Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.7% → 43.6%

Time: 39.6s

Alternatives: 31

Speedup: 5.6×

• 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: 30.7% 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: 43.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\\ t_2 := z \cdot y3 - x \cdot y2\\ t_3 := c \cdot y0 - a \cdot y1\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y5 \cdot \mathsf{fma}\left(i, y \cdot k - t \cdot j, \mathsf{fma}\left(t\_4, 0 - y0, a \cdot t\_1\right)\right)\\ t_6 := y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot t\_4\right) - c \cdot t\_1\right)\\ \mathbf{if}\;y5 \leq -4.25 \cdot 10^{+164}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y5 \leq -1.5 \cdot 10^{+35}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y5 \leq -1.85 \cdot 10^{-230}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, t\_2, \mathsf{fma}\left(y4, t\_4, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.65 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(t\_3, y2, y \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - j \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3 \cdot 10^{-101}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y5 \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(t\_3, x, k \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(0 - y5\right)\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2.1 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(y0, t\_2, \mathsf{fma}\left(i, x \cdot y - z \cdot t, y4 \cdot t\_1\right)\right) \cdot \left(0 - c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (fma t y2 (- 0.0 (* y y3))))
        (t_2 (- (* z y3) (* x y2)))
        (t_3 (- (* c y0) (* a y1)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (* y5 (fma i (- (* y k) (* t j)) (fma t_4 (- 0.0 y0) (* a t_1)))))
        (t_6 (* y4 (- (fma b (- (* t j) (* y k)) (* y1 t_4)) (* c t_1)))))
   (if (<= y5 -4.25e+164)
     t_5
     (if (<= y5 -1.5e+35)
       t_6
       (if (<= y5 -1.85e-230)
         (* y1 (fma a t_2 (fma y4 t_4 (* i (- (* x j) (* z k))))))
         (if (<= y5 2.65e-298)
           (*
            x
            (-
             (fma t_3 y2 (* y (fma a b (- 0.0 (* c i)))))
             (* j (fma b y0 (* i (- 0.0 y1))))))
           (if (<= y5 3e-101)
             t_6
             (if (<= y5 4.4e+39)
               (*
                y2
                (+
                 (fma t_3 x (* k (fma y1 y4 (* y0 (- 0.0 y5)))))
                 (* t (- (* a y5) (* c y4)))))
               (if (<= y5 2.1e+194)
                 (*
                  (fma y0 t_2 (fma i (- (* x y) (* z t)) (* y4 t_1)))
                  (- 0.0 c))
                 t_5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = fma(t, y2, (0.0 - (y * y3)));
	double t_2 = (z * y3) - (x * y2);
	double t_3 = (c * y0) - (a * y1);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = y5 * fma(i, ((y * k) - (t * j)), fma(t_4, (0.0 - y0), (a * t_1)));
	double t_6 = y4 * (fma(b, ((t * j) - (y * k)), (y1 * t_4)) - (c * t_1));
	double tmp;
	if (y5 <= -4.25e+164) {
		tmp = t_5;
	} else if (y5 <= -1.5e+35) {
		tmp = t_6;
	} else if (y5 <= -1.85e-230) {
		tmp = y1 * fma(a, t_2, fma(y4, t_4, (i * ((x * j) - (z * k)))));
	} else if (y5 <= 2.65e-298) {
		tmp = x * (fma(t_3, y2, (y * fma(a, b, (0.0 - (c * i))))) - (j * fma(b, y0, (i * (0.0 - y1)))));
	} else if (y5 <= 3e-101) {
		tmp = t_6;
	} else if (y5 <= 4.4e+39) {
		tmp = y2 * (fma(t_3, x, (k * fma(y1, y4, (y0 * (0.0 - y5))))) + (t * ((a * y5) - (c * y4))));
	} else if (y5 <= 2.1e+194) {
		tmp = fma(y0, t_2, fma(i, ((x * y) - (z * t)), (y4 * t_1))) * (0.0 - c);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = fma(t, y2, Float64(0.0 - Float64(y * y3)))
	t_2 = Float64(Float64(z * y3) - Float64(x * y2))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(y5 * fma(i, Float64(Float64(y * k) - Float64(t * j)), fma(t_4, Float64(0.0 - y0), Float64(a * t_1))))
	t_6 = Float64(y4 * Float64(fma(b, Float64(Float64(t * j) - Float64(y * k)), Float64(y1 * t_4)) - Float64(c * t_1)))
	tmp = 0.0
	if (y5 <= -4.25e+164)
		tmp = t_5;
	elseif (y5 <= -1.5e+35)
		tmp = t_6;
	elseif (y5 <= -1.85e-230)
		tmp = Float64(y1 * fma(a, t_2, fma(y4, t_4, Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (y5 <= 2.65e-298)
		tmp = Float64(x * Float64(fma(t_3, y2, Float64(y * fma(a, b, Float64(0.0 - Float64(c * i))))) - Float64(j * fma(b, y0, Float64(i * Float64(0.0 - y1))))));
	elseif (y5 <= 3e-101)
		tmp = t_6;
	elseif (y5 <= 4.4e+39)
		tmp = Float64(y2 * Float64(fma(t_3, x, Float64(k * fma(y1, y4, Float64(y0 * Float64(0.0 - y5))))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y5 <= 2.1e+194)
		tmp = Float64(fma(y0, t_2, fma(i, Float64(Float64(x * y) - Float64(z * t)), Float64(y4 * t_1))) * Float64(0.0 - c));
	else
		tmp = t_5;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * y2 + N[(0.0 - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 * N[(0.0 - y0), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -4.25e+164], t$95$5, If[LessEqual[y5, -1.5e+35], t$95$6, If[LessEqual[y5, -1.85e-230], N[(y1 * N[(a * t$95$2 + N[(y4 * t$95$4 + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.65e-298], N[(x * N[(N[(t$95$3 * y2 + N[(y * N[(a * b + N[(0.0 - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(b * y0 + N[(i * N[(0.0 - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3e-101], t$95$6, If[LessEqual[y5, 4.4e+39], N[(y2 * N[(N[(t$95$3 * x + N[(k * N[(y1 * y4 + N[(y0 * N[(0.0 - y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.1e+194], N[(N[(y0 * t$95$2 + N[(i * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.0 - c), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -4.25000000000000014e164 or 2.10000000000000016e194 < y5

   1. Initial program 30.0%

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

   3. Taylor expanded in y5 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

   5. Simplified 87.5%

      \[\leadsto \color{blue}{y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), \mathsf{fma}\left(k \cdot y2 - y3 \cdot j, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   if -4.25000000000000014e164 < y5 < -1.49999999999999995e35 or 2.65000000000000001e-298 < y5 < 3.0000000000000003e-101

   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. Add Preprocessing

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. sub-neg N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 67.9

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 67.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   if -1.49999999999999995e35 < y5 < -1.84999999999999991e-230

   1. Initial program 38.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 57.1%

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

   if -1.84999999999999991e-230 < y5 < 2.65000000000000001e-298

   1. Initial program 40.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 74.0%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   if 3.0000000000000003e-101 < y5 < 4.4000000000000003e39

   1. Initial program 25.7%

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

   3. Taylor expanded in y2 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 53.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \mathsf{fma}\left(y1, y4, 0 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 4.4000000000000003e39 < y5 < 2.10000000000000016e194

   1. Initial program 21.6%

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

   3. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 57.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right) \cdot \left(0 - c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -4.25 \cdot 10^{+164}:\\ \;\;\;\;y5 \cdot \mathsf{fma}\left(i, y \cdot k - t \cdot j, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.5 \cdot 10^{+35}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.85 \cdot 10^{-230}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.65 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, y \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - j \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3 \cdot 10^{-101}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(0 - y5\right)\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2.1 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(y0, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(i, x \cdot y - z \cdot t, y4 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right) \cdot \left(0 - c\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \mathsf{fma}\left(i, y \cdot k - t \cdot j, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := \left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t\_1 \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(y1 \cdot y4 - y0 \cdot y5\right) \cdot t\_2\\ \mathbf{if}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t\_1, y1 \cdot t\_2\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (- (* k y2) (* j y3)))
        (t_3
         (+
          (+
           (+
            (+
             (+
              (* (- (* a b) (* c i)) (- (* x y) (* z t)))
              (* (- (* b y0) (* i y1)) (- (* z k) (* x j))))
             (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))))
            (* t_1 (- (* b y4) (* i y5))))
           (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4))))
          (* (- (* y1 y4) (* y0 y5)) t_2))))
   (if (<= t_3 INFINITY)
     t_3
     (* y4 (- (fma b t_1 (* y1 t_2)) (* c (fma t y2 (- 0.0 (* y 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 = (t * j) - (y * k);
	double t_2 = (k * y2) - (j * y3);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_1 * ((b * y4) - (i * y5)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((y1 * y4) - (y0 * y5)) * t_2);
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = y4 * (fma(b, t_1, (y1 * t_2)) - (c * fma(t, y2, (0.0 - (y * 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(Float64(t * j) - Float64(y * k))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = 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(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t_1 * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(Float64(Float64(y1 * y4) - Float64(y0 * y5)) * t_2))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(y4 * Float64(fma(b, t_1, Float64(y1 * t_2)) - Float64(c * fma(t, y2, Float64(0.0 - Float64(y * y3))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $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] * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(y4 * N[(N[(b * t$95$1 + N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y2 + N[(0.0 - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. sub-neg N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 47.0

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 47.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(y1 \cdot y4 - y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) \leq \infty:\\ \;\;\;\;\left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(y1 \cdot y4 - y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 44.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\\ t_2 := \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\\ t_3 := \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := k \cdot y2 - j \cdot y3\\ t_6 := y5 \cdot \mathsf{fma}\left(i, y \cdot k - t \cdot j, \mathsf{fma}\left(t\_5, 0 - y0, a \cdot t\_3\right)\right)\\ t_7 := y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot t\_5\right) - c \cdot t\_3\right)\\ \mathbf{if}\;y5 \leq -2.85 \cdot 10^{+165}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y5 \leq -3.4 \cdot 10^{+35}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;y5 \leq -1 \cdot 10^{-236}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, t\_5, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 4.2 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(t\_4, y2, y \cdot t\_1\right) - j \cdot t\_2\right)\\ \mathbf{elif}\;y5 \leq 1.02 \cdot 10^{-53}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{+193}:\\ \;\;\;\;z \cdot \left(k \cdot t\_2 - \mathsf{fma}\left(y3, t\_4, t \cdot t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (fma a b (- 0.0 (* c i))))
        (t_2 (fma b y0 (* i (- 0.0 y1))))
        (t_3 (fma t y2 (- 0.0 (* y y3))))
        (t_4 (- (* c y0) (* a y1)))
        (t_5 (- (* k y2) (* j y3)))
        (t_6 (* y5 (fma i (- (* y k) (* t j)) (fma t_5 (- 0.0 y0) (* a t_3)))))
        (t_7 (* y4 (- (fma b (- (* t j) (* y k)) (* y1 t_5)) (* c t_3)))))
   (if (<= y5 -2.85e+165)
     t_6
     (if (<= y5 -3.4e+35)
       t_7
       (if (<= y5 -1e-236)
         (*
          y1
          (fma a (- (* z y3) (* x y2)) (fma y4 t_5 (* i (- (* x j) (* z k))))))
         (if (<= y5 4.2e-298)
           (* x (- (fma t_4 y2 (* y t_1)) (* j t_2)))
           (if (<= y5 1.02e-53)
             t_7
             (if (<= y5 6e+193)
               (* z (- (* k t_2) (fma y3 t_4 (* t t_1))))
               t_6))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = fma(a, b, (0.0 - (c * i)));
	double t_2 = fma(b, y0, (i * (0.0 - y1)));
	double t_3 = fma(t, y2, (0.0 - (y * y3)));
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (k * y2) - (j * y3);
	double t_6 = y5 * fma(i, ((y * k) - (t * j)), fma(t_5, (0.0 - y0), (a * t_3)));
	double t_7 = y4 * (fma(b, ((t * j) - (y * k)), (y1 * t_5)) - (c * t_3));
	double tmp;
	if (y5 <= -2.85e+165) {
		tmp = t_6;
	} else if (y5 <= -3.4e+35) {
		tmp = t_7;
	} else if (y5 <= -1e-236) {
		tmp = y1 * fma(a, ((z * y3) - (x * y2)), fma(y4, t_5, (i * ((x * j) - (z * k)))));
	} else if (y5 <= 4.2e-298) {
		tmp = x * (fma(t_4, y2, (y * t_1)) - (j * t_2));
	} else if (y5 <= 1.02e-53) {
		tmp = t_7;
	} else if (y5 <= 6e+193) {
		tmp = z * ((k * t_2) - fma(y3, t_4, (t * t_1)));
	} else {
		tmp = t_6;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = fma(a, b, Float64(0.0 - Float64(c * i)))
	t_2 = fma(b, y0, Float64(i * Float64(0.0 - y1)))
	t_3 = fma(t, y2, Float64(0.0 - Float64(y * y3)))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(Float64(k * y2) - Float64(j * y3))
	t_6 = Float64(y5 * fma(i, Float64(Float64(y * k) - Float64(t * j)), fma(t_5, Float64(0.0 - y0), Float64(a * t_3))))
	t_7 = Float64(y4 * Float64(fma(b, Float64(Float64(t * j) - Float64(y * k)), Float64(y1 * t_5)) - Float64(c * t_3)))
	tmp = 0.0
	if (y5 <= -2.85e+165)
		tmp = t_6;
	elseif (y5 <= -3.4e+35)
		tmp = t_7;
	elseif (y5 <= -1e-236)
		tmp = Float64(y1 * fma(a, Float64(Float64(z * y3) - Float64(x * y2)), fma(y4, t_5, Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (y5 <= 4.2e-298)
		tmp = Float64(x * Float64(fma(t_4, y2, Float64(y * t_1)) - Float64(j * t_2)));
	elseif (y5 <= 1.02e-53)
		tmp = t_7;
	elseif (y5 <= 6e+193)
		tmp = Float64(z * Float64(Float64(k * t_2) - fma(y3, t_4, Float64(t * t_1))));
	else
		tmp = t_6;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * b + N[(0.0 - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * y0 + N[(i * N[(0.0 - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * y2 + N[(0.0 - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(t$95$5 * N[(0.0 - y0), $MachinePrecision] + N[(a * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.85e+165], t$95$6, If[LessEqual[y5, -3.4e+35], t$95$7, If[LessEqual[y5, -1e-236], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$5 + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.2e-298], N[(x * N[(N[(t$95$4 * y2 + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.02e-53], t$95$7, If[LessEqual[y5, 6e+193], N[(z * N[(N[(k * t$95$2), $MachinePrecision] - N[(y3 * t$95$4 + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$6]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -2.85000000000000013e165 or 6e193 < y5

   1. Initial program 30.0%

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

   3. Taylor expanded in y5 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

   5. Simplified 87.5%

      \[\leadsto \color{blue}{y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), \mathsf{fma}\left(k \cdot y2 - y3 \cdot j, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   if -2.85000000000000013e165 < y5 < -3.4000000000000001e35 or 4.2000000000000001e-298 < y5 < 1.02000000000000002e-53

   1. Initial program 32.1%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. sub-neg N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 64.1

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 64.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   if -3.4000000000000001e35 < y5 < -1e-236

   1. Initial program 38.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 57.1%

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

   if -1e-236 < y5 < 4.2000000000000001e-298

   1. Initial program 40.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 74.0%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   if 1.02000000000000002e-53 < y5 < 6e193

