Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.4% → 44.0%

Time: 31.8s

Alternatives: 28

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: 29.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 44.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := b \cdot y0 - i \cdot y1\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := b \cdot y4 - i \cdot y5\\ t_5 := y \cdot \mathsf{fma}\left(t\_4, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ t_6 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+216}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, t\_1, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-248}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(t\_6, x, k \cdot t\_3\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-106}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(t, c \cdot i - a \cdot b, \mathsf{fma}\left(t\_6, -y3, k \cdot t\_2\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, t\_1, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+172}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(t\_4, -y, \mathsf{fma}\left(y2, t\_3, z \cdot t\_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t)))
        (t_2 (- (* b y0) (* i y1)))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4 (- (* b y4) (* i y5)))
        (t_5
         (*
          y
          (fma
           t_4
           (- k)
           (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5)))))))
        (t_6 (- (* c y0) (* a y1))))
   (if (<= y -2.3e+216)
     t_5
     (if (<= y -1.3e-164)
       (*
        a
        (fma
         (- (* x y2) (* z y3))
         (- y1)
         (fma b t_1 (* y5 (- (* t y2) (* y y3))))))
       (if (<= y 1.35e-248)
         (* y2 (+ (fma t_6 x (* k t_3)) (* t (- (* a y5) (* c y4)))))
         (if (<= y 9e-106)
           (* z (fma t (- (* c i) (* a b)) (fma t_6 (- y3) (* k t_2))))
           (if (<= y 4.2e+31)
             (*
              b
              (+
               (fma a t_1 (* y4 (- (* t j) (* y k))))
               (* y0 (- (* z k) (* x j)))))
             (if (<= y 1.22e+172)
               (* k (fma t_4 (- y) (fma y2 t_3 (* z t_2))))
               t_5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (z * t);
	double t_2 = (b * y0) - (i * y1);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (b * y4) - (i * y5);
	double t_5 = y * fma(t_4, -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	double t_6 = (c * y0) - (a * y1);
	double tmp;
	if (y <= -2.3e+216) {
		tmp = t_5;
	} else if (y <= -1.3e-164) {
		tmp = a * fma(((x * y2) - (z * y3)), -y1, fma(b, t_1, (y5 * ((t * y2) - (y * y3)))));
	} else if (y <= 1.35e-248) {
		tmp = y2 * (fma(t_6, x, (k * t_3)) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 9e-106) {
		tmp = z * fma(t, ((c * i) - (a * b)), fma(t_6, -y3, (k * t_2)));
	} else if (y <= 4.2e+31) {
		tmp = b * (fma(a, t_1, (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y <= 1.22e+172) {
		tmp = k * fma(t_4, -y, fma(y2, t_3, (z * t_2)));
	} 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 = Float64(Float64(x * y) - Float64(z * t))
	t_2 = Float64(Float64(b * y0) - Float64(i * y1))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(Float64(b * y4) - Float64(i * y5))
	t_5 = Float64(y * fma(t_4, Float64(-k), fma(Float64(Float64(a * b) - Float64(c * i)), x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))))
	t_6 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y <= -2.3e+216)
		tmp = t_5;
	elseif (y <= -1.3e-164)
		tmp = Float64(a * fma(Float64(Float64(x * y2) - Float64(z * y3)), Float64(-y1), fma(b, t_1, Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (y <= 1.35e-248)
		tmp = Float64(y2 * Float64(fma(t_6, x, Float64(k * t_3)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y <= 9e-106)
		tmp = Float64(z * fma(t, Float64(Float64(c * i) - Float64(a * b)), fma(t_6, Float64(-y3), Float64(k * t_2))));
	elseif (y <= 4.2e+31)
		tmp = Float64(b * Float64(fma(a, t_1, Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y <= 1.22e+172)
		tmp = Float64(k * fma(t_4, Float64(-y), fma(y2, t_3, Float64(z * t_2))));
	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[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(t$95$4 * (-k) + N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+216], t$95$5, If[LessEqual[y, -1.3e-164], N[(a * N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * (-y1) + N[(b * t$95$1 + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-248], N[(y2 * N[(N[(t$95$6 * x + N[(k * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-106], N[(z * N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 * (-y3) + N[(k * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+31], N[(b * N[(N[(a * t$95$1 + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e+172], N[(k * N[(t$95$4 * (-y) + N[(y2 * t$95$3 + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.29999999999999996e216 or 1.21999999999999999e172 < y

   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 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. lower-*.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Applied rewrites 69.8%

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

   if -2.29999999999999996e216 < y < -1.3000000000000001e-164

   1. Initial program 24.6%

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

   3. Taylor expanded in 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. lower-*.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. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. lower-neg.f64 N/A

