LessEqual[x, 1.3e-165], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-43], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.35000000000000018e109 or 4.39999999999999994e-43 < x

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 20.5%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 20.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 20.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 20.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 23.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 38.0%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 43.5%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 33.0%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -3.35000000000000018e109 < x < -4.3999999999999999e-182 or 1.30000000000000004e-165 < x < 4.39999999999999994e-43

   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. Step-by-step derivation

      1. +-commutative 29.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 31.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 31.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 31.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 33.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 31.5%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot \left(j \cdot y5\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 31.5%

         \[\leadsto \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \cdot \left(j \cdot y5\right) \]

      2. unsub-neg 31.5%

         \[\leadsto \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \cdot \left(j \cdot y5\right) \]

      3. *-commutative 31.5%

         \[\leadsto \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right) \cdot \left(j \cdot y5\right) \]

      4. *-commutative 31.5%

         \[\leadsto \left(y0 \cdot y3 - t \cdot i\right) \cdot \color{blue}{\left(y5 \cdot j\right)} \]

   7. Simplified 31.5%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 - t \cdot i\right) \cdot \left(y5 \cdot j\right)} \]

   8. Taylor expanded in y0 around inf 26.4%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]

   if -4.3999999999999999e-182 < x < 1.30000000000000004e-165

   1. Initial program 42.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 42.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 42.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 51.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 39.1%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 27.6%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)} \]

      2. +-commutative 27.6%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)} \]

      3. mul-1-neg 27.6%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right) \]

      4. unsub-neg 27.6%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)} \]

      5. *-commutative 27.6%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - \color{blue}{b \cdot y}\right) \]

   7. Simplified 27.6%

      \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - b \cdot y\right)} \]

   8. Taylor expanded in y1 around inf 25.7%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.35 \cdot 10^{+109}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-182}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-165}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-43}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]

Alternative 33: 22.2% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+109}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-165}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y3 (* j y5)))))
   (if (<= x -1.3e+109)
     (* i (* y1 (* x j)))
     (if (<= x -5.8e-182)
       t_1
       (if (<= x 1.3e-165)
         (* k (* y4 (* y1 y2)))
         (if (<= x 6e-43) t_1 (* j (* i (* x y1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (x <= -1.3e+109) {
		tmp = i * (y1 * (x * j));
	} else if (x <= -5.8e-182) {
		tmp = t_1;
	} else if (x <= 1.3e-165) {
		tmp = k * (y4 * (y1 * y2));
	} else if (x <= 6e-43) {
		tmp = t_1;
	} else {
		tmp = j * (i * (x * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y0 * (y3 * (j * y5))
    if (x <= (-1.3d+109)) then
        tmp = i * (y1 * (x * j))
    else if (x <= (-5.8d-182)) then
        tmp = t_1
    else if (x <= 1.3d-165) then
        tmp = k * (y4 * (y1 * y2))
    else if (x <= 6d-43) then
        tmp = t_1
    else
        tmp = j * (i * (x * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (x <= -1.3e+109) {
		tmp = i * (y1 * (x * j));
	} else if (x <= -5.8e-182) {
		tmp = t_1;
	} else if (x <= 1.3e-165) {
		tmp = k * (y4 * (y1 * y2));
	} else if (x <= 6e-43) {
		tmp = t_1;
	} else {
		tmp = j * (i * (x * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y3 * (j * y5))
	tmp = 0
	if x <= -1.3e+109:
		tmp = i * (y1 * (x * j))
	elif x <= -5.8e-182:
		tmp = t_1
	elif x <= 1.3e-165:
		tmp = k * (y4 * (y1 * y2))
	elif x <= 6e-43:
		tmp = t_1
	else:
		tmp = j * (i * (x * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(y3 * Float64(j * y5)))
	tmp = 0.0
	if (x <= -1.3e+109)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (x <= -5.8e-182)
		tmp = t_1;
	elseif (x <= 1.3e-165)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (x <= 6e-43)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y3 * (j * y5));
	tmp = 0.0;
	if (x <= -1.3e+109)
		tmp = i * (y1 * (x * j));
	elseif (x <= -5.8e-182)
		tmp = t_1;
	elseif (x <= 1.3e-165)
		tmp = k * (y4 * (y1 * y2));
	elseif (x <= 6e-43)
		tmp = t_1;
	else
		tmp = j * (i * (x * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+109], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-182], t$95$1, If[LessEqual[x, 1.3e-165], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-43], t$95$1, N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2999999999999999e109