   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. Add Preprocessing

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 58.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - k \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right) \cdot \left(0 - z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.85 \cdot 10^{+165}:\\ \;\;\;\;y5 \cdot \mathsf{fma}\left(i, y \cdot k - t \cdot j, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -3.4 \cdot 10^{+35}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1 \cdot 10^{-236}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 4.2 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, y \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - j \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.02 \cdot 10^{-53}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{+193}:\\ \;\;\;\;z \cdot \left(k \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right) - \mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \mathsf{fma}\left(i, y \cdot k - t \cdot j, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 44.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := y5 \cdot \mathsf{fma}\left(i, y \cdot k - t \cdot j, \mathsf{fma}\left(t\_3, 0 - y0, a \cdot t\_1\right)\right)\\ t_5 := y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot t\_3\right) - c \cdot t\_1\right)\\ \mathbf{if}\;y5 \leq -4.6 \cdot 10^{+166}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y5 \leq -2.2 \cdot 10^{+38}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y5 \leq -5.4 \cdot 10^{-238}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, t\_3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(t\_2, y2, y \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - j \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 5.4 \cdot 10^{-95}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y5 \leq 7.7 \cdot 10^{+62}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(t\_2, x, k \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(0 - y5\right)\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (fma t y2 (- 0.0 (* y y3))))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* k y2) (* j y3)))
        (t_4 (* y5 (fma i (- (* y k) (* t j)) (fma t_3 (- 0.0 y0) (* a t_1)))))
        (t_5 (* y4 (- (fma b (- (* t j) (* y k)) (* y1 t_3)) (* c t_1)))))
   (if (<= y5 -4.6e+166)
     t_4
     (if (<= y5 -2.2e+38)
       t_5
       (if (<= y5 -5.4e-238)
         (*
          y1
          (fma a (- (* z y3) (* x y2)) (fma y4 t_3 (* i (- (* x j) (* z k))))))
         (if (<= y5 1.15e-297)
           (*
            x
            (-
             (fma t_2 y2 (* y (fma a b (- 0.0 (* c i)))))
             (* j (fma b y0 (* i (- 0.0 y1))))))
           (if (<= y5 5.4e-95)
             t_5
             (if (<= y5 7.7e+62)
               (*
                y2
                (+
                 (fma t_2 x (* k (fma y1 y4 (* y0 (- 0.0 y5)))))
                 (* t (- (* a y5) (* c 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 = fma(t, y2, (0.0 - (y * y3)));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = y5 * fma(i, ((y * k) - (t * j)), fma(t_3, (0.0 - y0), (a * t_1)));
	double t_5 = y4 * (fma(b, ((t * j) - (y * k)), (y1 * t_3)) - (c * t_1));
	double tmp;
	if (y5 <= -4.6e+166) {
		tmp = t_4;
	} else if (y5 <= -2.2e+38) {
		tmp = t_5;
	} else if (y5 <= -5.4e-238) {
		tmp = y1 * fma(a, ((z * y3) - (x * y2)), fma(y4, t_3, (i * ((x * j) - (z * k)))));
	} else if (y5 <= 1.15e-297) {
		tmp = x * (fma(t_2, y2, (y * fma(a, b, (0.0 - (c * i))))) - (j * fma(b, y0, (i * (0.0 - y1)))));
	} else if (y5 <= 5.4e-95) {
		tmp = t_5;
	} else if (y5 <= 7.7e+62) {
		tmp = y2 * (fma(t_2, x, (k * fma(y1, y4, (y0 * (0.0 - y5))))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = fma(t, y2, Float64(0.0 - Float64(y * y3)))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(y5 * fma(i, Float64(Float64(y * k) - Float64(t * j)), fma(t_3, Float64(0.0 - y0), Float64(a * t_1))))
	t_5 = Float64(y4 * Float64(fma(b, Float64(Float64(t * j) - Float64(y * k)), Float64(y1 * t_3)) - Float64(c * t_1)))
	tmp = 0.0
	if (y5 <= -4.6e+166)
		tmp = t_4;
	elseif (y5 <= -2.2e+38)
		tmp = t_5;
	elseif (y5 <= -5.4e-238)
		tmp = Float64(y1 * fma(a, Float64(Float64(z * y3) - Float64(x * y2)), fma(y4, t_3, Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (y5 <= 1.15e-297)
		tmp = Float64(x * Float64(fma(t_2, y2, Float64(y * fma(a, b, Float64(0.0 - Float64(c * i))))) - Float64(j * fma(b, y0, Float64(i * Float64(0.0 - y1))))));
	elseif (y5 <= 5.4e-95)
		tmp = t_5;
	elseif (y5 <= 7.7e+62)
		tmp = Float64(y2 * Float64(fma(t_2, x, Float64(k * fma(y1, y4, Float64(y0 * Float64(0.0 - y5))))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * y2 + N[(0.0 - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(0.0 - y0), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -4.6e+166], t$95$4, If[LessEqual[y5, -2.2e+38], t$95$5, If[LessEqual[y5, -5.4e-238], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3 + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.15e-297], N[(x * N[(N[(t$95$2 * y2 + N[(y * N[(a * b + N[(0.0 - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(b * y0 + N[(i * N[(0.0 - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5.4e-95], t$95$5, If[LessEqual[y5, 7.7e+62], N[(y2 * N[(N[(t$95$2 * x + N[(k * N[(y1 * y4 + N[(y0 * N[(0.0 - y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -4.60000000000000015e166 or 7.7000000000000003e62 < y5

   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. Add Preprocessing

   3. Taylor expanded in y5 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

   5. Simplified 69.1%

      \[\leadsto \color{blue}{y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), \mathsf{fma}\left(k \cdot y2 - y3 \cdot j, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   if -4.60000000000000015e166 < y5 < -2.20000000000000006e38 or 1.15e-297 < y5 < 5.4e-95

   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. Add Preprocessing

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. sub-neg N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 67.9

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 67.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   if -2.20000000000000006e38 < y5 < -5.39999999999999981e-238

   1. Initial program 38.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 57.1%

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

   if -5.39999999999999981e-238 < y5 < 1.15e-297

   1. Initial program 40.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 74.0%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   if 5.4e-95 < y5 < 7.7000000000000003e62

   1. Initial program 28.8%

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

   3. Taylor expanded in y2 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 52.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \mathsf{fma}\left(y1, y4, 0 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -4.6 \cdot 10^{+166}:\\ \;\;\;\;y5 \cdot \mathsf{fma}\left(i, y \cdot k - t \cdot j, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.2 \cdot 10^{+38}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -5.4 \cdot 10^{-238}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, y \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - j \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 5.4 \cdot 10^{-95}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 7.7 \cdot 10^{+62}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(0 - y5\right)\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \mathsf{fma}\left(i, y \cdot k - t \cdot j, \mathsf{fma}\left(k \cdot y2 - j \cdot y3, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 45.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := b \cdot y4 - i \cdot y5\\ t_3 := z \cdot y3 - x \cdot y2\\ t_4 := a \cdot \mathsf{fma}\left(y1, t\_3, \mathsf{fma}\left(b, t\_1, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ t_5 := x \cdot j - z \cdot k\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+22}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-157}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, t\_3, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot t\_5\right)\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(t\_2, 0 - k, \mathsf{fma}\left(\mathsf{fma}\left(a, b, 0 - c \cdot i\right), x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-224}:\\ \;\;\;\;i \cdot \left(y1 \cdot t\_5 - \mathsf{fma}\left(c, t\_1, y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+173}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(t\_2, 0 - y, \mathsf{fma}\left(y2, \mathsf{fma}\left(y1, y4, y0 \cdot \left(0 - y5\right)\right), z \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t)))
        (t_2 (- (* b y4) (* i y5)))
        (t_3 (- (* z y3) (* x y2)))
        (t_4 (* a (fma y1 t_3 (fma b t_1 (* y5 (fma t y2 (- 0.0 (* y y3))))))))
        (t_5 (- (* x j) (* z k))))
   (if (<= a -3.6e+22)
     t_4
     (if (<= a -5.5e-157)
       (* y1 (fma a t_3 (fma y4 (- (* k y2) (* j y3)) (* i t_5))))
       (if (<= a 2.25e-281)
         (*
          y
          (fma
           t_2
           (- 0.0 k)
           (fma (fma a b (- 0.0 (* c i))) x (* y3 (- (* c y4) (* a y5))))))
         (if (<= a 1.7e-224)
           (* i (- (* y1 t_5) (fma c t_1 (* y5 (- (* t j) (* y k))))))
           (if (<= a 1.1e+173)
             (*
              k
              (fma
               t_2
               (- 0.0 y)
               (fma
                y2
                (fma y1 y4 (* y0 (- 0.0 y5)))
                (* z (fma b y0 (* i (- 0.0 y1)))))))
             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 = (x * y) - (z * t);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (z * y3) - (x * y2);
	double t_4 = a * fma(y1, t_3, fma(b, t_1, (y5 * fma(t, y2, (0.0 - (y * y3))))));
	double t_5 = (x * j) - (z * k);
	double tmp;
	if (a <= -3.6e+22) {
		tmp = t_4;
	} else if (a <= -5.5e-157) {
		tmp = y1 * fma(a, t_3, fma(y4, ((k * y2) - (j * y3)), (i * t_5)));
	} else if (a <= 2.25e-281) {
		tmp = y * fma(t_2, (0.0 - k), fma(fma(a, b, (0.0 - (c * i))), x, (y3 * ((c * y4) - (a * y5)))));
	} else if (a <= 1.7e-224) {
		tmp = i * ((y1 * t_5) - fma(c, t_1, (y5 * ((t * j) - (y * k)))));
	} else if (a <= 1.1e+173) {
		tmp = k * fma(t_2, (0.0 - y), fma(y2, fma(y1, y4, (y0 * (0.0 - y5))), (z * fma(b, y0, (i * (0.0 - y1))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	t_3 = Float64(Float64(z * y3) - Float64(x * y2))
	t_4 = Float64(a * fma(y1, t_3, fma(b, t_1, Float64(y5 * fma(t, y2, Float64(0.0 - Float64(y * y3)))))))
	t_5 = Float64(Float64(x * j) - Float64(z * k))
	tmp = 0.0
	if (a <= -3.6e+22)
		tmp = t_4;
	elseif (a <= -5.5e-157)
		tmp = Float64(y1 * fma(a, t_3, fma(y4, Float64(Float64(k * y2) - Float64(j * y3)), Float64(i * t_5))));
	elseif (a <= 2.25e-281)
		tmp = Float64(y * fma(t_2, Float64(0.0 - k), fma(fma(a, b, Float64(0.0 - Float64(c * i))), x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	elseif (a <= 1.7e-224)
		tmp = Float64(i * Float64(Float64(y1 * t_5) - fma(c, t_1, Float64(y5 * Float64(Float64(t * j) - Float64(y * k))))));
	elseif (a <= 1.1e+173)
		tmp = Float64(k * fma(t_2, Float64(0.0 - y), fma(y2, fma(y1, y4, Float64(y0 * Float64(0.0 - y5))), Float64(z * fma(b, y0, Float64(i * Float64(0.0 - y1)))))));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(y1 * t$95$3 + N[(b * t$95$1 + N[(y5 * N[(t * y2 + N[(0.0 - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+22], t$95$4, If[LessEqual[a, -5.5e-157], N[(y1 * N[(a * t$95$3 + N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] + N[(i * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-281], N[(y * N[(t$95$2 * N[(0.0 - k), $MachinePrecision] + N[(N[(a * b + N[(0.0 - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-224], N[(i * N[(N[(y1 * t$95$5), $MachinePrecision] - N[(c * t$95$1 + N[(y5 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+173], N[(k * N[(t$95$2 * N[(0.0 - y), $MachinePrecision] + N[(y2 * N[(y1 * y4 + N[(y0 * N[(0.0 - y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(b * y0 + N[(i * N[(0.0 - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.6e22 or 1.1e173 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

   5. Simplified 66.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   if -3.6e22 < a < -5.4999999999999998e-157

   1. Initial program 31.1%

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

   3. Taylor expanded in y1 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 60.4%

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

   if -5.4999999999999998e-157 < a < 2.24999999999999997e-281

   1. Initial program 23.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. neg-sub0 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{0 - k}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{0 - k}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      14. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - k, \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 56.0%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - k, \mathsf{fma}\left(\mathsf{fma}\left(a, b, 0 - c \cdot i\right), x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if 2.24999999999999997e-281 < a < 1.69999999999999996e-224

   1. Initial program 33.8%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 73.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   if 1.69999999999999996e-224 < a < 1.1e173

   1. Initial program 33.6%

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

   3. Taylor expanded in k around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. neg-mul-1 N/A

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

   5. Simplified 59.2%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - y, \mathsf{fma}\left(y2, \mathsf{fma}\left(y1, y4, 0 - y0 \cdot y5\right), z \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-157}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - k, \mathsf{fma}\left(\mathsf{fma}\left(a, b, 0 - c \cdot i\right), x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-224}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \mathsf{fma}\left(c, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+173}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - y, \mathsf{fma}\left(y2, \mathsf{fma}\left(y1, y4, y0 \cdot \left(0 - y5\right)\right), z \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 44.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := z \cdot y3 - x \cdot y2\\ t_3 := \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\\ t_4 := a \cdot \mathsf{fma}\left(y1, t\_2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot t\_3\right)\right)\\ \mathbf{if}\;a \leq -3.75 \cdot 10^{+24}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-141}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, t\_2, \mathsf{fma}\left(y4, t\_1, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq -1.36 \cdot 10^{-288}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot t\_1\right) - c \cdot t\_3\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-224}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+173}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - y, \mathsf{fma}\left(y2, \mathsf{fma}\left(y1, y4, y0 \cdot \left(0 - y5\right)\right), z \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* z y3) (* x y2)))
        (t_3 (fma t y2 (- 0.0 (* y y3))))
        (t_4 (* a (fma y1 t_2 (fma b (- (* x y) (* z t)) (* y5 t_3))))))
   (if (<= a -3.75e+24)
     t_4
     (if (<= a -5.4e-141)
       (* y1 (fma a t_2 (fma y4 t_1 (* i (- (* x j) (* z k))))))
       (if (<= a -1.36e-288)
         (* y4 (- (fma b (- (* t j) (* y k)) (* y1 t_1)) (* c t_3)))
         (if (<= a 1.65e-224)
           (* i (* t (fma c z (- 0.0 (* j y5)))))
           (if (<= a 2.15e+173)
             (*
              k
              (fma
               (- (* b y4) (* i y5))
               (- 0.0 y)
               (fma
                y2
                (fma y1 y4 (* y0 (- 0.0 y5)))
                (* z (fma b y0 (* i (- 0.0 y1)))))))
             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 = (k * y2) - (j * y3);
	double t_2 = (z * y3) - (x * y2);
	double t_3 = fma(t, y2, (0.0 - (y * y3)));
	double t_4 = a * fma(y1, t_2, fma(b, ((x * y) - (z * t)), (y5 * t_3)));
	double tmp;
	if (a <= -3.75e+24) {
		tmp = t_4;
	} else if (a <= -5.4e-141) {
		tmp = y1 * fma(a, t_2, fma(y4, t_1, (i * ((x * j) - (z * k)))));
	} else if (a <= -1.36e-288) {
		tmp = y4 * (fma(b, ((t * j) - (y * k)), (y1 * t_1)) - (c * t_3));
	} else if (a <= 1.65e-224) {
		tmp = i * (t * fma(c, z, (0.0 - (j * y5))));
	} else if (a <= 2.15e+173) {
		tmp = k * fma(((b * y4) - (i * y5)), (0.0 - y), fma(y2, fma(y1, y4, (y0 * (0.0 - y5))), (z * fma(b, y0, (i * (0.0 - y1))))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(z * y3) - Float64(x * y2))
	t_3 = fma(t, y2, Float64(0.0 - Float64(y * y3)))
	t_4 = Float64(a * fma(y1, t_2, fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * t_3))))
	tmp = 0.0
	if (a <= -3.75e+24)
		tmp = t_4;
	elseif (a <= -5.4e-141)
		tmp = Float64(y1 * fma(a, t_2, fma(y4, t_1, Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (a <= -1.36e-288)
		tmp = Float64(y4 * Float64(fma(b, Float64(Float64(t * j) - Float64(y * k)), Float64(y1 * t_1)) - Float64(c * t_3)));
	elseif (a <= 1.65e-224)
		tmp = Float64(i * Float64(t * fma(c, z, Float64(0.0 - Float64(j * y5)))));
	elseif (a <= 2.15e+173)
		tmp = Float64(k * fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(0.0 - y), fma(y2, fma(y1, y4, Float64(y0 * Float64(0.0 - y5))), Float64(z * fma(b, y0, Float64(i * Float64(0.0 - y1)))))));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * y2 + N[(0.0 - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(y1 * t$95$2 + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.75e+24], t$95$4, If[LessEqual[a, -5.4e-141], N[(y1 * N[(a * t$95$2 + N[(y4 * t$95$1 + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.36e-288], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-224], N[(i * N[(t * N[(c * z + N[(0.0 - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.15e+173], N[(k * N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(0.0 - y), $MachinePrecision] + N[(y2 * N[(y1 * y4 + N[(y0 * N[(0.0 - y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(b * y0 + N[(i * N[(0.0 - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.75000000000000007e24 or 2.15000000000000013e173 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

   5. Simplified 66.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   if -3.75000000000000007e24 < a < -5.4000000000000005e-141

   1. Initial program 31.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 62.3%

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

   if -5.4000000000000005e-141 < a < -1.36000000000000007e-288

   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. Add Preprocessing

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. sub-neg N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 57.9

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 57.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   if -1.36000000000000007e-288 < a < 1.6500000000000001e-224

   1. Initial program 25.2%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 58.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in t around -inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. +-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(c, z, -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 58.9

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-j\right)} \cdot y5\right)\right) \]