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

      15. sub-neg N/A

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

   5. Applied rewrites 63.4%

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

   if -1.3000000000000001e-164 < y < 1.35e-248

   1. Initial program 43.3%

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

   3. Taylor expanded in y2 around inf

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

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

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 57.8%

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

   if 1.35e-248 < y < 8.99999999999999911e-106

   1. Initial program 39.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

      6. lower-fma.f64 N/A

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

   5. Applied rewrites 53.7%

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

   if 8.99999999999999911e-106 < y < 4.19999999999999958e31

   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 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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 46.6

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

   5. Applied rewrites 46.6%

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

   if 4.19999999999999958e31 < y < 1.21999999999999999e172

   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 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. lower-*.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. Applied rewrites 68.2%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-248}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-106}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(t, c \cdot i - a \cdot b, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, -y3, k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+172}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 55.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot y2 - y \cdot y3\\ t_2 := x \cdot y - z \cdot t\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := \left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot t\_2 + \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right) + t\_3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + t\_1 \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{if}\;t\_4 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t\_3, -y1, \mathsf{fma}\left(b, t\_2, y5 \cdot t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

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

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * t_2) + Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(i * y1) - Float64(b * y0)))) + Float64(t_3 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(Float64(Float64(b * y4) - Float64(i * y5)) * Float64(Float64(t * j) - Float64(y * k)))) + Float64(t_1 * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (t_4 <= Inf)
		tmp = t_4;
	else
		tmp = Float64(a * fma(t_3, Float64(-y1), fma(b, t_2, Float64(y5 * 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[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, Infinity], t$95$4, N[(a * N[(t$95$3 * (-y1) + N[(b * t$95$2 + N[(y5 * t$95$1), $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 85.2%

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

   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 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. lower-*.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. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. lower-neg.f64 N/A

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

      15. sub-neg N/A

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

   5. Applied rewrites 44.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.0%

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

Alternative 3: 43.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := y \cdot \mathsf{fma}\left(t\_1, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ t_3 := x \cdot y - z \cdot t\\ t_4 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+216}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, t\_3, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-51}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot t\_4\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, t\_3, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+172}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(t\_1, -y, \mathsf{fma}\left(y2, t\_4, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2
         (*
          y
          (fma
           t_1
           (- k)
           (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5)))))))
        (t_3 (- (* x y) (* z t)))
        (t_4 (- (* y1 y4) (* y0 y5))))
   (if (<= y -2.3e+216)
     t_2
     (if (<= y -1.3e-164)
       (*
        a
        (fma
         (- (* x y2) (* z y3))
         (- y1)
         (fma b t_3 (* y5 (- (* t y2) (* y y3))))))
       (if (<= y 2.05e-51)
         (*
          y2
          (+
           (fma (- (* c y0) (* a y1)) x (* k t_4))
           (* t (- (* a y5) (* c y4)))))
         (if (<= y 4.2e+31)
           (*
            b
            (+
             (fma a t_3 (* y4 (- (* t j) (* y k))))
             (* y0 (- (* z k) (* x j)))))
           (if (<= y 1.22e+172)
             (* k (fma t_1 (- y) (fma y2 t_4 (* z (- (* b y0) (* i y1))))))
             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 = (b * y4) - (i * y5);
	double t_2 = y * fma(t_1, -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	double t_3 = (x * y) - (z * t);
	double t_4 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (y <= -2.3e+216) {
		tmp = t_2;
	} else if (y <= -1.3e-164) {
		tmp = a * fma(((x * y2) - (z * y3)), -y1, fma(b, t_3, (y5 * ((t * y2) - (y * y3)))));
	} else if (y <= 2.05e-51) {
		tmp = y2 * (fma(((c * y0) - (a * y1)), x, (k * t_4)) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 4.2e+31) {
		tmp = b * (fma(a, t_3, (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y <= 1.22e+172) {
		tmp = k * fma(t_1, -y, fma(y2, t_4, (z * ((b * y0) - (i * y1)))));
	} 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(b * y4) - Float64(i * y5))
	t_2 = Float64(y * fma(t_1, Float64(-k), fma(Float64(Float64(a * b) - Float64(c * i)), x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	t_4 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (y <= -2.3e+216)
		tmp = t_2;
	elseif (y <= -1.3e-164)
		tmp = Float64(a * fma(Float64(Float64(x * y2) - Float64(z * y3)), Float64(-y1), fma(b, t_3, Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (y <= 2.05e-51)
		tmp = Float64(y2 * Float64(fma(Float64(Float64(c * y0) - Float64(a * y1)), x, Float64(k * t_4)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y <= 4.2e+31)
		tmp = Float64(b * Float64(fma(a, t_3, Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y <= 1.22e+172)
		tmp = Float64(k * fma(t_1, Float64(-y), fma(y2, t_4, Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))));
	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[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t$95$1 * (-k) + N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+216], t$95$2, If[LessEqual[y, -1.3e-164], N[(a * N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * (-y1) + N[(b * t$95$3 + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-51], N[(y2 * N[(N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * x + N[(k * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+31], N[(b * N[(N[(a * t$95$3 + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e+172], N[(k * N[(t$95$1 * (-y) + N[(y2 * t$95$4 + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.29999999999999996e216 or 1.21999999999999999e172 < y