   1. Initial program 20.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 20.9%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 20.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 20.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 20.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 20.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 28.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 36.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 42.8%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -1.2999999999999999e109 < x < -5.79999999999999974e-182 or 1.30000000000000004e-165 < x < 6.00000000000000007e-43

   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. Step-by-step derivation

      1. +-commutative 29.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 31.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 31.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 31.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 33.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 31.5%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot \left(j \cdot y5\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 31.5%

         \[\leadsto \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right) \cdot \left(j \cdot y5\right) \]

      2. unsub-neg 31.5%

         \[\leadsto \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)} \cdot \left(j \cdot y5\right) \]

      3. *-commutative 31.5%

         \[\leadsto \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right) \cdot \left(j \cdot y5\right) \]

      4. *-commutative 31.5%

         \[\leadsto \left(y0 \cdot y3 - t \cdot i\right) \cdot \color{blue}{\left(y5 \cdot j\right)} \]

   7. Simplified 31.5%

      \[\leadsto \color{blue}{\left(y0 \cdot y3 - t \cdot i\right) \cdot \left(y5 \cdot j\right)} \]

   8. Taylor expanded in y0 around inf 26.4%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]

   if -5.79999999999999974e-182 < x < 1.30000000000000004e-165

   1. Initial program 42.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 42.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 42.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 51.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 39.1%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 27.6%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)} \]

      2. +-commutative 27.6%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)} \]

      3. mul-1-neg 27.6%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right) \]

      4. unsub-neg 27.6%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)} \]

      5. *-commutative 27.6%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - \color{blue}{b \cdot y}\right) \]

   7. Simplified 27.6%

      \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - b \cdot y\right)} \]

   8. Taylor expanded in y1 around inf 25.7%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if 6.00000000000000007e-43 < x

   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. Step-by-step derivation

      1. +-commutative 20.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 20.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 20.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 20.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 24.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 43.8%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 48.1%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 30.2%

      \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot x\right)\right)} \cdot j \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+109}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-182}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-165}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-43}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]

Alternative 34: 29.0% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+121}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -2.5e+121)
   (* i (* y1 (* x j)))
   (if (<= j 3.9e+38)
     (* c (* y4 (- (* y y3) (* t y2))))
     (* y4 (* y1 (* j (- y3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -2.5e+121) {
		tmp = i * (y1 * (x * j));
	} else if (j <= 3.9e+38) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y4 * (y1 * (j * -y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-2.5d+121)) then
        tmp = i * (y1 * (x * j))
    else if (j <= 3.9d+38) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = y4 * (y1 * (j * -y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -2.5e+121) {
		tmp = i * (y1 * (x * j));
	} else if (j <= 3.9e+38) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = y4 * (y1 * (j * -y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -2.5e+121:
		tmp = i * (y1 * (x * j))
	elif j <= 3.9e+38:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = y4 * (y1 * (j * -y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -2.5e+121)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (j <= 3.9e+38)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(y4 * Float64(y1 * Float64(j * Float64(-y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -2.5e+121)
		tmp = i * (y1 * (x * j));
	elseif (j <= 3.9e+38)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = y4 * (y1 * (j * -y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -2.5e+121], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.9e+38], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(y1 * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.50000000000000004e121

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 26.9%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 26.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 26.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 26.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 26.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 53.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 35.3%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 37.7%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if -2.50000000000000004e121 < j < 3.90000000000000023e38

   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. Step-by-step derivation

      1. associate-+l- 31.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 31.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 32.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 3.90000000000000023e38 < j

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 23.1%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 33.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 55.2%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y1 around -inf 43.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. associate-*r* 43.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

      2. neg-mul-1 43.0%

         \[\leadsto \left(\color{blue}{\left(-y1\right)} \cdot \left(y4 \cdot y3 - i \cdot x\right)\right) \cdot j \]