   8. Simplified 58.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \left(-j\right) \cdot y5\right)\right)} \]

   if 1.6500000000000001e-224 < a < 2.15000000000000013e173

   1. Initial program 33.6%

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

   3. Taylor expanded in k around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. neg-mul-1 N/A

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

   5. Simplified 59.2%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - y, \mathsf{fma}\left(y2, \mathsf{fma}\left(y1, y4, 0 - y0 \cdot y5\right), z \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.75 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-141}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq -1.36 \cdot 10^{-288}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-224}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+173}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - y, \mathsf{fma}\left(y2, \mathsf{fma}\left(y1, y4, y0 \cdot \left(0 - y5\right)\right), z \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 44.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := z \cdot y3 - x \cdot y2\\ t_3 := \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\\ t_4 := a \cdot \mathsf{fma}\left(y1, t\_2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot t\_3\right)\right)\\ t_5 := y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot t\_1\right) - c \cdot t\_3\right)\\ \mathbf{if}\;a \leq -9.6 \cdot 10^{+22}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-141}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, t\_2, \mathsf{fma}\left(y4, t\_1, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-258}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, y \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - j \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+173}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* z y3) (* x y2)))
        (t_3 (fma t y2 (- 0.0 (* y y3))))
        (t_4 (* a (fma y1 t_2 (fma b (- (* x y) (* z t)) (* y5 t_3)))))
        (t_5 (* y4 (- (fma b (- (* t j) (* y k)) (* y1 t_1)) (* c t_3)))))
   (if (<= a -9.6e+22)
     t_4
     (if (<= a -2.9e-141)
       (* y1 (fma a t_2 (fma y4 t_1 (* i (- (* x j) (* z k))))))
       (if (<= a 7.5e-258)
         t_5
         (if (<= a 9.5e-157)
           (*
            x
            (-
             (fma (- (* c y0) (* a y1)) y2 (* y (fma a b (- 0.0 (* c i)))))
             (* j (fma b y0 (* i (- 0.0 y1))))))
           (if (<= a 1.15e+173) t_5 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 = (k * y2) - (j * y3);
	double t_2 = (z * y3) - (x * y2);
	double t_3 = fma(t, y2, (0.0 - (y * y3)));
	double t_4 = a * fma(y1, t_2, fma(b, ((x * y) - (z * t)), (y5 * t_3)));
	double t_5 = y4 * (fma(b, ((t * j) - (y * k)), (y1 * t_1)) - (c * t_3));
	double tmp;
	if (a <= -9.6e+22) {
		tmp = t_4;
	} else if (a <= -2.9e-141) {
		tmp = y1 * fma(a, t_2, fma(y4, t_1, (i * ((x * j) - (z * k)))));
	} else if (a <= 7.5e-258) {
		tmp = t_5;
	} else if (a <= 9.5e-157) {
		tmp = x * (fma(((c * y0) - (a * y1)), y2, (y * fma(a, b, (0.0 - (c * i))))) - (j * fma(b, y0, (i * (0.0 - y1)))));
	} else if (a <= 1.15e+173) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(z * y3) - Float64(x * y2))
	t_3 = fma(t, y2, Float64(0.0 - Float64(y * y3)))
	t_4 = Float64(a * fma(y1, t_2, fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * t_3))))
	t_5 = Float64(y4 * Float64(fma(b, Float64(Float64(t * j) - Float64(y * k)), Float64(y1 * t_1)) - Float64(c * t_3)))
	tmp = 0.0
	if (a <= -9.6e+22)
		tmp = t_4;
	elseif (a <= -2.9e-141)
		tmp = Float64(y1 * fma(a, t_2, fma(y4, t_1, Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (a <= 7.5e-258)
		tmp = t_5;
	elseif (a <= 9.5e-157)
		tmp = Float64(x * Float64(fma(Float64(Float64(c * y0) - Float64(a * y1)), y2, Float64(y * fma(a, b, Float64(0.0 - Float64(c * i))))) - Float64(j * fma(b, y0, Float64(i * Float64(0.0 - y1))))));
	elseif (a <= 1.15e+173)
		tmp = t_5;
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * y2 + N[(0.0 - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(y1 * t$95$2 + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.6e+22], t$95$4, If[LessEqual[a, -2.9e-141], N[(y1 * N[(a * t$95$2 + N[(y4 * t$95$1 + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-258], t$95$5, If[LessEqual[a, 9.5e-157], N[(x * N[(N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * y2 + N[(y * N[(a * b + N[(0.0 - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(b * y0 + N[(i * N[(0.0 - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+173], t$95$5, t$95$4]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.6e22 or 1.14999999999999997e173 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

   5. Simplified 66.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   if -9.6e22 < a < -2.9e-141

   1. Initial program 31.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 62.3%

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

   if -2.9e-141 < a < 7.4999999999999998e-258 or 9.50000000000000019e-157 < a < 1.14999999999999997e173

   1. Initial program 29.1%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. sub-neg N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 51.9

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 51.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   if 7.4999999999999998e-258 < a < 9.50000000000000019e-157

   1. Initial program 36.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 65.3%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-141}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-258}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, y \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - j \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+173}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 42.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y3 - x \cdot y2\\ t_2 := a \cdot \mathsf{fma}\left(y1, t\_1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ t_3 := y1 \cdot \mathsf{fma}\left(a, t\_1, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{if}\;a \leq -2.65 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-157}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-284}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-229}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+62}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z y3) (* x y2)))
        (t_2
         (*
          a
          (fma
           y1
           t_1
           (fma b (- (* x y) (* z t)) (* y5 (fma t y2 (- 0.0 (* y y3))))))))
        (t_3
         (*
          y1
          (fma
           a
           t_1
           (fma y4 (- (* k y2) (* j y3)) (* i (- (* x j) (* z k))))))))
   (if (<= a -2.65e+22)
     t_2
     (if (<= a -5.5e-157)
       t_3
       (if (<= a -7.5e-284)
         (* i (* y (- (* k y5) (* x c))))
         (if (<= a 6.2e-229)
           (* i (* t (fma c z (- 0.0 (* j y5)))))
           (if (<= a 1.6e+62) 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 = (z * y3) - (x * y2);
	double t_2 = a * fma(y1, t_1, fma(b, ((x * y) - (z * t)), (y5 * fma(t, y2, (0.0 - (y * y3))))));
	double t_3 = y1 * fma(a, t_1, fma(y4, ((k * y2) - (j * y3)), (i * ((x * j) - (z * k)))));
	double tmp;
	if (a <= -2.65e+22) {
		tmp = t_2;
	} else if (a <= -5.5e-157) {
		tmp = t_3;
	} else if (a <= -7.5e-284) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (a <= 6.2e-229) {
		tmp = i * (t * fma(c, z, (0.0 - (j * y5))));
	} else if (a <= 1.6e+62) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * y3) - Float64(x * y2))
	t_2 = Float64(a * fma(y1, t_1, fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * fma(t, y2, Float64(0.0 - Float64(y * y3)))))))
	t_3 = Float64(y1 * fma(a, t_1, fma(y4, Float64(Float64(k * y2) - Float64(j * y3)), Float64(i * Float64(Float64(x * j) - Float64(z * k))))))
	tmp = 0.0
	if (a <= -2.65e+22)
		tmp = t_2;
	elseif (a <= -5.5e-157)
		tmp = t_3;
	elseif (a <= -7.5e-284)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (a <= 6.2e-229)
		tmp = Float64(i * Float64(t * fma(c, z, Float64(0.0 - Float64(j * y5)))));
	elseif (a <= 1.6e+62)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * t$95$1 + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(t * y2 + N[(0.0 - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y1 * N[(a * t$95$1 + N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.65e+22], t$95$2, If[LessEqual[a, -5.5e-157], t$95$3, If[LessEqual[a, -7.5e-284], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-229], N[(i * N[(t * N[(c * z + N[(0.0 - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+62], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.6499999999999999e22 or 1.59999999999999992e62 < a

   1. Initial program 32.3%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

   5. Simplified 63.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   if -2.6499999999999999e22 < a < -5.4999999999999998e-157 or 6.2000000000000002e-229 < a < 1.59999999999999992e62

   1. Initial program 33.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 49.9%

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

   if -5.4999999999999998e-157 < a < -7.4999999999999999e-284

   1. Initial program 27.5%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 42.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in y around -inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(c \cdot x\right)\right)}\right)\right) \]

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 49.3

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

   8. Simplified 49.3%

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

   if -7.4999999999999999e-284 < a < 6.2000000000000002e-229

   1. Initial program 28.4%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 57.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in t around -inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. +-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(c, z, -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 62.5

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-j\right)} \cdot y5\right)\right) \]

   8. Simplified 62.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \left(-j\right) \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-157}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-284}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-229}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+62}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, t\_1, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ t_3 := \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\\ \mathbf{if}\;y1 \leq -2.7 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -1.25 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, y \cdot t\_3\right) - j \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 5.4 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - k, \mathsf{fma}\left(t\_3, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 29000000:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot t\_1\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2
         (*
          y1
          (fma
           a
           (- (* z y3) (* x y2))
           (fma y4 t_1 (* i (- (* x j) (* z k)))))))
        (t_3 (fma a b (- 0.0 (* c i)))))
   (if (<= y1 -2.7e+146)
     t_2
     (if (<= y1 -1.25e-30)
       (*
        x
        (-
         (fma (- (* c y0) (* a y1)) y2 (* y t_3))
         (* j (fma b y0 (* i (- 0.0 y1))))))
       (if (<= y1 5.4e-205)
         (*
          y
          (fma
           (- (* b y4) (* i y5))
           (- 0.0 k)
           (fma t_3 x (* y3 (- (* c y4) (* a y5))))))
         (if (<= y1 29000000.0)
           (*
            y4
            (-
             (fma b (- (* t j) (* y k)) (* y1 t_1))
             (* c (fma t y2 (- 0.0 (* y y3))))))
           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 * fma(a, ((z * y3) - (x * y2)), fma(y4, t_1, (i * ((x * j) - (z * k)))));
	double t_3 = fma(a, b, (0.0 - (c * i)));
	double tmp;
	if (y1 <= -2.7e+146) {
		tmp = t_2;
	} else if (y1 <= -1.25e-30) {
		tmp = x * (fma(((c * y0) - (a * y1)), y2, (y * t_3)) - (j * fma(b, y0, (i * (0.0 - y1)))));
	} else if (y1 <= 5.4e-205) {
		tmp = y * fma(((b * y4) - (i * y5)), (0.0 - k), fma(t_3, x, (y3 * ((c * y4) - (a * y5)))));
	} else if (y1 <= 29000000.0) {
		tmp = y4 * (fma(b, ((t * j) - (y * k)), (y1 * t_1)) - (c * fma(t, y2, (0.0 - (y * y3)))));
	} 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(k * y2) - Float64(j * y3))
	t_2 = Float64(y1 * fma(a, Float64(Float64(z * y3) - Float64(x * y2)), fma(y4, t_1, Float64(i * Float64(Float64(x * j) - Float64(z * k))))))
	t_3 = fma(a, b, Float64(0.0 - Float64(c * i)))
	tmp = 0.0
	if (y1 <= -2.7e+146)
		tmp = t_2;
	elseif (y1 <= -1.25e-30)
		tmp = Float64(x * Float64(fma(Float64(Float64(c * y0) - Float64(a * y1)), y2, Float64(y * t_3)) - Float64(j * fma(b, y0, Float64(i * Float64(0.0 - y1))))));
	elseif (y1 <= 5.4e-205)
		tmp = Float64(y * fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(0.0 - k), fma(t_3, x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	elseif (y1 <= 29000000.0)
		tmp = Float64(y4 * Float64(fma(b, Float64(Float64(t * j) - Float64(y * k)), Float64(y1 * t_1)) - Float64(c * fma(t, y2, Float64(0.0 - Float64(y * y3))))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1 + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * b + N[(0.0 - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -2.7e+146], t$95$2, If[LessEqual[y1, -1.25e-30], N[(x * N[(N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * y2 + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(j * N[(b * y0 + N[(i * N[(0.0 - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.4e-205], N[(y * N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(0.0 - k), $MachinePrecision] + N[(t$95$3 * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 29000000.0], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y2 + N[(0.0 - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -2.69999999999999989e146 or 2.9e7 < y1

   1. Initial program 29.3%

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

   3. Taylor expanded in y1 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 64.6%

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

   if -2.69999999999999989e146 < y1 < -1.24999999999999993e-30

   1. Initial program 27.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 64.5%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   if -1.24999999999999993e-30 < y1 < 5.4000000000000002e-205

   1. Initial program 35.7%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. neg-mul-1 N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. neg-sub0 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{0 - k}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{0 - k}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      14. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - k, \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 50.7%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - k, \mathsf{fma}\left(\mathsf{fma}\left(a, b, 0 - c \cdot i\right), x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if 5.4000000000000002e-205 < y1 < 2.9e7

   1. Initial program 32.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. sub-neg N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 58.4

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.7 \cdot 10^{+146}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.25 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, y \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - j \cdot \mathsf{fma}\left(b, y0, i \cdot \left(0 - y1\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 5.4 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, 0 - k, \mathsf{fma}\left(\mathsf{fma}\left(a, b, 0 - c \cdot i\right), x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 29000000:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := z \cdot y3 - x \cdot y2\\ t_3 := \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\\ t_4 := a \cdot \mathsf{fma}\left(y1, t\_2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot t\_3\right)\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+22}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-141}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, t\_2, \mathsf{fma}\left(y4, t\_1, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+178}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot t\_1\right) - c \cdot t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* z y3) (* x y2)))
        (t_3 (fma t y2 (- 0.0 (* y y3))))
        (t_4 (* a (fma y1 t_2 (fma b (- (* x y) (* z t)) (* y5 t_3))))))
   (if (<= a -1.65e+22)
     t_4
     (if (<= a -4.7e-141)
       (* y1 (fma a t_2 (fma y4 t_1 (* i (- (* x j) (* z k))))))
       (if (<= a 1.7e+178)
         (* y4 (- (fma b (- (* t j) (* y k)) (* y1 t_1)) (* c t_3)))
         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 = (k * y2) - (j * y3);
	double t_2 = (z * y3) - (x * y2);
	double t_3 = fma(t, y2, (0.0 - (y * y3)));
	double t_4 = a * fma(y1, t_2, fma(b, ((x * y) - (z * t)), (y5 * t_3)));
	double tmp;
	if (a <= -1.65e+22) {
		tmp = t_4;
	} else if (a <= -4.7e-141) {
		tmp = y1 * fma(a, t_2, fma(y4, t_1, (i * ((x * j) - (z * k)))));
	} else if (a <= 1.7e+178) {
		tmp = y4 * (fma(b, ((t * j) - (y * k)), (y1 * t_1)) - (c * t_3));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(z * y3) - Float64(x * y2))
	t_3 = fma(t, y2, Float64(0.0 - Float64(y * y3)))
	t_4 = Float64(a * fma(y1, t_2, fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * t_3))))
	tmp = 0.0
	if (a <= -1.65e+22)
		tmp = t_4;
	elseif (a <= -4.7e-141)
		tmp = Float64(y1 * fma(a, t_2, fma(y4, t_1, Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (a <= 1.7e+178)
		tmp = Float64(y4 * Float64(fma(b, Float64(Float64(t * j) - Float64(y * k)), Float64(y1 * t_1)) - Float64(c * t_3)));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * y2 + N[(0.0 - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(y1 * t$95$2 + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e+22], t$95$4, If[LessEqual[a, -4.7e-141], N[(y1 * N[(a * t$95$2 + N[(y4 * t$95$1 + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+178], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6499999999999999e22 or 1.7000000000000001e178 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

   5. Simplified 66.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   if -1.6499999999999999e22 < a < -4.6999999999999998e-141

   1. Initial program 31.0%

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

   3. Taylor expanded in y1 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 62.3%

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

   if -4.6999999999999998e-141 < a < 1.7000000000000001e178

   1. Initial program 30.7%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. sub-neg N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 47.4

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 47.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-141}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+178}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{-282}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(0 - y5\right)\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-19}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+126}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;j \leq 10^{+256}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.35e+44)
   (* i (* j (- (* x y1) (* t y5))))
   (if (<= j -1.95e-282)
     (*
      y2
      (+
       (fma (- (* c y0) (* a y1)) x (* k (fma y1 y4 (* y0 (- 0.0 y5)))))
       (* t (- (* a y5) (* c y4)))))
     (if (<= j 1.8e-19)
       (*
        a
        (fma
         y1
         (- (* z y3) (* x y2))
         (fma b (- (* x y) (* z t)) (* y5 (fma t y2 (- 0.0 (* y y3)))))))
       (if (<= j 2.5e+126)
         (* (* z k) (- (* b y0) (* i y1)))
         (if (<= j 1e+256)
           (* j (* y4 (- (* t b) (* y1 y3))))
           (* y5 (* j (- (* y0 y3) (* t i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.35e+44) {
		tmp = i * (j * ((x * y1) - (t * y5)));
	} else if (j <= -1.95e-282) {
		tmp = y2 * (fma(((c * y0) - (a * y1)), x, (k * fma(y1, y4, (y0 * (0.0 - y5))))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 1.8e-19) {
		tmp = a * fma(y1, ((z * y3) - (x * y2)), fma(b, ((x * y) - (z * t)), (y5 * fma(t, y2, (0.0 - (y * y3))))));
	} else if (j <= 2.5e+126) {
		tmp = (z * k) * ((b * y0) - (i * y1));
	} else if (j <= 1e+256) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else {
		tmp = y5 * (j * ((y0 * y3) - (t * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.35e+44)
		tmp = Float64(i * Float64(j * Float64(Float64(x * y1) - Float64(t * y5))));
	elseif (j <= -1.95e-282)
		tmp = Float64(y2 * Float64(fma(Float64(Float64(c * y0) - Float64(a * y1)), x, Float64(k * fma(y1, y4, Float64(y0 * Float64(0.0 - y5))))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= 1.8e-19)
		tmp = Float64(a * fma(y1, Float64(Float64(z * y3) - Float64(x * y2)), fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * fma(t, y2, Float64(0.0 - Float64(y * y3)))))));
	elseif (j <= 2.5e+126)
		tmp = Float64(Float64(z * k) * Float64(Float64(b * y0) - Float64(i * y1)));
	elseif (j <= 1e+256)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = Float64(y5 * Float64(j * Float64(Float64(y0 * y3) - Float64(t * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.35e+44], N[(i * N[(j * N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.95e-282], N[(y2 * N[(N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * x + N[(k * N[(y1 * y4 + N[(y0 * N[(0.0 - y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.8e-19], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(t * y2 + N[(0.0 - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e+126], N[(N[(z * k), $MachinePrecision] * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1e+256], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(j * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.35e44