   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 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. lower-*.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Applied rewrites 69.8%

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

   if -2.29999999999999996e216 < y < -1.3000000000000001e-164

   1. Initial program 24.6%

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

   3. Taylor expanded in 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. lower-*.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. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. lower-neg.f64 N/A

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

      15. sub-neg N/A

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

   5. Applied rewrites 63.4%

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

   if -1.3000000000000001e-164 < y < 2.04999999999999987e-51

   1. Initial program 41.4%

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

   3. Taylor expanded in 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. lower-*.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. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 46.3%

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

   if 2.04999999999999987e-51 < y < 4.19999999999999958e31

   1. Initial program 17.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 67.0

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

   5. Applied rewrites 67.0%

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

   if 4.19999999999999958e31 < y < 1.21999999999999999e172

   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 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. lower-*.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. Applied rewrites 68.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-51}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+172}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 44.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ t_2 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot t\_2\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-267}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+45}:\\ \;\;\;\;y5 \cdot \left(a \cdot t\_2 - \mathsf{fma}\left(i, t \cdot j - y \cdot k, y0 \cdot \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y
          (fma
           (- (* b y4) (* i y5))
           (- k)
           (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5)))))))
        (t_2 (- (* t y2) (* y y3))))
   (if (<= y -2.3e+216)
     t_1
     (if (<= y -1.3e-164)
       (*
        a
        (fma
         (- (* x y2) (* z y3))
         (- y1)
         (fma b (- (* x y) (* z t)) (* y5 t_2))))
       (if (<= y 2.3e-267)
         (*
          y2
          (+
           (fma (- (* c y0) (* a y1)) x (* k (- (* y1 y4) (* y0 y5))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= y 9e+45)
           (*
            y5
            (-
             (* a t_2)
             (fma i (- (* t j) (* y k)) (* y0 (fma k y2 (* j (- y3)))))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * fma(((b * y4) - (i * y5)), -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	double t_2 = (t * y2) - (y * y3);
	double tmp;
	if (y <= -2.3e+216) {
		tmp = t_1;
	} else if (y <= -1.3e-164) {
		tmp = a * fma(((x * y2) - (z * y3)), -y1, fma(b, ((x * y) - (z * t)), (y5 * t_2)));
	} else if (y <= 2.3e-267) {
		tmp = y2 * (fma(((c * y0) - (a * y1)), x, (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 9e+45) {
		tmp = y5 * ((a * t_2) - fma(i, ((t * j) - (y * k)), (y0 * fma(k, y2, (j * -y3)))));
	} 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(y * fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(-k), fma(Float64(Float64(a * b) - Float64(c * i)), x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))))
	t_2 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y <= -2.3e+216)
		tmp = t_1;
	elseif (y <= -1.3e-164)
		tmp = Float64(a * fma(Float64(Float64(x * y2) - Float64(z * y3)), Float64(-y1), fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * t_2))));
	elseif (y <= 2.3e-267)
		tmp = Float64(y2 * Float64(fma(Float64(Float64(c * y0) - Float64(a * y1)), x, Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y <= 9e+45)
		tmp = Float64(y5 * Float64(Float64(a * t_2) - fma(i, Float64(Float64(t * j) - Float64(y * k)), Float64(y0 * fma(k, y2, Float64(j * Float64(-y3)))))));
	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[(y * N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * (-k) + N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+216], t$95$1, If[LessEqual[y, -1.3e-164], N[(a * N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * (-y1) + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-267], N[(y2 * N[(N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * x + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+45], N[(y5 * N[(N[(a * t$95$2), $MachinePrecision] - N[(i * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * y2 + N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.29999999999999996e216 or 8.9999999999999997e45 < y

   1. Initial program 23.5%

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

   3. Taylor expanded in 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. lower-*.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Applied rewrites 65.1%

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

   if -2.29999999999999996e216 < y < -1.3000000000000001e-164

   1. Initial program 24.6%

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

   3. Taylor expanded in 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. lower-*.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. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. lower-neg.f64 N/A

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

      15. sub-neg N/A

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

   5. Applied rewrites 63.4%

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

   if -1.3000000000000001e-164 < y < 2.30000000000000005e-267

   1. Initial program 45.3%

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

   3. Taylor expanded in 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. lower-*.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. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 58.2%