   7. Simplified 43.0%

      \[\leadsto \color{blue}{\left(\left(-y1\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)\right)} \cdot j \]

   8. Taylor expanded in y4 around inf 38.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+121}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \end{array} \]

Alternative 35: 19.4% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq 5 \cdot 10^{-13}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 5e-13) (* c (* y4 (* y y3))) (* c (* y0 (* x y2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= 5e-13) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= 5d-13) then
        tmp = c * (y4 * (y * y3))
    else
        tmp = c * (y0 * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= 5e-13) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= 5e-13:
		tmp = c * (y4 * (y * y3))
	else:
		tmp = c * (y0 * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= 5e-13)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	else
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= 5e-13)
		tmp = c * (y4 * (y * y3));
	else
		tmp = c * (y0 * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, 5e-13], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < 4.9999999999999999e-13

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 29.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 19.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if 4.9999999999999999e-13 < y2

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 27.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 37.3%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 37.3%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 31.3%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 31.3%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 31.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around inf 31.1%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq 5 \cdot 10^{-13}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]

Alternative 36: 19.4% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq 4.7 \cdot 10^{-74}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 4.7e-74) (* i (* y1 (* x j))) (* c (* y0 (* x y2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= 4.7e-74) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= 4.7d-74) then
        tmp = i * (y1 * (x * j))
    else
        tmp = c * (y0 * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= 4.7e-74) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= 4.7e-74:
		tmp = i * (y1 * (x * j))
	else:
		tmp = c * (y0 * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= 4.7e-74)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	else
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= 4.7e-74)
		tmp = i * (y1 * (x * j));
	else
		tmp = c * (y0 * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, 4.7e-74], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < 4.7000000000000001e-74

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 27.9%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 29.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 29.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 29.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 41.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 25.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]

   6. Taylor expanded in y1 around inf 19.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]

   if 4.7000000000000001e-74 < y2

   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. Step-by-step derivation

      1. +-commutative 30.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 30.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 30.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 30.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 43.0%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.0%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 43.0%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in c around inf 36.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.8%

         \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

      2. *-commutative 36.8%

         \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

      3. associate-*l* 31.8%

         \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

      4. *-commutative 31.8%

         \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Simplified 31.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   10. Taylor expanded in x around inf 29.0%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq 4.7 \cdot 10^{-74}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]

Alternative 37: 16.9% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* c (* y0 (* x y2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return c * (y0 * (x * y2));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = c * (y0 * (x * y2))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return c * (y0 * (x * y2));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return c * (y0 * (x * y2))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(c * Float64(y0 * Float64(x * y2)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = c * (y0 * (x * y2));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 28.7%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Step-by-step derivation

   1. +-commutative 28.7%

      \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   2. fma-def 29.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. *-commutative 29.5%

      \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   4. *-commutative 29.5%

      \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

3. Simplified 32.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

4. Taylor expanded in y0 around inf 34.2%

   \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
5. Step-by-step derivation

   1. mul-1-neg 34.2%

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

6. Simplified 34.2%

   \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

7. Taylor expanded in c around inf 24.2%

   \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative 24.2%

      \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot x - y3 \cdot z\right) \cdot y0\right)} \]

   2. *-commutative 24.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right) \cdot y0\right) \]

   3. associate-*l* 23.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot y0} \]

   4. *-commutative 23.9%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

9. Simplified 23.9%

   \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

10. Taylor expanded in x around inf 14.0%

    \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]

11. Final simplification 14.0%

    \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right) \]

Developer target: 28.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t_9\\ t_11 := t_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t_4 \cdot t_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t_3 \cdot t_1 - t_14\right)\right) + \left(t_8 - \left(t_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t_13\right)\right) + \left(t_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t_10 - \left(y \cdot x - z \cdot t\right) \cdot t_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t_8 - \left(t_11 - t_6\right)\right) - \left(\frac{t_3}{\frac{1}{t_1}} - t_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t_2 - \left(t_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t_5\right) - t_17 \cdot t_1\right) + t_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023174 
(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)))))