   1. Initial program 32.6%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 52.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{\left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)} \cdot \left(0 - i\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)} \cdot \left(0 - i\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \left(j \cdot \color{blue}{\left(t \cdot y5 - x \cdot y1\right)}\right) \cdot \left(0 - i\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \left(j \cdot \left(\color{blue}{t \cdot y5} - x \cdot y1\right)\right) \cdot \left(0 - i\right) \]

      4. *-lowering-*.f64 62.0

         \[\leadsto \left(j \cdot \left(t \cdot y5 - \color{blue}{x \cdot y1}\right)\right) \cdot \left(0 - i\right) \]

   8. Simplified 62.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)} \cdot \left(0 - i\right) \]

   if -1.35e44 < j < -1.95000000000000019e-282

   1. Initial program 41.6%

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

   3. Taylor expanded in y2 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 52.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \mathsf{fma}\left(y1, y4, 0 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if -1.95000000000000019e-282 < j < 1.8000000000000001e-19

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

   5. Simplified 47.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   if 1.8000000000000001e-19 < j < 2.49999999999999989e126

   1. Initial program 31.3%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 65.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - k \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right) \cdot \left(0 - z\right)} \]

   6. Taylor expanded in k around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 54.0

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

   8. Simplified 54.0%

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

   if 2.49999999999999989e126 < j < 1e256

   1. Initial program 9.6%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. sub-neg N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 65.9

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 65.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 66.2

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

   8. Simplified 66.2%

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

   if 1e256 < j

   1. Initial program 25.4%

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

   3. Taylor expanded in y5 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

   5. Simplified 67.4%

      \[\leadsto \color{blue}{y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), \mathsf{fma}\left(k \cdot y2 - y3 \cdot j, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(j \cdot \left(y0 \cdot y3 + \color{blue}{\left(\mathsf{neg}\left(i \cdot t\right)\right)}\right)\right) \]

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 83.6

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

   8. Simplified 83.6%

      \[\leadsto y5 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{-282}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \mathsf{fma}\left(y1, y4, y0 \cdot \left(0 - y5\right)\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-19}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+126}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;j \leq 10^{+256}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y5 \cdot \left(y2 \cdot \mathsf{fma}\left(a, t, k \cdot \left(0 - y0\right)\right)\right)\\ \mathbf{if}\;y5 \leq -9.8 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 1120:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 4.5 \cdot 10^{+123}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 7.6 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq 1.2 \cdot 10^{+259}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y5 (* y2 (fma a t (* k (- 0.0 y0)))))))
   (if (<= y5 -9.8e+169)
     t_1
     (if (<= y5 1120.0)
       (*
        y1
        (fma
         a
         (- (* z y3) (* x y2))
         (fma y4 (- (* k y2) (* j y3)) (* i (- (* x j) (* z k))))))
       (if (<= y5 4.5e+123)
         (* i (* t (fma c z (- 0.0 (* j y5)))))
         (if (<= y5 7.6e+163)
           (* x (* y (- (* a b) (* c i))))
           (if (<= y5 1.2e+259) t_1 (* y5 (* j (- (* y0 y3) (* t i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y5 * (y2 * fma(a, t, (k * (0.0 - y0))));
	double tmp;
	if (y5 <= -9.8e+169) {
		tmp = t_1;
	} else if (y5 <= 1120.0) {
		tmp = y1 * fma(a, ((z * y3) - (x * y2)), fma(y4, ((k * y2) - (j * y3)), (i * ((x * j) - (z * k)))));
	} else if (y5 <= 4.5e+123) {
		tmp = i * (t * fma(c, z, (0.0 - (j * y5))));
	} else if (y5 <= 7.6e+163) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y5 <= 1.2e+259) {
		tmp = t_1;
	} else {
		tmp = y5 * (j * ((y0 * y3) - (t * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y5 * Float64(y2 * fma(a, t, Float64(k * Float64(0.0 - y0)))))
	tmp = 0.0
	if (y5 <= -9.8e+169)
		tmp = t_1;
	elseif (y5 <= 1120.0)
		tmp = Float64(y1 * fma(a, Float64(Float64(z * y3) - Float64(x * y2)), fma(y4, Float64(Float64(k * y2) - Float64(j * y3)), Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (y5 <= 4.5e+123)
		tmp = Float64(i * Float64(t * fma(c, z, Float64(0.0 - Float64(j * y5)))));
	elseif (y5 <= 7.6e+163)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y5 <= 1.2e+259)
		tmp = t_1;
	else
		tmp = Float64(y5 * Float64(j * Float64(Float64(y0 * y3) - Float64(t * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y5 * N[(y2 * N[(a * t + N[(k * N[(0.0 - y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -9.8e+169], t$95$1, If[LessEqual[y5, 1120.0], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.5e+123], N[(i * N[(t * N[(c * z + N[(0.0 - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.6e+163], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.2e+259], t$95$1, N[(y5 * N[(j * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -9.80000000000000053e169 or 7.60000000000000017e163 < y5 < 1.2e259

   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. Add Preprocessing

   3. Taylor expanded in y5 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

   5. Simplified 77.9%

      \[\leadsto \color{blue}{y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), \mathsf{fma}\left(k \cdot y2 - y3 \cdot j, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(y2 \cdot \mathsf{fma}\left(a, t, \color{blue}{\mathsf{neg}\left(k \cdot y0\right)}\right)\right) \]

      5. neg-sub0 N/A

         \[\leadsto y5 \cdot \left(y2 \cdot \mathsf{fma}\left(a, t, \color{blue}{0 - k \cdot y0}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto y5 \cdot \left(y2 \cdot \mathsf{fma}\left(a, t, \color{blue}{0 - k \cdot y0}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto y5 \cdot \left(y2 \cdot \mathsf{fma}\left(a, t, 0 - \color{blue}{y0 \cdot k}\right)\right) \]

      8. *-lowering-*.f64 78.1

         \[\leadsto y5 \cdot \left(y2 \cdot \mathsf{fma}\left(a, t, 0 - \color{blue}{y0 \cdot k}\right)\right) \]

   8. Simplified 78.1%

      \[\leadsto y5 \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(a, t, 0 - y0 \cdot k\right)\right)} \]

   if -9.80000000000000053e169 < y5 < 1120

   1. Initial program 35.7%

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

   3. Taylor expanded in y1 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 48.6%

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

   if 1120 < y5 < 4.49999999999999983e123

   1. Initial program 28.9%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 51.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in t around -inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. +-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(c, z, -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 52.8

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-j\right)} \cdot y5\right)\right) \]

   8. Simplified 52.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \left(-j\right) \cdot y5\right)\right)} \]

   if 4.49999999999999983e123 < y5 < 7.60000000000000017e163

   1. Initial program 7.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 60.2%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 60.2

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

   8. Simplified 60.2%

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

   if 1.2e259 < y5

   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. Add Preprocessing

   3. Taylor expanded in y5 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), \mathsf{fma}\left(k \cdot y2 - y3 \cdot j, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(j \cdot \left(y0 \cdot y3 + \color{blue}{\left(\mathsf{neg}\left(i \cdot t\right)\right)}\right)\right) \]

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 85.9

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

   8. Simplified 85.9%

      \[\leadsto y5 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -9.8 \cdot 10^{+169}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \mathsf{fma}\left(a, t, k \cdot \left(0 - y0\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1120:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, k \cdot y2 - j \cdot y3, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 4.5 \cdot 10^{+123}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 7.6 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq 1.2 \cdot 10^{+259}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \mathsf{fma}\left(a, t, k \cdot \left(0 - y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+240}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.08 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-228}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(y \cdot y5 - z \cdot y1\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+256}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -2.4e+240)
   (* i (* t (fma c z (- 0.0 (* j y5)))))
   (if (<= j -1.08e+30)
     (* x (* j (- (* i y1) (* b y0))))
     (if (<= j 1.7e-228)
       (* i (* y (- (* k y5) (* x c))))
       (if (<= j 6.3e-142)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= j 1.95e+34)
           (* (* i k) (- (* y y5) (* z y1)))
           (if (<= j 3.2e+125)
             (* x (* y (- (* a b) (* c i))))
             (if (<= j 3.7e+256)
               (* j (* y4 (- (* t b) (* y1 y3))))
               (* y5 (* j (- (* y0 y3) (* t i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -2.4e+240) {
		tmp = i * (t * fma(c, z, (0.0 - (j * y5))));
	} else if (j <= -1.08e+30) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (j <= 1.7e-228) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (j <= 6.3e-142) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= 1.95e+34) {
		tmp = (i * k) * ((y * y5) - (z * y1));
	} else if (j <= 3.2e+125) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (j <= 3.7e+256) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else {
		tmp = y5 * (j * ((y0 * y3) - (t * i)));
	}
	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 <= -2.4e+240)
		tmp = Float64(i * Float64(t * fma(c, z, Float64(0.0 - Float64(j * y5)))));
	elseif (j <= -1.08e+30)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (j <= 1.7e-228)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (j <= 6.3e-142)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (j <= 1.95e+34)
		tmp = Float64(Float64(i * k) * Float64(Float64(y * y5) - Float64(z * y1)));
	elseif (j <= 3.2e+125)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (j <= 3.7e+256)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = Float64(y5 * Float64(j * Float64(Float64(y0 * y3) - Float64(t * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -2.4e+240], N[(i * N[(t * N[(c * z + N[(0.0 - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.08e+30], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-228], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.3e-142], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.95e+34], N[(N[(i * k), $MachinePrecision] * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e+125], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e+256], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(j * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -2.3999999999999999e240

   1. Initial program 28.6%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in t around -inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. +-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(c, z, -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 71.5

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-j\right)} \cdot y5\right)\right) \]

   8. Simplified 71.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \left(-j\right) \cdot y5\right)\right)} \]

   if -2.3999999999999999e240 < j < -1.08e30

   1. Initial program 32.4%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 45.6%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 53.5

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

   8. Simplified 53.5%

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

   if -1.08e30 < j < 1.69999999999999995e-228

   1. Initial program 38.2%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 40.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in y around -inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(c \cdot x\right)\right)}\right)\right) \]

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 38.1

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

   8. Simplified 38.1%

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

   if 1.69999999999999995e-228 < j < 6.2999999999999998e-142

   1. Initial program 47.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 74.2%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 67.1

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

   8. Simplified 67.1%

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

   if 6.2999999999999998e-142 < j < 1.9500000000000001e34

   1. Initial program 26.4%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 44.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in k around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 50.9

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

   8. Simplified 50.9%

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

   if 1.9500000000000001e34 < j < 3.19999999999999983e125

   1. Initial program 41.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 53.0%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 53.5

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

   8. Simplified 53.5%

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

   if 3.19999999999999983e125 < j < 3.70000000000000031e256

   1. Initial program 9.6%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. sub-neg N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 65.9

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 65.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 66.2

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

   8. Simplified 66.2%

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

   if 3.70000000000000031e256 < j

   1. Initial program 25.4%

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

   3. Taylor expanded in y5 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. sub-neg N/A

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

   5. Simplified 67.4%

      \[\leadsto \color{blue}{y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), \mathsf{fma}\left(k \cdot y2 - y3 \cdot j, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(j \cdot \left(y0 \cdot y3 + \color{blue}{\left(\mathsf{neg}\left(i \cdot t\right)\right)}\right)\right) \]

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 83.6

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

   8. Simplified 83.6%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+240}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.08 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-228}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(y \cdot y5 - z \cdot y1\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+256}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.8 \cdot 10^{+239}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-228}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 28000000000:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(0 - k, y, t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -6.8e+239)
   (* i (* t (fma c z (- 0.0 (* j y5)))))
   (if (<= j -4.2e+31)
     (* x (* j (- (* i y1) (* b y0))))
     (if (<= j 1.7e-228)
       (* i (* y (- (* k y5) (* x c))))
       (if (<= j 4.8e-152)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= j 28000000000.0)
           (* b (* y0 (fma k z (* j (- 0.0 x)))))
           (if (<= j 1.16e+120)
             (* x (* y (- (* a b) (* c i))))
             (* b (* y4 (fma (- 0.0 k) y (* t j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -6.8e+239) {
		tmp = i * (t * fma(c, z, (0.0 - (j * y5))));
	} else if (j <= -4.2e+31) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (j <= 1.7e-228) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (j <= 4.8e-152) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= 28000000000.0) {
		tmp = b * (y0 * fma(k, z, (j * (0.0 - x))));
	} else if (j <= 1.16e+120) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else {
		tmp = b * (y4 * fma((0.0 - k), y, (t * j)));
	}
	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 <= -6.8e+239)
		tmp = Float64(i * Float64(t * fma(c, z, Float64(0.0 - Float64(j * y5)))));
	elseif (j <= -4.2e+31)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (j <= 1.7e-228)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (j <= 4.8e-152)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (j <= 28000000000.0)
		tmp = Float64(b * Float64(y0 * fma(k, z, Float64(j * Float64(0.0 - x)))));
	elseif (j <= 1.16e+120)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	else
		tmp = Float64(b * Float64(y4 * fma(Float64(0.0 - k), y, Float64(t * j))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -6.8e+239], N[(i * N[(t * N[(c * z + N[(0.0 - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.2e+31], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-228], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.8e-152], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 28000000000.0], N[(b * N[(y0 * N[(k * z + N[(j * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.16e+120], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y4 * N[(N[(0.0 - k), $MachinePrecision] * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -6.79999999999999998e239

   1. Initial program 28.6%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in t around -inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. +-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(c, z, -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 71.5

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-j\right)} \cdot y5\right)\right) \]

   8. Simplified 71.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \left(-j\right) \cdot y5\right)\right)} \]

   if -6.79999999999999998e239 < j < -4.19999999999999958e31

   1. Initial program 32.4%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 45.6%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 53.5

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

   8. Simplified 53.5%

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

   if -4.19999999999999958e31 < j < 1.69999999999999995e-228

   1. Initial program 38.2%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. neg-mul-1 N/A

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

      5. *-lowering-*.f64 N/A

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

   5. Simplified 40.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in y around -inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(c \cdot x\right)\right)}\right)\right) \]

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 38.1

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

   8. Simplified 38.1%

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

   if 1.69999999999999995e-228 < j < 4.8e-152

   1. Initial program 50.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

   5. Simplified 72.4%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 64.7

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

   8. Simplified 64.7%

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

   if 4.8e-152 < j < 2.8e10

   1. Initial program 26.6%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-commutative N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. --lowering--.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 40.6

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

   5. Simplified 40.6%

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

   6. Taylor expanded in y0 around inf

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

      1. *-lowering-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z + \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(k, z, \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot x\right)\right) \]

      7. neg-lowering-neg.f64 44.2

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-j\right)} \cdot x\right)\right) \]

   8. Simplified 44.2%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \mathsf{fma}\left(k, z, \left(-j\right) \cdot x\right)\right)} \]

   if 2.8e10 < j < 1.16000000000000003e120

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 50.1%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\left(a \cdot b - c \cdot i\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{a \cdot b} - c \cdot i\right)\right) \]

      4. *-lowering-*.f64 55.0

         \[\leadsto x \cdot \left(y \cdot \left(a \cdot b - \color{blue}{c \cdot i}\right)\right) \]

   8. Simplified 55.0%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if 1.16000000000000003e120 < j

   1. Initial program 13.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y4 \cdot \left(\color{blue}{\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{j \cdot t - k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - \color{blue}{k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, \color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      11. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

      14. sub-neg N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\left(t \cdot y2 + \left(\mathsf{neg}\left(y \cdot y3\right)\right)\right)}\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\mathsf{fma}\left(t, y2, \mathsf{neg}\left(y \cdot y3\right)\right)}\right) \]

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 55.1

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 55.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(k \cdot y\right)\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(k \cdot y\right)\right) + j \cdot t\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{-1 \cdot \left(k \cdot y\right)} + j \cdot t\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot y} + j \cdot t\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot k, y, j \cdot t\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      10. *-lowering-*.f64 59.6

          \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, \color{blue}{j \cdot t}\right)\right) \]