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

   if 2.30000000000000005e-267 < y < 8.9999999999999997e45

   1. Initial program 33.3%

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

   3. Taylor expanded in y5 around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 50.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-267}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+45}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \mathsf{fma}\left(i, t \cdot j - y \cdot k, y0 \cdot \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-275}:\\ \;\;\;\;y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-309}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(x, y0, t \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot a\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          b
          (+
           (fma a (- (* x y) (* z t)) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= b -5.5e-44)
     t_1
     (if (<= b -3.5e-275)
       (* y2 (* t (fma a y5 (* y4 (- c)))))
       (if (<= b -3e-309)
         (* c (* y2 (fma x y0 (* t (- y4)))))
         (if (<= b 9.5e+27)
           (+
            (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
            (* (* t a) (* y2 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 = b * (fma(a, ((x * y) - (z * t)), (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (b <= -5.5e-44) {
		tmp = t_1;
	} else if (b <= -3.5e-275) {
		tmp = y2 * (t * fma(a, y5, (y4 * -c)));
	} else if (b <= -3e-309) {
		tmp = c * (y2 * fma(x, y0, (t * -y4)));
	} else if (b <= 9.5e+27) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + ((t * a) * (y2 * 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(b * Float64(fma(a, Float64(Float64(x * y) - Float64(z * t)), Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (b <= -5.5e-44)
		tmp = t_1;
	elseif (b <= -3.5e-275)
		tmp = Float64(y2 * Float64(t * fma(a, y5, Float64(y4 * Float64(-c)))));
	elseif (b <= -3e-309)
		tmp = Float64(c * Float64(y2 * fma(x, y0, Float64(t * Float64(-y4)))));
	elseif (b <= 9.5e+27)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(t * a) * Float64(y2 * 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[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e-44], t$95$1, If[LessEqual[b, -3.5e-275], N[(y2 * N[(t * N[(a * y5 + N[(y4 * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-309], N[(c * N[(y2 * N[(x * y0 + N[(t * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+27], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.49999999999999993e-44 or 9.4999999999999997e27 < b

   1. Initial program 22.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 55.5

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

   5. Applied rewrites 55.5%

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

   if -5.49999999999999993e-44 < b < -3.49999999999999969e-275

   1. Initial program 34.2%

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

   3. Taylor expanded in 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. lower-*.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. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 50.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto y2 \cdot \color{blue}{\left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 + \left(\mathsf{neg}\left(c \cdot y4\right)\right)\right)}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(a, y5, \mathsf{neg}\left(c \cdot y4\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \mathsf{neg}\left(\color{blue}{y4 \cdot c}\right)\right)\right) \]

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

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \color{blue}{y4 \cdot \left(\mathsf{neg}\left(c\right)\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \color{blue}{\left(-1 \cdot c\right)}\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \color{blue}{y4 \cdot \left(-1 \cdot c\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \color{blue}{\left(\mathsf{neg}\left(c\right)\right)}\right)\right) \]

      9. lower-neg.f64 56.6

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

   8. Applied rewrites 56.6%

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

   if -3.49999999999999969e-275 < b < -3.000000000000001e-309

   1. Initial program 1.3%

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

   3. Taylor expanded in y2 around inf

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

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

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 63.3%

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

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

         \[\leadsto c \cdot \left(\color{blue}{\mathsf{fma}\left(x, y0, -1 \cdot \left(t \cdot y4\right)\right)} \cdot y2\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(x, y0, \color{blue}{\mathsf{neg}\left(t \cdot y4\right)}\right) \cdot y2\right) \]

      8. *-commutative N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(x, y0, \mathsf{neg}\left(\color{blue}{y4 \cdot t}\right)\right) \cdot y2\right) \]

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

         \[\leadsto c \cdot \left(\mathsf{fma}\left(x, y0, \color{blue}{y4 \cdot \left(\mathsf{neg}\left(t\right)\right)}\right) \cdot y2\right) \]

      10. mul-1-neg N/A

          \[\leadsto c \cdot \left(\mathsf{fma}\left(x, y0, y4 \cdot \color{blue}{\left(-1 \cdot t\right)}\right) \cdot y2\right) \]

      11. lower-*.f64 N/A

          \[\leadsto c \cdot \left(\mathsf{fma}\left(x, y0, \color{blue}{y4 \cdot \left(-1 \cdot t\right)}\right) \cdot y2\right) \]

      12. mul-1-neg N/A

          \[\leadsto c \cdot \left(\mathsf{fma}\left(x, y0, y4 \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \cdot y2\right) \]

      13. lower-neg.f64 88.3

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

   8. Applied rewrites 88.3%

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

   if -3.000000000000001e-309 < b < 9.4999999999999997e27

   1. Initial program 44.9%

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

   3. Taylor expanded in y5 around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 43.9

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

   5. Applied rewrites 43.9%

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

   6. Taylor expanded in y2 around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 49.6

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

   8. Applied rewrites 49.6%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y2 \cdot y5\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-275}:\\ \;\;\;\;y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-309}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(x, y0, t \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot a\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := y \cdot \mathsf{fma}\left(t\_1, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+216}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+37}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+172}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(t\_1, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2
         (*
          y
          (fma
           t_1
           (- k)
           (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5))))))))
   (if (<= y -2.3e+216)
     t_2
     (if (<= y 1.45e+37)
       (*
        a
        (fma
         (- (* x y2) (* z y3))
         (- y1)
         (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
       (if (<= y 1.22e+172)
         (*
          k
          (fma
           t_1
           (- y)
           (fma y2 (- (* y1 y4) (* y0 y5)) (* z (- (* b y0) (* i y1))))))
         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 = (b * y4) - (i * y5);
	double t_2 = y * fma(t_1, -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	double tmp;
	if (y <= -2.3e+216) {
		tmp = t_2;
	} else if (y <= 1.45e+37) {
		tmp = a * fma(((x * y2) - (z * y3)), -y1, fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} else if (y <= 1.22e+172) {
		tmp = k * fma(t_1, -y, fma(y2, ((y1 * y4) - (y0 * y5)), (z * ((b * y0) - (i * y1)))));
	} 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(b * y4) - Float64(i * y5))
	t_2 = Float64(y * fma(t_1, Float64(-k), fma(Float64(Float64(a * b) - Float64(c * i)), x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))))
	tmp = 0.0
	if (y <= -2.3e+216)
		tmp = t_2;
	elseif (y <= 1.45e+37)
		tmp = Float64(a * fma(Float64(Float64(x * y2) - Float64(z * y3)), Float64(-y1), fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (y <= 1.22e+172)
		tmp = Float64(k * fma(t_1, Float64(-y), fma(y2, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))));
	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[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t$95$1 * (-k) + N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+216], t$95$2, If[LessEqual[y, 1.45e+37], N[(a * N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * (-y1) + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e+172], N[(k * N[(t$95$1 * (-y) + N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.29999999999999996e216 or 1.21999999999999999e172 < y

   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 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. lower-*.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Applied rewrites 69.8%

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

   if -2.29999999999999996e216 < y < 1.44999999999999989e37

   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 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. lower-*.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. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. lower-neg.f64 N/A

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

      15. sub-neg N/A

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

   5. Applied rewrites 48.6%

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

   if 1.44999999999999989e37 < y < 1.21999999999999999e172

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. Applied rewrites 69.6%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+37}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+172}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-243}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot a\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          x
          (+
           (fma (- (* a b) (* c i)) y (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= x -2.1e+48)
     t_1
     (if (<= x 4e-243)
       (+
        (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
        (* (* t a) (* y2 y5)))
       (if (<= x 1.7e+158)
         (*
          a
          (fma
           (- (* x y2) (* z y3))
           (- y1)
           (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (fma(((a * b) - (c * i)), y, (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (x <= -2.1e+48) {
		tmp = t_1;
	} else if (x <= 4e-243) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + ((t * a) * (y2 * y5));
	} else if (x <= 1.7e+158) {
		tmp = a * fma(((x * y2) - (z * y3)), -y1, fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} 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(x * Float64(fma(Float64(Float64(a * b) - Float64(c * i)), y, Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (x <= -2.1e+48)
		tmp = t_1;
	elseif (x <= 4e-243)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(t * a) * Float64(y2 * y5)));
	elseif (x <= 1.7e+158)
		tmp = Float64(a * fma(Float64(Float64(x * y2) - Float64(z * y3)), Float64(-y1), fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	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[(x * N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * y + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+48], t$95$1, If[LessEqual[x, 4e-243], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+158], N[(a * N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * (-y1) + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0999999999999998e48 or 1.7e158 < x

   1. Initial program 29.4%

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

   3. Taylor expanded in 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. lower-*.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. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 68.6

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

   5. Applied rewrites 68.6%

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

   if -2.0999999999999998e48 < x < 3.99999999999999998e-243

   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 y5 around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 38.6

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

   5. Applied rewrites 38.6%

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

   6. Taylor expanded in y2 around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 42.9

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

   8. Applied rewrites 42.9%

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

   if 3.99999999999999998e-243 < x < 1.7e158

   1. Initial program 34.4%

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

   3. Taylor expanded in 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. lower-*.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. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. lower-neg.f64 N/A

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

      15. sub-neg N/A

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

   5. Applied rewrites 53.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-243}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot a\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+158}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;k \leq -7 \cdot 10^{+88}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, t\_1, a \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot t\_1 + \left(t \cdot a\right) \cdot \left(y2 \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5))))
   (if (<= k -7e+88)
     (* y2 (fma k t_1 (* a (* t y5))))
     (if (<= k 4.4e+36)
       (*
        a
        (fma
         (- (* x y2) (* z y3))
         (- y1)
         (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
       (+ (* (- (* k y2) (* j y3)) t_1) (* (* t a) (* y2 y5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (k <= -7e+88) {
		tmp = y2 * fma(k, t_1, (a * (t * y5)));
	} else if (k <= 4.4e+36) {
		tmp = a * fma(((x * y2) - (z * y3)), -y1, fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} else {
		tmp = (((k * y2) - (j * y3)) * t_1) + ((t * a) * (y2 * y5));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (k <= -7e+88)
		tmp = Float64(y2 * fma(k, t_1, Float64(a * Float64(t * y5))));
	elseif (k <= 4.4e+36)
		tmp = Float64(a * fma(Float64(Float64(x * y2) - Float64(z * y3)), Float64(-y1), fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	else
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_1) + Float64(Float64(t * a) * Float64(y2 * y5)));
	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[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -7e+88], N[(y2 * N[(k * t$95$1 + N[(a * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.4e+36], N[(a * N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * (-y1) + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if k < -6.9999999999999995e88