   8. Simplified 59.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.8 \cdot 10^{+239}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-228}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 28000000000:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(0 - k, y, t \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+240}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-287}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 55000000000:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(0 - k, y, t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.1e+240)
   (* i (* t (fma c z (- 0.0 (* j y5)))))
   (if (<= j -8.5e+32)
     (* x (* j (- (* i y1) (* b y0))))
     (if (<= j -2.35e-287)
       (* i (* y (- (* k y5) (* x c))))
       (if (<= j 8.5e-155)
         (* x (* a (- (* y b) (* y1 y2))))
         (if (<= j 55000000000.0)
           (* b (* y0 (fma k z (* j (- 0.0 x)))))
           (if (<= j 2.3e+126)
             (* x (* y (- (* a b) (* c i))))
             (* b (* y4 (fma (- 0.0 k) y (* t j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.1e+240) {
		tmp = i * (t * fma(c, z, (0.0 - (j * y5))));
	} else if (j <= -8.5e+32) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (j <= -2.35e-287) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (j <= 8.5e-155) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (j <= 55000000000.0) {
		tmp = b * (y0 * fma(k, z, (j * (0.0 - x))));
	} else if (j <= 2.3e+126) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else {
		tmp = b * (y4 * fma((0.0 - k), y, (t * j)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.1e+240)
		tmp = Float64(i * Float64(t * fma(c, z, Float64(0.0 - Float64(j * y5)))));
	elseif (j <= -8.5e+32)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (j <= -2.35e-287)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (j <= 8.5e-155)
		tmp = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (j <= 55000000000.0)
		tmp = Float64(b * Float64(y0 * fma(k, z, Float64(j * Float64(0.0 - x)))));
	elseif (j <= 2.3e+126)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	else
		tmp = Float64(b * Float64(y4 * fma(Float64(0.0 - k), y, Float64(t * j))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.1e+240], N[(i * N[(t * N[(c * z + N[(0.0 - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e+32], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.35e-287], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e-155], N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 55000000000.0], N[(b * N[(y0 * N[(k * z + N[(j * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e+126], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y4 * N[(N[(0.0 - k), $MachinePrecision] * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.1000000000000001e240

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(c, z, -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 71.5

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-j\right)} \cdot y5\right)\right) \]

   8. Simplified 71.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \left(-j\right) \cdot y5\right)\right)} \]

   if -1.1000000000000001e240 < j < -8.4999999999999998e32

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 45.6%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{i \cdot y1} - b \cdot y0\right)\right) \]

      4. *-lowering-*.f64 53.5

         \[\leadsto x \cdot \left(j \cdot \left(i \cdot y1 - \color{blue}{b \cdot y0}\right)\right) \]

   8. Simplified 53.5%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -8.4999999999999998e32 < j < -2.3499999999999999e-287

   1. Initial program 41.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 42.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(c \cdot x\right)\right)}\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{k \cdot y5} - c \cdot x\right)\right) \]

      8. *-lowering-*.f64 42.5

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 - \color{blue}{c \cdot x}\right)\right) \]

   8. Simplified 42.5%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(k \cdot y5 - c \cdot x\right)\right)} \]

   if -2.3499999999999999e-287 < j < 8.4999999999999996e-155

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 50.6%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(y1 \cdot y2\right) + b \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(y1 \cdot y2\right) + b \cdot y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto x \cdot \left(a \cdot \color{blue}{\left(b \cdot y + -1 \cdot \left(y1 \cdot y2\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto x \cdot \left(a \cdot \left(b \cdot y + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y2\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto x \cdot \left(a \cdot \color{blue}{\left(b \cdot y - y1 \cdot y2\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(a \cdot \color{blue}{\left(b \cdot y - y1 \cdot y2\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(a \cdot \left(\color{blue}{b \cdot y} - y1 \cdot y2\right)\right) \]

      7. *-lowering-*.f64 39.5

         \[\leadsto x \cdot \left(a \cdot \left(b \cdot y - \color{blue}{y1 \cdot y2}\right)\right) \]

   8. Simplified 39.5%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(b \cdot y - y1 \cdot y2\right)\right)} \]

   if 8.4999999999999996e-155 < j < 5.5e10

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 40.6

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 40.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z + \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(k, z, \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right)} \cdot x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right) \cdot x}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot x\right)\right) \]

      7. neg-lowering-neg.f64 44.2

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-j\right)} \cdot x\right)\right) \]

   8. Simplified 44.2%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \mathsf{fma}\left(k, z, \left(-j\right) \cdot x\right)\right)} \]

   if 5.5e10 < j < 2.3000000000000001e126

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 50.1%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\left(a \cdot b - c \cdot i\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{a \cdot b} - c \cdot i\right)\right) \]

      4. *-lowering-*.f64 55.0

         \[\leadsto x \cdot \left(y \cdot \left(a \cdot b - \color{blue}{c \cdot i}\right)\right) \]

   8. Simplified 55.0%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if 2.3000000000000001e126 < j

   1. Initial program 13.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y4 \cdot \left(\color{blue}{\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{j \cdot t - k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - \color{blue}{k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, \color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      11. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

      14. sub-neg N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\left(t \cdot y2 + \left(\mathsf{neg}\left(y \cdot y3\right)\right)\right)}\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\mathsf{fma}\left(t, y2, \mathsf{neg}\left(y \cdot y3\right)\right)}\right) \]

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 55.1

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 55.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(k \cdot y\right)\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(k \cdot y\right)\right) + j \cdot t\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{-1 \cdot \left(k \cdot y\right)} + j \cdot t\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot y} + j \cdot t\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot k, y, j \cdot t\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      10. *-lowering-*.f64 59.6

          \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, \color{blue}{j \cdot t}\right)\right) \]

   8. Simplified 59.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+240}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-287}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 55000000000:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(0 - k, y, t \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.4% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ t_2 := c \cdot \left(y2 \cdot \mathsf{fma}\left(0 - t, y4, x \cdot y0\right)\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+174}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(0 - k, y, t \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{+161}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* t (- (* j y4) (* z a)))))
        (t_2 (* c (* y2 (fma (- 0.0 t) y4 (* x y0))))))
   (if (<= z -7.2e+174)
     (* b (* y0 (fma k z (* j (- 0.0 x)))))
     (if (<= z -5.5e-43)
       t_1
       (if (<= z -1.08e-157)
         (* b (* y4 (fma (- 0.0 k) y (* t j))))
         (if (<= z 1.5e-209)
           t_2
           (if (<= z 1.65e-54)
             (* a (* y5 (- (* t y2) (* y y3))))
             (if (<= z 2.02e+161) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (t * ((j * y4) - (z * a)));
	double t_2 = c * (y2 * fma((0.0 - t), y4, (x * y0)));
	double tmp;
	if (z <= -7.2e+174) {
		tmp = b * (y0 * fma(k, z, (j * (0.0 - x))));
	} else if (z <= -5.5e-43) {
		tmp = t_1;
	} else if (z <= -1.08e-157) {
		tmp = b * (y4 * fma((0.0 - k), y, (t * j)));
	} else if (z <= 1.5e-209) {
		tmp = t_2;
	} else if (z <= 1.65e-54) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (z <= 2.02e+161) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))))
	t_2 = Float64(c * Float64(y2 * fma(Float64(0.0 - t), y4, Float64(x * y0))))
	tmp = 0.0
	if (z <= -7.2e+174)
		tmp = Float64(b * Float64(y0 * fma(k, z, Float64(j * Float64(0.0 - x)))));
	elseif (z <= -5.5e-43)
		tmp = t_1;
	elseif (z <= -1.08e-157)
		tmp = Float64(b * Float64(y4 * fma(Float64(0.0 - k), y, Float64(t * j))));
	elseif (z <= 1.5e-209)
		tmp = t_2;
	elseif (z <= 1.65e-54)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (z <= 2.02e+161)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y2 * N[(N[(0.0 - t), $MachinePrecision] * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+174], N[(b * N[(y0 * N[(k * z + N[(j * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-43], t$95$1, If[LessEqual[z, -1.08e-157], N[(b * N[(y4 * N[(N[(0.0 - k), $MachinePrecision] * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-209], t$95$2, If[LessEqual[z, 1.65e-54], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.02e+161], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.2000000000000003e174

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 43.4

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z + \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(k, z, \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right)} \cdot x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right) \cdot x}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot x\right)\right) \]

      7. neg-lowering-neg.f64 60.4

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-j\right)} \cdot x\right)\right) \]

   8. Simplified 60.4%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \mathsf{fma}\left(k, z, \left(-j\right) \cdot x\right)\right)} \]

   if -7.2000000000000003e174 < z < -5.50000000000000013e-43 or 2.0200000000000001e161 < z

   1. Initial program 31.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 34.7

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 34.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 46.8

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 46.8%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   if -5.50000000000000013e-43 < z < -1.0799999999999999e-157

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y4 \cdot \left(\color{blue}{\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{j \cdot t - k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - \color{blue}{k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, \color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      11. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

      14. sub-neg N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\left(t \cdot y2 + \left(\mathsf{neg}\left(y \cdot y3\right)\right)\right)}\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\mathsf{fma}\left(t, y2, \mathsf{neg}\left(y \cdot y3\right)\right)}\right) \]

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 50.5

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 50.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(k \cdot y\right)\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(k \cdot y\right)\right) + j \cdot t\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{-1 \cdot \left(k \cdot y\right)} + j \cdot t\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot y} + j \cdot t\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot k, y, j \cdot t\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      10. *-lowering-*.f64 50.6

          \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, \color{blue}{j \cdot t}\right)\right) \]

   8. Simplified 50.6%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]

   if -1.0799999999999999e-157 < z < 1.4999999999999999e-209 or 1.64999999999999996e-54 < z < 2.0200000000000001e161

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 52.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right) \cdot \left(0 - c\right)} \]

   6. Taylor expanded in y2 around -inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot t\right) \cdot y4} + x \cdot y0\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot t, y4, x \cdot y0\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      7. *-lowering-*.f64 45.5

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, \color{blue}{x \cdot y0}\right)\right) \]

   8. Simplified 45.5%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)} \]

   if 1.4999999999999999e-209 < z < 1.64999999999999996e-54

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - z \cdot y3\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)}\right)\right)\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

      5. *-lowering-*.f64 45.4

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   8. Simplified 45.4%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+174}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(0 - k, y, t \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-209}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(0 - t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{+161}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(0 - t, y4, x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+240}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-228}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+121}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{+256}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.5e+240)
   (* i (* t (fma c z (- 0.0 (* j y5)))))
   (if (<= j -1.02e+32)
     (* x (* j (- (* i y1) (* b y0))))
     (if (<= j 1.6e-228)
       (* i (* y (- (* k y5) (* x c))))
       (if (<= j 1.4e-141)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= j 5e+121)
           (* (* z k) (- (* b y0) (* i y1)))
           (if (<= j 2.35e+256)
             (* j (* y4 (- (* t b) (* y1 y3))))
             (* y5 (* j (- (* y0 y3) (* t i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.5e+240) {
		tmp = i * (t * fma(c, z, (0.0 - (j * y5))));
	} else if (j <= -1.02e+32) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (j <= 1.6e-228) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (j <= 1.4e-141) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= 5e+121) {
		tmp = (z * k) * ((b * y0) - (i * y1));
	} else if (j <= 2.35e+256) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else {
		tmp = y5 * (j * ((y0 * y3) - (t * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.5e+240)
		tmp = Float64(i * Float64(t * fma(c, z, Float64(0.0 - Float64(j * y5)))));
	elseif (j <= -1.02e+32)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (j <= 1.6e-228)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (j <= 1.4e-141)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (j <= 5e+121)
		tmp = Float64(Float64(z * k) * Float64(Float64(b * y0) - Float64(i * y1)));
	elseif (j <= 2.35e+256)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = Float64(y5 * Float64(j * Float64(Float64(y0 * y3) - Float64(t * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.5e+240], N[(i * N[(t * N[(c * z + N[(0.0 - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.02e+32], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.6e-228], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.4e-141], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e+121], N[(N[(z * k), $MachinePrecision] * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.35e+256], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(j * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.4999999999999999e240

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(c, z, -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 71.5

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-j\right)} \cdot y5\right)\right) \]

   8. Simplified 71.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \left(-j\right) \cdot y5\right)\right)} \]

   if -1.4999999999999999e240 < j < -1.0199999999999999e32

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 45.6%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{i \cdot y1} - b \cdot y0\right)\right) \]

      4. *-lowering-*.f64 53.5

         \[\leadsto x \cdot \left(j \cdot \left(i \cdot y1 - \color{blue}{b \cdot y0}\right)\right) \]

   8. Simplified 53.5%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -1.0199999999999999e32 < j < 1.60000000000000011e-228

   1. Initial program 38.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 40.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(c \cdot x\right)\right)}\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{k \cdot y5} - c \cdot x\right)\right) \]

      8. *-lowering-*.f64 38.1

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 - \color{blue}{c \cdot x}\right)\right) \]

   8. Simplified 38.1%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(k \cdot y5 - c \cdot x\right)\right)} \]

   if 1.60000000000000011e-228 < j < 1.40000000000000006e-141

   1. Initial program 47.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(\color{blue}{c \cdot y0} - a \cdot y1\right)\right) \]

      4. *-lowering-*.f64 67.1

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - \color{blue}{a \cdot y1}\right)\right) \]

   8. Simplified 67.1%

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   if 1.40000000000000006e-141 < j < 5.00000000000000007e121

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \color{blue}{\left(-1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-1 \cdot z\right)} \]

   5. Simplified 62.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - k \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right) \cdot \left(0 - z\right)} \]

   6. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot k\right)} \cdot \left(b \cdot y0 - i \cdot y1\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot k\right)} \cdot \left(b \cdot y0 - i \cdot y1\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \left(z \cdot k\right) \cdot \color{blue}{\left(b \cdot y0 - i \cdot y1\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(z \cdot k\right) \cdot \left(\color{blue}{b \cdot y0} - i \cdot y1\right) \]

      7. *-lowering-*.f64 48.0

         \[\leadsto \left(z \cdot k\right) \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right) \]

   8. Simplified 48.0%

      \[\leadsto \color{blue}{\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

   if 5.00000000000000007e121 < j < 2.34999999999999984e256

   1. Initial program 9.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y4 \cdot \left(\color{blue}{\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{j \cdot t - k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - \color{blue}{k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, \color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      11. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

      14. sub-neg N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\left(t \cdot y2 + \left(\mathsf{neg}\left(y \cdot y3\right)\right)\right)}\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\mathsf{fma}\left(t, y2, \mathsf{neg}\left(y \cdot y3\right)\right)}\right) \]

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 65.9

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 65.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      8. *-lowering-*.f64 66.2

         \[\leadsto j \cdot \left(y4 \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 66.2%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   if 2.34999999999999984e256 < j

   1. Initial program 25.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + \left(-1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} + \left(-1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto y5 \cdot \left(\color{blue}{i \cdot \left(\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)\right)} + \left(-1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto y5 \cdot \color{blue}{\mathsf{fma}\left(i, \mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right), -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)}, -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\color{blue}{\left(j \cdot t - k \cdot y\right)}\right), -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(\color{blue}{t \cdot j} - k \cdot y\right)\right), -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(\color{blue}{t \cdot j} - k \cdot y\right)\right), -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - \color{blue}{k \cdot y}\right)\right), -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - k \cdot y\right)\right), \color{blue}{-1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), \mathsf{fma}\left(k \cdot y2 - y3 \cdot j, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y5 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y5 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y5 \cdot \left(j \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(j \cdot \left(y0 \cdot y3 + \color{blue}{\left(\mathsf{neg}\left(i \cdot t\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y5 \cdot \left(j \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto y5 \cdot \left(j \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto y5 \cdot \left(j \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto y5 \cdot \left(j \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto y5 \cdot \left(j \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \]

      9. *-lowering-*.f64 83.6

         \[\leadsto y5 \cdot \left(j \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \]

   8. Simplified 83.6%

      \[\leadsto y5 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+240}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-228}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+121}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{+256}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 31.2% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+123}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;b \leq -3.35 \cdot 10^{-205}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(0 - t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-238}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+51}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+206}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(0 - k, y, t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -9.8e+123)
   (* b (* t (- (* j y4) (* z a))))
   (if (<= b -3.35e-205)
     (* c (* y2 (fma (- 0.0 t) y4 (* x y0))))
     (if (<= b 2.9e-238)
       (* y4 (* c (- (* y y3) (* t y2))))
       (if (<= b 8e+51)
         (* i (* y (- (* k y5) (* x c))))
         (if (<= b 1.2e+206)
           (* b (* y0 (fma k z (* j (- 0.0 x)))))
           (* b (* y4 (fma (- 0.0 k) y (* t j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -9.8e+123) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (b <= -3.35e-205) {
		tmp = c * (y2 * fma((0.0 - t), y4, (x * y0)));
	} else if (b <= 2.9e-238) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 8e+51) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (b <= 1.2e+206) {
		tmp = b * (y0 * fma(k, z, (j * (0.0 - x))));
	} else {
		tmp = b * (y4 * fma((0.0 - k), y, (t * j)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -9.8e+123)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (b <= -3.35e-205)
		tmp = Float64(c * Float64(y2 * fma(Float64(0.0 - t), y4, Float64(x * y0))));
	elseif (b <= 2.9e-238)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (b <= 8e+51)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (b <= 1.2e+206)
		tmp = Float64(b * Float64(y0 * fma(k, z, Float64(j * Float64(0.0 - x)))));
	else
		tmp = Float64(b * Float64(y4 * fma(Float64(0.0 - k), y, Float64(t * j))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -9.8e+123], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.35e-205], N[(c * N[(y2 * N[(N[(0.0 - t), $MachinePrecision] * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e-238], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e+51], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e+206], N[(b * N[(y0 * N[(k * z + N[(j * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y4 * N[(N[(0.0 - k), $MachinePrecision] * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -9.79999999999999952e123