   1. Initial program 19.2%

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

   3. Taylor expanded in y5 around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 38.6

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

   5. Applied rewrites 38.6%

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

   6. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 53.1

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

   8. Applied rewrites 53.1%

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

   if -6.9999999999999995e88 < k < 4.40000000000000001e36

   1. Initial program 34.4%

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

   3. Taylor expanded in 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. lower-*.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. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. lower-neg.f64 N/A

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

      15. sub-neg N/A

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

   5. Applied rewrites 50.2%

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

   if 4.40000000000000001e36 < k

   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

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 37.7

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

   5. Applied rewrites 37.7%

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

   6. Taylor expanded in y2 around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 54.2

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

   8. Applied rewrites 54.2%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -7 \cdot 10^{+88}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, a \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(x \cdot y2 - z \cdot y3, -y1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot a\right) \cdot \left(y2 \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 31.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+245}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+104}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-292}:\\ \;\;\;\;y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-129}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(a, x, k \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= b -7.8e+245)
     (* b (* k (- (* z y0) (* y y4))))
     (if (<= b -7.2e+104)
       (* (* b y4) (- (* t j) (* y k)))
       (if (<= b -3.45e-43)
         t_1
         (if (<= b -1.7e-292)
           (* y2 (* t (fma a y5 (* y4 (- c)))))
           (if (<= b 1.06e-129)
             (* y1 (* a (fma (- x) y2 (* z y3))))
             (if (<= b 2.1e-9)
               (* (* y3 y5) (- (* j y0) (* y a)))
               (if (<= b 3e+34)
                 (* y0 (* y2 (fma x c (* k (- y5)))))
                 (if (<= b 3.2e+124)
                   (* b (* y (fma a x (* k (- y4)))))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (b <= -7.8e+245) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (b <= -7.2e+104) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (b <= -3.45e-43) {
		tmp = t_1;
	} else if (b <= -1.7e-292) {
		tmp = y2 * (t * fma(a, y5, (y4 * -c)));
	} else if (b <= 1.06e-129) {
		tmp = y1 * (a * fma(-x, y2, (z * y3)));
	} else if (b <= 2.1e-9) {
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	} else if (b <= 3e+34) {
		tmp = y0 * (y2 * fma(x, c, (k * -y5)));
	} else if (b <= 3.2e+124) {
		tmp = b * (y * fma(a, x, (k * -y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (b <= -7.8e+245)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (b <= -7.2e+104)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	elseif (b <= -3.45e-43)
		tmp = t_1;
	elseif (b <= -1.7e-292)
		tmp = Float64(y2 * Float64(t * fma(a, y5, Float64(y4 * Float64(-c)))));
	elseif (b <= 1.06e-129)
		tmp = Float64(y1 * Float64(a * fma(Float64(-x), y2, Float64(z * y3))));
	elseif (b <= 2.1e-9)
		tmp = Float64(Float64(y3 * y5) * Float64(Float64(j * y0) - Float64(y * a)));
	elseif (b <= 3e+34)
		tmp = Float64(y0 * Float64(y2 * fma(x, c, Float64(k * Float64(-y5)))));
	elseif (b <= 3.2e+124)
		tmp = Float64(b * Float64(y * fma(a, x, Float64(k * Float64(-y4)))));
	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[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.8e+245], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.2e+104], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.45e-43], t$95$1, If[LessEqual[b, -1.7e-292], N[(y2 * N[(t * N[(a * y5 + N[(y4 * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.06e-129], N[(y1 * N[(a * N[((-x) * y2 + N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-9], N[(N[(y3 * y5), $MachinePrecision] * N[(N[(j * y0), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+34], N[(y0 * N[(y2 * N[(x * c + N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+124], N[(b * N[(y * N[(a * x + N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -7.7999999999999996e245

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 79.9

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

   5. Applied rewrites 79.9%

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

   6. Taylor expanded in k around -inf

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 61.2

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

   8. Applied rewrites 61.2%

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

   if -7.7999999999999996e245 < b < -7.20000000000000001e104

   1. Initial program 23.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 52.7

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

   5. Applied rewrites 52.7%

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

   6. Taylor expanded in y4 around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 71.9

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

   8. Applied rewrites 71.9%

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

   if -7.20000000000000001e104 < b < -3.44999999999999982e-43 or 3.19999999999999993e124 < b

   1. Initial program 17.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. lower-*.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. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. lower-neg.f64 N/A