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 65.1

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 65.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 71.0

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 71.0%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   if -9.79999999999999952e123 < b < -3.35000000000000005e-205

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 41.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right) \cdot \left(0 - c\right)} \]

   6. Taylor expanded in y2 around -inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot t\right) \cdot y4} + x \cdot y0\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot t, y4, x \cdot y0\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      7. *-lowering-*.f64 43.6

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, \color{blue}{x \cdot y0}\right)\right) \]

   8. Simplified 43.6%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)} \]

   if -3.35000000000000005e-205 < b < 2.8999999999999998e-238

   1. Initial program 40.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y4 \cdot \left(\color{blue}{\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{j \cdot t - k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - \color{blue}{k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, \color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      11. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

      14. sub-neg N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\left(t \cdot y2 + \left(\mathsf{neg}\left(y \cdot y3\right)\right)\right)}\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\mathsf{fma}\left(t, y2, \mathsf{neg}\left(y \cdot y3\right)\right)}\right) \]

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 52.2

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 52.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(\color{blue}{y \cdot y3} - t \cdot y2\right)\right) \]

      4. *-lowering-*.f64 43.9

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3 - \color{blue}{t \cdot y2}\right)\right) \]

   8. Simplified 43.9%

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if 2.8999999999999998e-238 < b < 8e51

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 48.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(c \cdot x\right)\right)}\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{k \cdot y5} - c \cdot x\right)\right) \]

      8. *-lowering-*.f64 42.5

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 - \color{blue}{c \cdot x}\right)\right) \]

   8. Simplified 42.5%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(k \cdot y5 - c \cdot x\right)\right)} \]

   if 8e51 < b < 1.2e206

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 50.9

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 50.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z + \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(k, z, \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right)} \cdot x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right) \cdot x}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot x\right)\right) \]

      7. neg-lowering-neg.f64 44.6

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-j\right)} \cdot x\right)\right) \]

   8. Simplified 44.6%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \mathsf{fma}\left(k, z, \left(-j\right) \cdot x\right)\right)} \]

   if 1.2e206 < b

   1. Initial program 5.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y4 \cdot \left(\color{blue}{\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{j \cdot t - k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - \color{blue}{k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, \color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      11. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

      14. sub-neg N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\left(t \cdot y2 + \left(\mathsf{neg}\left(y \cdot y3\right)\right)\right)}\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\mathsf{fma}\left(t, y2, \mathsf{neg}\left(y \cdot y3\right)\right)}\right) \]

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 76.5

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 76.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(k \cdot y\right)\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(k \cdot y\right)\right) + j \cdot t\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{-1 \cdot \left(k \cdot y\right)} + j \cdot t\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot y} + j \cdot t\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot k, y, j \cdot t\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      10. *-lowering-*.f64 71.1

          \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, \color{blue}{j \cdot t}\right)\right) \]

   8. Simplified 71.1%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+123}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;b \leq -3.35 \cdot 10^{-205}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(0 - t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-238}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+51}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+206}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(0 - k, y, t \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.2% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \mathsf{fma}\left(0 - t, y4, x \cdot y0\right)\right)\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-161}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (fma (- 0.0 t) y4 (* x y0))))))
   (if (<= z -2.15e+43)
     (* b (* y0 (fma k z (* j (- 0.0 x)))))
     (if (<= z -5e-161)
       (* i (* y (- (* k y5) (* x c))))
       (if (<= z 2.5e-240)
         t_1
         (if (<= z 9e-34)
           (* x (* j (- (* i y1) (* b y0))))
           (if (<= z 8.2e+161) t_1 (* b (* t (- (* j y4) (* z a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * fma((0.0 - t), y4, (x * y0)));
	double tmp;
	if (z <= -2.15e+43) {
		tmp = b * (y0 * fma(k, z, (j * (0.0 - x))));
	} else if (z <= -5e-161) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (z <= 2.5e-240) {
		tmp = t_1;
	} else if (z <= 9e-34) {
		tmp = x * (j * ((i * y1) - (b * y0)));
	} else if (z <= 8.2e+161) {
		tmp = t_1;
	} else {
		tmp = b * (t * ((j * y4) - (z * a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * fma(Float64(0.0 - t), y4, Float64(x * y0))))
	tmp = 0.0
	if (z <= -2.15e+43)
		tmp = Float64(b * Float64(y0 * fma(k, z, Float64(j * Float64(0.0 - x)))));
	elseif (z <= -5e-161)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (z <= 2.5e-240)
		tmp = t_1;
	elseif (z <= 9e-34)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (z <= 8.2e+161)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(N[(0.0 - t), $MachinePrecision] * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e+43], N[(b * N[(y0 * N[(k * z + N[(j * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-161], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-240], t$95$1, If[LessEqual[z, 9e-34], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+161], t$95$1, N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.15e43

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 37.2

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 37.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z + \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(k, z, \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right)} \cdot x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right) \cdot x}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot x\right)\right) \]

      7. neg-lowering-neg.f64 45.1

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-j\right)} \cdot x\right)\right) \]

   8. Simplified 45.1%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \mathsf{fma}\left(k, z, \left(-j\right) \cdot x\right)\right)} \]

   if -2.15e43 < z < -4.9999999999999999e-161

   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. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(c \cdot x\right)\right)}\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{k \cdot y5} - c \cdot x\right)\right) \]

      8. *-lowering-*.f64 38.9

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 - \color{blue}{c \cdot x}\right)\right) \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(k \cdot y5 - c \cdot x\right)\right)} \]

   if -4.9999999999999999e-161 < z < 2.5000000000000002e-240 or 9.00000000000000085e-34 < z < 8.2000000000000002e161

   1. Initial program 29.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right) \cdot \left(0 - c\right)} \]

   6. Taylor expanded in y2 around -inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot t\right) \cdot y4} + x \cdot y0\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot t, y4, x \cdot y0\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      7. *-lowering-*.f64 49.6

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, \color{blue}{x \cdot y0}\right)\right) \]

   8. Simplified 49.6%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)} \]

   if 2.5000000000000002e-240 < z < 9.00000000000000085e-34

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 53.2%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{i \cdot y1} - b \cdot y0\right)\right) \]

      4. *-lowering-*.f64 46.7

         \[\leadsto x \cdot \left(j \cdot \left(i \cdot y1 - \color{blue}{b \cdot y0}\right)\right) \]

   8. Simplified 46.7%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 8.2000000000000002e161 < z

   1. Initial program 34.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 43.6

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 57.6

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 57.6%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-161}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-240}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(0 - t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+161}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(0 - t, y4, x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+123}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;b \leq -1.38 \cdot 10^{-198}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(0 - t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-120}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+50}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{+206}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(0 - k, y, t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -4.3e+123)
   (* b (* t (- (* j y4) (* z a))))
   (if (<= b -1.38e-198)
     (* c (* y2 (fma (- 0.0 t) y4 (* x y0))))
     (if (<= b 2.9e-120)
       (* i (* t (fma c z (- 0.0 (* j y5)))))
       (if (<= b 6.8e+50)
         (* i (* y (- (* k y5) (* x c))))
         (if (<= b 7.6e+206)
           (* b (* y0 (fma k z (* j (- 0.0 x)))))
           (* b (* y4 (fma (- 0.0 k) y (* t j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -4.3e+123) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (b <= -1.38e-198) {
		tmp = c * (y2 * fma((0.0 - t), y4, (x * y0)));
	} else if (b <= 2.9e-120) {
		tmp = i * (t * fma(c, z, (0.0 - (j * y5))));
	} else if (b <= 6.8e+50) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (b <= 7.6e+206) {
		tmp = b * (y0 * fma(k, z, (j * (0.0 - x))));
	} else {
		tmp = b * (y4 * fma((0.0 - k), y, (t * j)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -4.3e+123)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (b <= -1.38e-198)
		tmp = Float64(c * Float64(y2 * fma(Float64(0.0 - t), y4, Float64(x * y0))));
	elseif (b <= 2.9e-120)
		tmp = Float64(i * Float64(t * fma(c, z, Float64(0.0 - Float64(j * y5)))));
	elseif (b <= 6.8e+50)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (b <= 7.6e+206)
		tmp = Float64(b * Float64(y0 * fma(k, z, Float64(j * Float64(0.0 - x)))));
	else
		tmp = Float64(b * Float64(y4 * fma(Float64(0.0 - k), y, Float64(t * j))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -4.3e+123], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.38e-198], N[(c * N[(y2 * N[(N[(0.0 - t), $MachinePrecision] * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e-120], N[(i * N[(t * N[(c * z + N[(0.0 - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e+50], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.6e+206], N[(b * N[(y0 * N[(k * z + N[(j * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y4 * N[(N[(0.0 - k), $MachinePrecision] * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.29999999999999986e123

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 65.1

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 65.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 71.0

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 71.0%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   if -4.29999999999999986e123 < b < -1.3800000000000001e-198

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 40.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right) \cdot \left(0 - c\right)} \]

   6. Taylor expanded in y2 around -inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot t\right) \cdot y4} + x \cdot y0\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot t, y4, x \cdot y0\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      7. *-lowering-*.f64 42.3

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, \color{blue}{x \cdot y0}\right)\right) \]

   8. Simplified 42.3%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)} \]

   if -1.3800000000000001e-198 < b < 2.9e-120

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 43.4%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(c, z, -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 37.2

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-j\right)} \cdot y5\right)\right) \]

   8. Simplified 37.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \left(-j\right) \cdot y5\right)\right)} \]

   if 2.9e-120 < b < 6.7999999999999997e50

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 49.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(c \cdot x\right)\right)}\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{k \cdot y5} - c \cdot x\right)\right) \]

      8. *-lowering-*.f64 45.2

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 - \color{blue}{c \cdot x}\right)\right) \]

   8. Simplified 45.2%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(k \cdot y5 - c \cdot x\right)\right)} \]

   if 6.7999999999999997e50 < b < 7.5999999999999997e206

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 50.9

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 50.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z + \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(k, z, \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right)} \cdot x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right) \cdot x}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot x\right)\right) \]

      7. neg-lowering-neg.f64 44.6

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-j\right)} \cdot x\right)\right) \]

   8. Simplified 44.6%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \mathsf{fma}\left(k, z, \left(-j\right) \cdot x\right)\right)} \]

   if 7.5999999999999997e206 < b

   1. Initial program 5.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y4 \cdot \left(\color{blue}{\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{j \cdot t - k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - \color{blue}{k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, \color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      11. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

      14. sub-neg N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\left(t \cdot y2 + \left(\mathsf{neg}\left(y \cdot y3\right)\right)\right)}\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\mathsf{fma}\left(t, y2, \mathsf{neg}\left(y \cdot y3\right)\right)}\right) \]

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 76.5

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 76.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(k \cdot y\right)\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(k \cdot y\right)\right) + j \cdot t\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{-1 \cdot \left(k \cdot y\right)} + j \cdot t\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot y} + j \cdot t\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot k, y, j \cdot t\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      10. *-lowering-*.f64 71.1

          \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, \color{blue}{j \cdot t}\right)\right) \]

   8. Simplified 71.1%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+123}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;b \leq -1.38 \cdot 10^{-198}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(0 - t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-120}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+50}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{+206}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(0 - k, y, t \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 32.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.6 \cdot 10^{+42}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-228}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{+129}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+256}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -4.6e+42)
   (* i (* j (- (* x y1) (* t y5))))
   (if (<= j 1.7e-228)
     (* i (* y (- (* k y5) (* x c))))
     (if (<= j 1.65e-141)
       (* x (* y2 (- (* c y0) (* a y1))))
       (if (<= j 2.15e+129)
         (* (* z k) (- (* b y0) (* i y1)))
         (if (<= j 1.48e+256)
           (* j (* y4 (- (* t b) (* y1 y3))))
           (* y5 (* j (- (* y0 y3) (* t i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -4.6e+42) {
		tmp = i * (j * ((x * y1) - (t * y5)));
	} else if (j <= 1.7e-228) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (j <= 1.65e-141) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= 2.15e+129) {
		tmp = (z * k) * ((b * y0) - (i * y1));
	} else if (j <= 1.48e+256) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else {
		tmp = y5 * (j * ((y0 * y3) - (t * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-4.6d+42)) then
        tmp = i * (j * ((x * y1) - (t * y5)))
    else if (j <= 1.7d-228) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (j <= 1.65d-141) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (j <= 2.15d+129) then
        tmp = (z * k) * ((b * y0) - (i * y1))
    else if (j <= 1.48d+256) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else
        tmp = y5 * (j * ((y0 * y3) - (t * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -4.6e+42) {
		tmp = i * (j * ((x * y1) - (t * y5)));
	} else if (j <= 1.7e-228) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (j <= 1.65e-141) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (j <= 2.15e+129) {
		tmp = (z * k) * ((b * y0) - (i * y1));
	} else if (j <= 1.48e+256) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else {
		tmp = y5 * (j * ((y0 * y3) - (t * i)));
	}
	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 <= -4.6e+42:
		tmp = i * (j * ((x * y1) - (t * y5)))
	elif j <= 1.7e-228:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif j <= 1.65e-141:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif j <= 2.15e+129:
		tmp = (z * k) * ((b * y0) - (i * y1))
	elif j <= 1.48e+256:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	else:
		tmp = y5 * (j * ((y0 * y3) - (t * i)))
	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 <= -4.6e+42)
		tmp = Float64(i * Float64(j * Float64(Float64(x * y1) - Float64(t * y5))));
	elseif (j <= 1.7e-228)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (j <= 1.65e-141)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (j <= 2.15e+129)
		tmp = Float64(Float64(z * k) * Float64(Float64(b * y0) - Float64(i * y1)));
	elseif (j <= 1.48e+256)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = Float64(y5 * Float64(j * Float64(Float64(y0 * y3) - Float64(t * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -4.6e+42)
		tmp = i * (j * ((x * y1) - (t * y5)));
	elseif (j <= 1.7e-228)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (j <= 1.65e-141)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (j <= 2.15e+129)
		tmp = (z * k) * ((b * y0) - (i * y1));
	elseif (j <= 1.48e+256)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	else
		tmp = y5 * (j * ((y0 * y3) - (t * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -4.6e+42], N[(i * N[(j * N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-228], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.65e-141], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.15e+129], N[(N[(z * k), $MachinePrecision] * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e+256], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(j * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -4.6e42

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 52.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{\left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)} \cdot \left(0 - i\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)} \cdot \left(0 - i\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \left(j \cdot \color{blue}{\left(t \cdot y5 - x \cdot y1\right)}\right) \cdot \left(0 - i\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \left(j \cdot \left(\color{blue}{t \cdot y5} - x \cdot y1\right)\right) \cdot \left(0 - i\right) \]

      4. *-lowering-*.f64 62.0

         \[\leadsto \left(j \cdot \left(t \cdot y5 - \color{blue}{x \cdot y1}\right)\right) \cdot \left(0 - i\right) \]

   8. Simplified 62.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)} \cdot \left(0 - i\right) \]

   if -4.6e42 < j < 1.69999999999999995e-228

   1. Initial program 37.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 41.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(c \cdot x\right)\right)}\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{k \cdot y5} - c \cdot x\right)\right) \]

      8. *-lowering-*.f64 37.3

         \[\leadsto i \cdot \left(y \cdot \left(k \cdot y5 - \color{blue}{c \cdot x}\right)\right) \]

   8. Simplified 37.3%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(k \cdot y5 - c \cdot x\right)\right)} \]

   if 1.69999999999999995e-228 < j < 1.65e-141

   1. Initial program 47.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(\color{blue}{c \cdot y0} - a \cdot y1\right)\right) \]

      4. *-lowering-*.f64 67.1

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - \color{blue}{a \cdot y1}\right)\right) \]

   8. Simplified 67.1%

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   if 1.65e-141 < j < 2.1500000000000001e129

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \color{blue}{\left(-1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-1 \cdot z\right)} \]

   5. Simplified 62.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - k \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right) \cdot \left(0 - z\right)} \]

   6. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot k\right)} \cdot \left(b \cdot y0 - i \cdot y1\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot k\right)} \cdot \left(b \cdot y0 - i \cdot y1\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \left(z \cdot k\right) \cdot \color{blue}{\left(b \cdot y0 - i \cdot y1\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(z \cdot k\right) \cdot \left(\color{blue}{b \cdot y0} - i \cdot y1\right) \]

      7. *-lowering-*.f64 48.0

         \[\leadsto \left(z \cdot k\right) \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right) \]

   8. Simplified 48.0%

      \[\leadsto \color{blue}{\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

   if 2.1500000000000001e129 < j < 1.47999999999999996e256

   1. Initial program 9.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y4 \cdot \left(\color{blue}{\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{j \cdot t - k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. *-commutative N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, \color{blue}{t \cdot j} - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - \color{blue}{k \cdot y}, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, \color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      11. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