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

      15. sub-neg N/A

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

   5. Applied rewrites 55.0%

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

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 52.6

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

   8. Applied rewrites 52.6%

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

   if -3.44999999999999982e-43 < b < -1.70000000000000009e-292

   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 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. lower-*.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. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 51.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto y2 \cdot \color{blue}{\left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 + \left(\mathsf{neg}\left(c \cdot y4\right)\right)\right)}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(a, y5, \mathsf{neg}\left(c \cdot y4\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \mathsf{neg}\left(\color{blue}{y4 \cdot c}\right)\right)\right) \]

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

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \color{blue}{y4 \cdot \left(\mathsf{neg}\left(c\right)\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \color{blue}{\left(-1 \cdot c\right)}\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \color{blue}{y4 \cdot \left(-1 \cdot c\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \color{blue}{\left(\mathsf{neg}\left(c\right)\right)}\right)\right) \]

      9. lower-neg.f64 53.6

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

   8. Applied rewrites 53.6%

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

   if -1.70000000000000009e-292 < b < 1.0600000000000001e-129

   1. Initial program 45.3%

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

   3. Taylor expanded in 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. lower-*.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. lower-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. Applied rewrites 52.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 53.6

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

   8. Applied rewrites 53.6%

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

   if 1.0600000000000001e-129 < b < 2.10000000000000019e-9

   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 y5 around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 47.4

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

   8. Applied rewrites 47.4%

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

   if 2.10000000000000019e-9 < b < 3.00000000000000018e34

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 32.3%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\mathsf{fma}\left(x, c, -1 \cdot \left(k \cdot y5\right)\right)} \cdot y2\right) \]

      7. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{\mathsf{neg}\left(k \cdot y5\right)}\right) \cdot y2\right) \]

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

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      9. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      11. mul-1-neg N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      12. lower-neg.f64 56.6

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

   8. Applied rewrites 56.6%

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

   if 3.00000000000000018e34 < b < 3.19999999999999993e124

   1. Initial program 44.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 44.3

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

   5. Applied rewrites 44.3%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(a, x, \color{blue}{\left(\mathsf{neg}\left(k\right)\right)} \cdot y4\right)\right) \]

      7. lower-neg.f64 48.6

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

   8. Applied rewrites 48.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+245}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+104}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-292}:\\ \;\;\;\;y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-129}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(a, x, k \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+104}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-292}:\\ \;\;\;\;y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-129}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(a, x, k \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= b -7.2e+104)
     (* (* b y4) (- (* t j) (* y k)))
     (if (<= b -3.45e-43)
       t_1
       (if (<= b -1.7e-292)
         (* y2 (* t (fma a y5 (* y4 (- c)))))
         (if (<= b 1.06e-129)
           (* y1 (* a (fma (- x) y2 (* z y3))))
           (if (<= b 2.1e-9)
             (* (* y3 y5) (- (* j y0) (* y a)))
             (if (<= b 3e+34)
               (* y0 (* y2 (fma x c (* k (- y5)))))
               (if (<= b 3.2e+124)
                 (* b (* y (fma a x (* k (- y4)))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (b <= -7.2e+104) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (b <= -3.45e-43) {
		tmp = t_1;
	} else if (b <= -1.7e-292) {
		tmp = y2 * (t * fma(a, y5, (y4 * -c)));
	} else if (b <= 1.06e-129) {
		tmp = y1 * (a * fma(-x, y2, (z * y3)));
	} else if (b <= 2.1e-9) {
		tmp = (y3 * y5) * ((j * y0) - (y * a));
	} else if (b <= 3e+34) {
		tmp = y0 * (y2 * fma(x, c, (k * -y5)));
	} else if (b <= 3.2e+124) {
		tmp = b * (y * fma(a, x, (k * -y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (b <= -7.2e+104)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	elseif (b <= -3.45e-43)
		tmp = t_1;
	elseif (b <= -1.7e-292)
		tmp = Float64(y2 * Float64(t * fma(a, y5, Float64(y4 * Float64(-c)))));
	elseif (b <= 1.06e-129)
		tmp = Float64(y1 * Float64(a * fma(Float64(-x), y2, Float64(z * y3))));
	elseif (b <= 2.1e-9)
		tmp = Float64(Float64(y3 * y5) * Float64(Float64(j * y0) - Float64(y * a)));
	elseif (b <= 3e+34)
		tmp = Float64(y0 * Float64(y2 * fma(x, c, Float64(k * Float64(-y5)))));
	elseif (b <= 3.2e+124)
		tmp = Float64(b * Float64(y * fma(a, x, Float64(k * Float64(-y4)))));
	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[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+104], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.45e-43], t$95$1, If[LessEqual[b, -1.7e-292], N[(y2 * N[(t * N[(a * y5 + N[(y4 * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.06e-129], N[(y1 * N[(a * N[((-x) * y2 + N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-9], N[(N[(y3 * y5), $MachinePrecision] * N[(N[(j * y0), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+34], N[(y0 * N[(y2 * N[(x * c + N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+124], N[(b * N[(y * N[(a * x + N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -7.20000000000000001e104