      14. sub-neg N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\left(t \cdot y2 + \left(\mathsf{neg}\left(y \cdot y3\right)\right)\right)}\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \color{blue}{\mathsf{fma}\left(t, y2, \mathsf{neg}\left(y \cdot y3\right)\right)}\right) \]

      16. neg-sub0 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, \color{blue}{0 - y \cdot y3}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

      19. *-lowering-*.f64 65.9

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - \color{blue}{y3 \cdot y}\right)\right) \]

   5. Simplified 65.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \left(b \cdot t + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t - y1 \cdot y3\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

      8. *-lowering-*.f64 66.2

         \[\leadsto j \cdot \left(y4 \cdot \left(b \cdot t - \color{blue}{y1 \cdot y3}\right)\right) \]

   8. Simplified 66.2%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   if 1.47999999999999996e256 < j

   1. Initial program 25.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + \left(-1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} + \left(-1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto y5 \cdot \left(\color{blue}{i \cdot \left(\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)\right)} + \left(-1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto y5 \cdot \color{blue}{\mathsf{fma}\left(i, \mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right), -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)}, -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\color{blue}{\left(j \cdot t - k \cdot y\right)}\right), -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(\color{blue}{t \cdot j} - k \cdot y\right)\right), -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(\color{blue}{t \cdot j} - k \cdot y\right)\right), -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - \color{blue}{k \cdot y}\right)\right), -1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - k \cdot y\right)\right), \color{blue}{-1 \cdot \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), \mathsf{fma}\left(k \cdot y2 - y3 \cdot j, 0 - y0, a \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto y5 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y5 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y5 \cdot \left(j \cdot \color{blue}{\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(j \cdot \left(y0 \cdot y3 + \color{blue}{\left(\mathsf{neg}\left(i \cdot t\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y5 \cdot \left(j \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto y5 \cdot \left(j \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto y5 \cdot \left(j \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto y5 \cdot \left(j \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto y5 \cdot \left(j \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \]

      9. *-lowering-*.f64 83.6

         \[\leadsto y5 \cdot \left(j \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \]

   8. Simplified 83.6%

      \[\leadsto y5 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.6 \cdot 10^{+42}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-228}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{+129}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+256}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 33.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -3.2 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 8.5 \cdot 10^{-173}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 5.3 \cdot 10^{-8}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;y5 \leq 9.8 \cdot 10^{+116}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= y5 -3.2e+94)
     t_1
     (if (<= y5 8.5e-173)
       (* b (* y0 (fma k z (* j (- 0.0 x)))))
       (if (<= y5 5.3e-8)
         (* b (* t (- (* j y4) (* z a))))
         (if (<= y5 9.8e+116) (* i (* t (fma c z (- 0.0 (* j y5))))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y5 <= -3.2e+94) {
		tmp = t_1;
	} else if (y5 <= 8.5e-173) {
		tmp = b * (y0 * fma(k, z, (j * (0.0 - x))));
	} else if (y5 <= 5.3e-8) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (y5 <= 9.8e+116) {
		tmp = i * (t * fma(c, z, (0.0 - (j * y5))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (y5 <= -3.2e+94)
		tmp = t_1;
	elseif (y5 <= 8.5e-173)
		tmp = Float64(b * Float64(y0 * fma(k, z, Float64(j * Float64(0.0 - x)))));
	elseif (y5 <= 5.3e-8)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (y5 <= 9.8e+116)
		tmp = Float64(i * Float64(t * fma(c, z, Float64(0.0 - Float64(j * y5)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3.2e+94], t$95$1, If[LessEqual[y5, 8.5e-173], N[(b * N[(y0 * N[(k * z + N[(j * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5.3e-8], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9.8e+116], N[(i * N[(t * N[(c * z + N[(0.0 - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -3.20000000000000014e94 or 9.7999999999999996e116 < y5

   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. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - z \cdot y3\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)}\right)\right)\right) \]

   5. Simplified 52.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

      5. *-lowering-*.f64 51.3

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   8. Simplified 51.3%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if -3.20000000000000014e94 < y5 < 8.4999999999999996e-173

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 37.4

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 37.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z + \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(k, z, \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right)} \cdot x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right) \cdot x}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot x\right)\right) \]

      7. neg-lowering-neg.f64 38.7

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-j\right)} \cdot x\right)\right) \]

   8. Simplified 38.7%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \mathsf{fma}\left(k, z, \left(-j\right) \cdot x\right)\right)} \]

   if 8.4999999999999996e-173 < y5 < 5.2999999999999998e-8

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 45.6

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 51.2

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 51.2%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   if 5.2999999999999998e-8 < y5 < 9.7999999999999996e116

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 47.4%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(c, z, -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-1 \cdot j\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 51.3

         \[\leadsto i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \color{blue}{\left(-j\right)} \cdot y5\right)\right) \]

   8. Simplified 51.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \mathsf{fma}\left(c, z, \left(-j\right) \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.2 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 8.5 \cdot 10^{-173}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 5.3 \cdot 10^{-8}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;y5 \leq 9.8 \cdot 10^{+116}:\\ \;\;\;\;i \cdot \left(t \cdot \mathsf{fma}\left(c, z, 0 - j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 25.2% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{if}\;j \leq -1.4 \cdot 10^{+240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.78 \cdot 10^{+112}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+118}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(0 - y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* t (* j y4)))))
   (if (<= j -1.4e+240)
     t_1
     (if (<= j -1.78e+112)
       (* i (* j (* x y1)))
       (if (<= j 1.35e-223)
         (* a (* y5 (- (* t y2) (* y y3))))
         (if (<= j 6.8e+118) (* (* i k) (* z (- 0.0 y1))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (t * (j * y4));
	double tmp;
	if (j <= -1.4e+240) {
		tmp = t_1;
	} else if (j <= -1.78e+112) {
		tmp = i * (j * (x * y1));
	} else if (j <= 1.35e-223) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 6.8e+118) {
		tmp = (i * k) * (z * (0.0 - y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * (j * y4))
    if (j <= (-1.4d+240)) then
        tmp = t_1
    else if (j <= (-1.78d+112)) then
        tmp = i * (j * (x * y1))
    else if (j <= 1.35d-223) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (j <= 6.8d+118) then
        tmp = (i * k) * (z * (0.0d0 - y1))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (t * (j * y4));
	double tmp;
	if (j <= -1.4e+240) {
		tmp = t_1;
	} else if (j <= -1.78e+112) {
		tmp = i * (j * (x * y1));
	} else if (j <= 1.35e-223) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 6.8e+118) {
		tmp = (i * k) * (z * (0.0 - y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (t * (j * y4))
	tmp = 0
	if j <= -1.4e+240:
		tmp = t_1
	elif j <= -1.78e+112:
		tmp = i * (j * (x * y1))
	elif j <= 1.35e-223:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif j <= 6.8e+118:
		tmp = (i * k) * (z * (0.0 - y1))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(t * Float64(j * y4)))
	tmp = 0.0
	if (j <= -1.4e+240)
		tmp = t_1;
	elseif (j <= -1.78e+112)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (j <= 1.35e-223)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (j <= 6.8e+118)
		tmp = Float64(Float64(i * k) * Float64(z * Float64(0.0 - y1)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (t * (j * y4));
	tmp = 0.0;
	if (j <= -1.4e+240)
		tmp = t_1;
	elseif (j <= -1.78e+112)
		tmp = i * (j * (x * y1));
	elseif (j <= 1.35e-223)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (j <= 6.8e+118)
		tmp = (i * k) * (z * (0.0 - y1));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.4e+240], t$95$1, If[LessEqual[j, -1.78e+112], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.35e-223], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.8e+118], N[(N[(i * k), $MachinePrecision] * N[(z * N[(0.0 - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.4000000000000001e240 or 6.79999999999999973e118 < j

   1. Initial program 17.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 43.5

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 49.2

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 49.2%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 52.5

          \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]

   11. Simplified 52.5%

       \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]

   if -1.4000000000000001e240 < j < -1.78e112

   1. Initial program 42.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 50.5%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{i \cdot y1} - b \cdot y0\right)\right) \]

      4. *-lowering-*.f64 58.2

         \[\leadsto x \cdot \left(j \cdot \left(i \cdot y1 - \color{blue}{b \cdot y0}\right)\right) \]

   8. Simplified 58.2%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

       4. *-lowering-*.f64 54.6

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   11. Simplified 54.6%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -1.78e112 < j < 1.34999999999999994e-223

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - z \cdot y3\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)}\right)\right)\right) \]

   5. Simplified 42.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

      5. *-lowering-*.f64 33.4

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   8. Simplified 33.4%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if 1.34999999999999994e-223 < j < 6.79999999999999973e118

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 42.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right)} \cdot \left(y \cdot y5 - y1 \cdot z\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \left(i \cdot k\right) \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right) \]

      6. *-lowering-*.f64 39.5

         \[\leadsto \left(i \cdot k\right) \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right) \]

   8. Simplified 39.5%

      \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(i \cdot k\right) \cdot \left(y1 \cdot z\right)}\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(\mathsf{neg}\left(y1 \cdot z\right)\right)} \]

       4. mul-1-neg N/A

          \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot z\right)\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(-1 \cdot \left(y1 \cdot z\right)\right)} \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(i \cdot k\right)} \cdot \left(-1 \cdot \left(y1 \cdot z\right)\right) \]

       7. mul-1-neg N/A

          \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)} \]

       8. neg-sub0 N/A

          \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(0 - y1 \cdot z\right)} \]

       9. --lowering--.f64 N/A

          \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(0 - y1 \cdot z\right)} \]

       10. *-commutative N/A

           \[\leadsto \left(i \cdot k\right) \cdot \left(0 - \color{blue}{z \cdot y1}\right) \]

       11. *-lowering-*.f64 33.5

           \[\leadsto \left(i \cdot k\right) \cdot \left(0 - \color{blue}{z \cdot y1}\right) \]

   11. Simplified 33.5%

       \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(0 - z \cdot y1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+240}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.78 \cdot 10^{+112}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+118}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(0 - y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.8% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -9 \cdot 10^{+25}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -9.4 \cdot 10^{-291}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq 5.8 \cdot 10^{-204}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(y \cdot y5\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(0 - y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -9e+25)
   (* i (* j (* x y1)))
   (if (<= y1 -9.4e-291)
     (* y0 (* b (* z k)))
     (if (<= y1 5.8e-204)
       (* (* i k) (* y y5))
       (if (<= y1 1.15e+18)
         (* b (* t (* j y4)))
         (* (* i k) (* z (- 0.0 y1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -9e+25) {
		tmp = i * (j * (x * y1));
	} else if (y1 <= -9.4e-291) {
		tmp = y0 * (b * (z * k));
	} else if (y1 <= 5.8e-204) {
		tmp = (i * k) * (y * y5);
	} else if (y1 <= 1.15e+18) {
		tmp = b * (t * (j * y4));
	} else {
		tmp = (i * k) * (z * (0.0 - y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-9d+25)) then
        tmp = i * (j * (x * y1))
    else if (y1 <= (-9.4d-291)) then
        tmp = y0 * (b * (z * k))
    else if (y1 <= 5.8d-204) then
        tmp = (i * k) * (y * y5)
    else if (y1 <= 1.15d+18) then
        tmp = b * (t * (j * y4))
    else
        tmp = (i * k) * (z * (0.0d0 - y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -9e+25) {
		tmp = i * (j * (x * y1));
	} else if (y1 <= -9.4e-291) {
		tmp = y0 * (b * (z * k));
	} else if (y1 <= 5.8e-204) {
		tmp = (i * k) * (y * y5);
	} else if (y1 <= 1.15e+18) {
		tmp = b * (t * (j * y4));
	} else {
		tmp = (i * k) * (z * (0.0 - y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -9e+25:
		tmp = i * (j * (x * y1))
	elif y1 <= -9.4e-291:
		tmp = y0 * (b * (z * k))
	elif y1 <= 5.8e-204:
		tmp = (i * k) * (y * y5)
	elif y1 <= 1.15e+18:
		tmp = b * (t * (j * y4))
	else:
		tmp = (i * k) * (z * (0.0 - y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -9e+25)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y1 <= -9.4e-291)
		tmp = Float64(y0 * Float64(b * Float64(z * k)));
	elseif (y1 <= 5.8e-204)
		tmp = Float64(Float64(i * k) * Float64(y * y5));
	elseif (y1 <= 1.15e+18)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	else
		tmp = Float64(Float64(i * k) * Float64(z * Float64(0.0 - y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -9e+25)
		tmp = i * (j * (x * y1));
	elseif (y1 <= -9.4e-291)
		tmp = y0 * (b * (z * k));
	elseif (y1 <= 5.8e-204)
		tmp = (i * k) * (y * y5);
	elseif (y1 <= 1.15e+18)
		tmp = b * (t * (j * y4));
	else
		tmp = (i * k) * (z * (0.0 - y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -9e+25], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -9.4e-291], N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.8e-204], N[(N[(i * k), $MachinePrecision] * N[(y * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.15e+18], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * k), $MachinePrecision] * N[(z * N[(0.0 - y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -9.0000000000000006e25

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 48.2%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{i \cdot y1} - b \cdot y0\right)\right) \]

      4. *-lowering-*.f64 40.9

         \[\leadsto x \cdot \left(j \cdot \left(i \cdot y1 - \color{blue}{b \cdot y0}\right)\right) \]

   8. Simplified 40.9%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

       4. *-lowering-*.f64 43.9

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   11. Simplified 43.9%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -9.0000000000000006e25 < y1 < -9.3999999999999997e-291

   1. Initial program 34.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \color{blue}{\left(-1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-1 \cdot z\right)} \]

   5. Simplified 46.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - k \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right) \cdot \left(0 - z\right)} \]

   6. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot k\right)} \cdot \left(b \cdot y0 - i \cdot y1\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot k\right)} \cdot \left(b \cdot y0 - i \cdot y1\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \left(z \cdot k\right) \cdot \color{blue}{\left(b \cdot y0 - i \cdot y1\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(z \cdot k\right) \cdot \left(\color{blue}{b \cdot y0} - i \cdot y1\right) \]

      7. *-lowering-*.f64 32.2

         \[\leadsto \left(z \cdot k\right) \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right) \]

   8. Simplified 32.2%

      \[\leadsto \color{blue}{\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right) \cdot b} \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\left(k \cdot y0\right) \cdot z\right)} \cdot b \]

       3. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y0 \cdot k\right)} \cdot z\right) \cdot b \]

       4. associate-*l* N/A

          \[\leadsto \color{blue}{\left(y0 \cdot \left(k \cdot z\right)\right)} \cdot b \]

       5. associate-*r* N/A

          \[\leadsto \color{blue}{y0 \cdot \left(\left(k \cdot z\right) \cdot b\right)} \]

       6. *-commutative N/A

          \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)} \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{y0 \cdot \left(b \cdot \left(k \cdot z\right)\right)} \]

       8. *-lowering-*.f64 N/A

          \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)} \]

       9. *-lowering-*.f64 29.2

          \[\leadsto y0 \cdot \left(b \cdot \color{blue}{\left(k \cdot z\right)}\right) \]

   11. Simplified 29.2%

       \[\leadsto \color{blue}{y0 \cdot \left(b \cdot \left(k \cdot z\right)\right)} \]

   if -9.3999999999999997e-291 < y1 < 5.80000000000000018e-204

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 42.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right)} \cdot \left(y \cdot y5 - y1 \cdot z\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \left(i \cdot k\right) \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right) \]

      6. *-lowering-*.f64 39.2

         \[\leadsto \left(i \cdot k\right) \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right) \]

   8. Simplified 39.2%

      \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(y \cdot y5\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 39.2

          \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(y \cdot y5\right)} \]

   11. Simplified 39.2%

       \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(y \cdot y5\right)} \]

   if 5.80000000000000018e-204 < y1 < 1.15e18

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 40.9

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 40.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 41.4

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 41.4%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 38.9

          \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]

   11. Simplified 38.9%

       \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]

   if 1.15e18 < y1

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 39.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right)} \cdot \left(y \cdot y5 - y1 \cdot z\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \left(i \cdot k\right) \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right) \]

      6. *-lowering-*.f64 40.2

         \[\leadsto \left(i \cdot k\right) \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right) \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(i \cdot k\right) \cdot \left(y1 \cdot z\right)}\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(\mathsf{neg}\left(y1 \cdot z\right)\right)} \]

       4. mul-1-neg N/A

          \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot z\right)\right)} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(-1 \cdot \left(y1 \cdot z\right)\right)} \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(i \cdot k\right)} \cdot \left(-1 \cdot \left(y1 \cdot z\right)\right) \]

       7. mul-1-neg N/A

          \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)} \]

       8. neg-sub0 N/A

          \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(0 - y1 \cdot z\right)} \]

       9. --lowering--.f64 N/A

          \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(0 - y1 \cdot z\right)} \]

       10. *-commutative N/A

           \[\leadsto \left(i \cdot k\right) \cdot \left(0 - \color{blue}{z \cdot y1}\right) \]

       11. *-lowering-*.f64 36.2

           \[\leadsto \left(i \cdot k\right) \cdot \left(0 - \color{blue}{z \cdot y1}\right) \]

   11. Simplified 36.2%

       \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(0 - z \cdot y1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -9 \cdot 10^{+25}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -9.4 \cdot 10^{-291}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq 5.8 \cdot 10^{-204}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(y \cdot y5\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(0 - y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 33.2% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -1.04 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 2.05 \cdot 10^{-172}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= y5 -1.04e+95)
     t_1
     (if (<= y5 2.05e-172)
       (* b (* y0 (fma k z (* j (- 0.0 x)))))
       (if (<= y5 1.4e+175) (* b (* t (- (* j y4) (* z a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y5 <= -1.04e+95) {
		tmp = t_1;
	} else if (y5 <= 2.05e-172) {
		tmp = b * (y0 * fma(k, z, (j * (0.0 - x))));
	} else if (y5 <= 1.4e+175) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (y5 <= -1.04e+95)
		tmp = t_1;
	elseif (y5 <= 2.05e-172)
		tmp = Float64(b * Float64(y0 * fma(k, z, Float64(j * Float64(0.0 - x)))));
	elseif (y5 <= 1.4e+175)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.04e+95], t$95$1, If[LessEqual[y5, 2.05e-172], N[(b * N[(y0 * N[(k * z + N[(j * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.4e+175], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -1.04e95 or 1.4000000000000001e175 < y5

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - z \cdot y3\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)}\right)\right)\right) \]

   5. Simplified 54.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

      5. *-lowering-*.f64 56.1

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   8. Simplified 56.1%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if -1.04e95 < y5 < 2.05e-172

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 37.4

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 37.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z + \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(k, z, \left(\mathsf{neg}\left(j\right)\right) \cdot x\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right)} \cdot x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-1 \cdot j\right) \cdot x}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \cdot x\right)\right) \]

      7. neg-lowering-neg.f64 38.7

         \[\leadsto b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, \color{blue}{\left(-j\right)} \cdot x\right)\right) \]

   8. Simplified 38.7%

      \[\leadsto b \cdot \color{blue}{\left(y0 \cdot \mathsf{fma}\left(k, z, \left(-j\right) \cdot x\right)\right)} \]

   if 2.05e-172 < y5 < 1.4000000000000001e175

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 36.5

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 36.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 39.4

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 39.4%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.04 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 2.05 \cdot 10^{-172}:\\ \;\;\;\;b \cdot \left(y0 \cdot \mathsf{fma}\left(k, z, j \cdot \left(0 - x\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 32.6% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -8 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 1.56 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= y5 -8e+95)
     t_1
     (if (<= y5 1.56e+175) (* b (* t (- (* j y4) (* z a)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y5 <= -8e+95) {
		tmp = t_1;
	} else if (y5 <= 1.56e+175) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    if (y5 <= (-8d+95)) then
        tmp = t_1
    else if (y5 <= 1.56d+175) then
        tmp = b * (t * ((j * y4) - (z * a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y5 <= -8e+95) {
		tmp = t_1;
	} else if (y5 <= 1.56e+175) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if y5 <= -8e+95:
		tmp = t_1
	elif y5 <= 1.56e+175:
		tmp = b * (t * ((j * y4) - (z * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (y5 <= -8e+95)
		tmp = t_1;
	elseif (y5 <= 1.56e+175)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (y5 <= -8e+95)
		tmp = t_1;
	elseif (y5 <= 1.56e+175)
		tmp = b * (t * ((j * y4) - (z * a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -8e+95], t$95$1, If[LessEqual[y5, 1.56e+175], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y5 < -8.00000000000000016e95 or 1.55999999999999992e175 < y5

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{x \cdot y2} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - z \cdot y3\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)}\right)\right)\right) \]

   5. Simplified 54.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(x \cdot y2 - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \mathsf{fma}\left(t, y2, 0 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

      5. *-lowering-*.f64 56.1

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   8. Simplified 56.1%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if -8.00000000000000016e95 < y5 < 1.55999999999999992e175

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 37.0

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 37.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 33.8

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 33.8%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -8 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 1.56 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 22.0% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{if}\;j \leq -1.22 \cdot 10^{+240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+105}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* t (* j y4)))))
   (if (<= j -1.22e+240)
     t_1
     (if (<= j -6.6e+18)
       (* i (* j (* x y1)))
       (if (<= j 4e+105) (* y0 (* b (* z k))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (t * (j * y4));
	double tmp;
	if (j <= -1.22e+240) {
		tmp = t_1;
	} else if (j <= -6.6e+18) {
		tmp = i * (j * (x * y1));
	} else if (j <= 4e+105) {
		tmp = y0 * (b * (z * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * (j * y4))
    if (j <= (-1.22d+240)) then
        tmp = t_1
    else if (j <= (-6.6d+18)) then
        tmp = i * (j * (x * y1))
    else if (j <= 4d+105) then
        tmp = y0 * (b * (z * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (t * (j * y4));
	double tmp;
	if (j <= -1.22e+240) {
		tmp = t_1;
	} else if (j <= -6.6e+18) {
		tmp = i * (j * (x * y1));
	} else if (j <= 4e+105) {
		tmp = y0 * (b * (z * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (t * (j * y4))
	tmp = 0
	if j <= -1.22e+240:
		tmp = t_1
	elif j <= -6.6e+18:
		tmp = i * (j * (x * y1))
	elif j <= 4e+105:
		tmp = y0 * (b * (z * k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(t * Float64(j * y4)))
	tmp = 0.0
	if (j <= -1.22e+240)
		tmp = t_1;
	elseif (j <= -6.6e+18)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (j <= 4e+105)
		tmp = Float64(y0 * Float64(b * Float64(z * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (t * (j * y4));
	tmp = 0.0;
	if (j <= -1.22e+240)
		tmp = t_1;
	elseif (j <= -6.6e+18)
		tmp = i * (j * (x * y1));
	elseif (j <= 4e+105)
		tmp = y0 * (b * (z * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.22e+240], t$95$1, If[LessEqual[j, -6.6e+18], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e+105], N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.2200000000000001e240 or 3.9999999999999998e105 < j

   1. Initial program 16.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 42.0

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 49.2

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 49.2%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 52.4

          \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]

   11. Simplified 52.4%

       \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]

   if -1.2200000000000001e240 < j < -6.6e18

   1. Initial program 30.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{i \cdot y1} - b \cdot y0\right)\right) \]

      4. *-lowering-*.f64 51.0

         \[\leadsto x \cdot \left(j \cdot \left(i \cdot y1 - \color{blue}{b \cdot y0}\right)\right) \]

   8. Simplified 51.0%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

       4. *-lowering-*.f64 41.5

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   11. Simplified 41.5%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -6.6e18 < j < 3.9999999999999998e105

   1. Initial program 37.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \color{blue}{\left(-1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-1 \cdot z\right)} \]

   5. Simplified 46.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \mathsf{fma}\left(a, b, 0 - c \cdot i\right)\right) - k \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right) \cdot \left(0 - z\right)} \]

   6. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot k\right)} \cdot \left(b \cdot y0 - i \cdot y1\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot k\right)} \cdot \left(b \cdot y0 - i \cdot y1\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \left(z \cdot k\right) \cdot \color{blue}{\left(b \cdot y0 - i \cdot y1\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(z \cdot k\right) \cdot \left(\color{blue}{b \cdot y0} - i \cdot y1\right) \]

      7. *-lowering-*.f64 34.9

         \[\leadsto \left(z \cdot k\right) \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right) \]

   8. Simplified 34.9%

      \[\leadsto \color{blue}{\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right) \cdot b} \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\left(k \cdot y0\right) \cdot z\right)} \cdot b \]

       3. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(y0 \cdot k\right)} \cdot z\right) \cdot b \]

       4. associate-*l* N/A

          \[\leadsto \color{blue}{\left(y0 \cdot \left(k \cdot z\right)\right)} \cdot b \]

       5. associate-*r* N/A

          \[\leadsto \color{blue}{y0 \cdot \left(\left(k \cdot z\right) \cdot b\right)} \]

       6. *-commutative N/A

          \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)} \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{y0 \cdot \left(b \cdot \left(k \cdot z\right)\right)} \]

       8. *-lowering-*.f64 N/A

          \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)} \]

       9. *-lowering-*.f64 25.3

          \[\leadsto y0 \cdot \left(b \cdot \color{blue}{\left(k \cdot z\right)}\right) \]

   11. Simplified 25.3%

       \[\leadsto \color{blue}{y0 \cdot \left(b \cdot \left(k \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.22 \cdot 10^{+240}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+105}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 20.0% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -8.5 \cdot 10^{-34}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{-206}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -8.5e-34)
   (* i (* j (* x y1)))
   (if (<= y1 3.5e-206) (* i (* k (* y y5))) (* b (* j (* t y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -8.5e-34) {
		tmp = i * (j * (x * y1));
	} else if (y1 <= 3.5e-206) {
		tmp = i * (k * (y * y5));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-8.5d-34)) then
        tmp = i * (j * (x * y1))
    else if (y1 <= 3.5d-206) then
        tmp = i * (k * (y * y5))
    else
        tmp = b * (j * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -8.5e-34) {
		tmp = i * (j * (x * y1));
	} else if (y1 <= 3.5e-206) {
		tmp = i * (k * (y * y5));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -8.5e-34:
		tmp = i * (j * (x * y1))
	elif y1 <= 3.5e-206:
		tmp = i * (k * (y * y5))
	else:
		tmp = b * (j * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -8.5e-34)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y1 <= 3.5e-206)
		tmp = Float64(i * Float64(k * Float64(y * y5)));
	else
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -8.5e-34)
		tmp = i * (j * (x * y1));
	elseif (y1 <= 3.5e-206)
		tmp = i * (k * (y * y5));
	else
		tmp = b * (j * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -8.5e-34], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.5e-206], N[(i * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -8.5000000000000001e-34

   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. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 52.1%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{i \cdot y1} - b \cdot y0\right)\right) \]

      4. *-lowering-*.f64 39.2

         \[\leadsto x \cdot \left(j \cdot \left(i \cdot y1 - \color{blue}{b \cdot y0}\right)\right) \]

   8. Simplified 39.2%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

       4. *-lowering-*.f64 39.0

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   11. Simplified 39.0%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -8.5000000000000001e-34 < y1 < 3.49999999999999989e-206

   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. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 47.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(0 - i\right)} \]

   6. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot k\right)} \cdot \left(y \cdot y5 - y1 \cdot z\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \left(i \cdot k\right) \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \left(i \cdot k\right) \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right) \]

      6. *-lowering-*.f64 28.4

         \[\leadsto \left(i \cdot k\right) \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right) \]

   8. Simplified 28.4%

      \[\leadsto \color{blue}{\left(i \cdot k\right) \cdot \left(y \cdot y5 - y1 \cdot z\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y \cdot y5\right)\right)} \]

       3. *-lowering-*.f64 23.8

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y \cdot y5\right)}\right) \]

   11. Simplified 23.8%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5\right)\right)} \]

   if 3.49999999999999989e-206 < y1

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 40.5

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 40.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 35.8

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 35.8%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-lowering-*.f64 29.5

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]

   11. Simplified 29.5%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -8.5 \cdot 10^{-34}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{-206}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.3% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{if}\;t \leq -165000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+90}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (* t y4)))))
   (if (<= t -165000000.0) t_1 (if (<= t 1.7e+90) (* i (* j (* x y1))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * (t * y4));
	double tmp;
	if (t <= -165000000.0) {
		tmp = t_1;
	} else if (t <= 1.7e+90) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (j * (t * y4))
    if (t <= (-165000000.0d0)) then
        tmp = t_1
    else if (t <= 1.7d+90) then
        tmp = i * (j * (x * y1))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * (t * y4));
	double tmp;
	if (t <= -165000000.0) {
		tmp = t_1;
	} else if (t <= 1.7e+90) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (j * (t * y4))
	tmp = 0
	if t <= -165000000.0:
		tmp = t_1
	elif t <= 1.7e+90:
		tmp = i * (j * (x * y1))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(t * y4)))
	tmp = 0.0
	if (t <= -165000000.0)
		tmp = t_1;
	elseif (t <= 1.7e+90)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (j * (t * y4));
	tmp = 0.0;
	if (t <= -165000000.0)
		tmp = t_1;
	elseif (t <= 1.7e+90)
		tmp = i * (j * (x * y1));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -165000000.0], t$95$1, If[LessEqual[t, 1.7e+90], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65e8 or 1.70000000000000009e90 < t

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      16. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

      17. *-lowering-*.f64 39.3

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 39.3%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      7. *-lowering-*.f64 47.2

         \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

   8. Simplified 47.2%

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-lowering-*.f64 32.8

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]

   11. Simplified 32.8%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

   if -1.65e8 < t < 1.70000000000000009e90

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Simplified 40.5%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, y2, \mathsf{fma}\left(a, b, 0 - c \cdot i\right) \cdot y\right) - j \cdot \mathsf{fma}\left(b, y0, 0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{i \cdot y1} - b \cdot y0\right)\right) \]

      4. *-lowering-*.f64 26.6

         \[\leadsto x \cdot \left(j \cdot \left(i \cdot y1 - \color{blue}{b \cdot y0}\right)\right) \]

   8. Simplified 26.6%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

       4. *-lowering-*.f64 22.9

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   11. Simplified 22.9%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -165000000:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+90}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 17.3% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(t \cdot \left(j \cdot y4\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* b (* t (* j y4))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return b * (t * (j * y4));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = b * (t * (j * y4))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return b * (t * (j * y4));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return b * (t * (j * y4))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(b * Float64(t * Float64(j * y4)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = b * (t * (j * y4));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.8%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   2. --lowering--.f64 N/A

      \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. accelerator-lowering-fma.f64 N/A

      \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   5. *-commutative N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   9. --lowering--.f64 N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   10. *-commutative N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   11. *-lowering-*.f64 N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   14. --lowering--.f64 N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

   16. *-commutative N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   17. *-lowering-*.f64 34.5

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

5. Simplified 34.5%

   \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

6. Taylor expanded in t around inf

   \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   2. +-commutative N/A

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

   3. mul-1-neg N/A

      \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

   4. unsub-neg N/A

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

   7. *-lowering-*.f64 32.0

      \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

8. Simplified 32.0%

   \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

9. Taylor expanded in j around inf

   \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]
10. Step-by-step derivation

    1. *-lowering-*.f64 19.8

       \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]

11. Simplified 19.8%

    \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]
12. Add Preprocessing

Alternative 31: 17.2% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* b (* j (* t y4))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return b * (j * (t * y4));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = b * (j * (t * y4))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return b * (j * (t * y4));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return b * (j * (t * y4))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(b * Float64(j * Float64(t * y4)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = b * (j * (t * y4));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.8%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   2. --lowering--.f64 N/A

      \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   3. accelerator-lowering-fma.f64 N/A

      \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{x \cdot y - t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   5. *-commutative N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, \color{blue}{y \cdot x} - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - \color{blue}{t \cdot z}, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, \color{blue}{y4 \cdot \left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   9. --lowering--.f64 N/A

      \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   10. *-commutative N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   11. *-lowering-*.f64 N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - \color{blue}{k \cdot y}\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   14. --lowering--.f64 N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

   16. *-commutative N/A

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   17. *-lowering-*.f64 34.5

       \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

5. Simplified 34.5%

   \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

6. Taylor expanded in t around inf

   \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]

   2. +-commutative N/A

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)}\right) \]

   3. mul-1-neg N/A

      \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 + \color{blue}{\left(\mathsf{neg}\left(a \cdot z\right)\right)}\right)\right) \]

   4. unsub-neg N/A

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)}\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto b \cdot \left(t \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

   7. *-lowering-*.f64 32.0

      \[\leadsto b \cdot \left(t \cdot \left(j \cdot y4 - \color{blue}{a \cdot z}\right)\right) \]

8. Simplified 32.0%

   \[\leadsto b \cdot \color{blue}{\left(t \cdot \left(j \cdot y4 - a \cdot z\right)\right)} \]

9. Taylor expanded in j around inf

   \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
10. Step-by-step derivation

    1. *-lowering-*.f64 N/A

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

    2. *-lowering-*.f64 N/A

       \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

    3. *-lowering-*.f64 19.1

       \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]

11. Simplified 19.1%

    \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
12. Add Preprocessing

Developer Target 1: 28.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t\_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t\_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t\_9\\ t_11 := t\_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t\_4 \cdot t\_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t\_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t\_3 \cdot t\_1 - t\_14\right)\right) + \left(t\_8 - \left(t\_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t\_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t\_13\right)\right) + \left(t\_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t\_10 - \left(y \cdot x - z \cdot t\right) \cdot t\_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t\_8 - \left(t\_11 - t\_6\right)\right) - \left(\frac{t\_3}{\frac{1}{t\_1}} - t\_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t\_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t\_2 - \left(t\_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t\_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t\_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t\_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t\_5\right) - t\_17 \cdot t\_1\right) + t\_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024196 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y4 -7206256231996481000000000000000000000000000000000000000000000) (- (- (* (- (* 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 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3364603505246317/1000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* 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 -3000016263921529/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* 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 1343792624811499/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* 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 29872667587737/6250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* 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 4570448308253367/20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* 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)))))