   1. Initial program 19.4%

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

   3. Taylor expanded in 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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 64.1

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

   5. Applied rewrites 64.1%

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

   6. Taylor expanded in y4 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. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 56.2

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

   8. Applied rewrites 56.2%

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

   if -7.20000000000000001e104 < b < -3.44999999999999982e-43 or 3.19999999999999993e124 < b

   1. Initial program 17.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. lower-*.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. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. lower-neg.f64 N/A

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

      15. sub-neg N/A

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

   5. Applied rewrites 55.0%

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

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 52.6

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

   8. Applied rewrites 52.6%

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

   if -3.44999999999999982e-43 < b < -1.70000000000000009e-292

   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 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. lower-*.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. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 51.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto y2 \cdot \color{blue}{\left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 + \left(\mathsf{neg}\left(c \cdot y4\right)\right)\right)}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(a, y5, \mathsf{neg}\left(c \cdot y4\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \mathsf{neg}\left(\color{blue}{y4 \cdot c}\right)\right)\right) \]

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

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \color{blue}{y4 \cdot \left(\mathsf{neg}\left(c\right)\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \color{blue}{\left(-1 \cdot c\right)}\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \color{blue}{y4 \cdot \left(-1 \cdot c\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \color{blue}{\left(\mathsf{neg}\left(c\right)\right)}\right)\right) \]

      9. lower-neg.f64 53.6

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

   8. Applied rewrites 53.6%

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

   if -1.70000000000000009e-292 < b < 1.0600000000000001e-129

   1. Initial program 45.3%

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

   3. Taylor expanded in 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. lower-*.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. lower-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. Applied rewrites 52.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 53.6

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

   8. Applied rewrites 53.6%

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

   if 1.0600000000000001e-129 < b < 2.10000000000000019e-9

   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 y5 around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 47.4

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

   8. Applied rewrites 47.4%

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

   if 2.10000000000000019e-9 < b < 3.00000000000000018e34

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 32.3%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\mathsf{fma}\left(x, c, -1 \cdot \left(k \cdot y5\right)\right)} \cdot y2\right) \]

      7. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{\mathsf{neg}\left(k \cdot y5\right)}\right) \cdot y2\right) \]

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

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      9. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      11. mul-1-neg N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      12. lower-neg.f64 56.6

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

   8. Applied rewrites 56.6%

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

   if 3.00000000000000018e34 < b < 3.19999999999999993e124

   1. Initial program 44.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 44.3

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

   5. Applied rewrites 44.3%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(a, x, \color{blue}{\left(\mathsf{neg}\left(k\right)\right)} \cdot y4\right)\right) \]

      7. lower-neg.f64 48.6

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

   8. Applied rewrites 48.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+104}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-292}:\\ \;\;\;\;y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-129}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;\left(y3 \cdot y5\right) \cdot \left(j \cdot y0 - y \cdot a\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(a, x, k \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 31.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+104}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-292}:\\ \;\;\;\;y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-124}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 10^{-82}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(a, x, k \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= b -7.2e+104)
     (* (* b y4) (- (* t j) (* y k)))
     (if (<= b -3.45e-43)
       t_1
       (if (<= b -1.7e-292)
         (* y2 (* t (fma a y5 (* y4 (- c)))))
         (if (<= b 1.42e-124)
           (* y1 (* a (fma (- x) y2 (* z y3))))
           (if (<= b 1e-82)
             (* y5 (* j (* y0 y3)))
             (if (<= b 3e+34)
               (* y0 (* y2 (fma x c (* k (- y5)))))
               (if (<= b 3.2e+124)
                 (* b (* y (fma a x (* k (- y4)))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (b <= -7.2e+104) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (b <= -3.45e-43) {
		tmp = t_1;
	} else if (b <= -1.7e-292) {
		tmp = y2 * (t * fma(a, y5, (y4 * -c)));
	} else if (b <= 1.42e-124) {
		tmp = y1 * (a * fma(-x, y2, (z * y3)));
	} else if (b <= 1e-82) {
		tmp = y5 * (j * (y0 * y3));
	} else if (b <= 3e+34) {
		tmp = y0 * (y2 * fma(x, c, (k * -y5)));
	} else if (b <= 3.2e+124) {
		tmp = b * (y * fma(a, x, (k * -y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (b <= -7.2e+104)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	elseif (b <= -3.45e-43)
		tmp = t_1;
	elseif (b <= -1.7e-292)
		tmp = Float64(y2 * Float64(t * fma(a, y5, Float64(y4 * Float64(-c)))));
	elseif (b <= 1.42e-124)
		tmp = Float64(y1 * Float64(a * fma(Float64(-x), y2, Float64(z * y3))));
	elseif (b <= 1e-82)
		tmp = Float64(y5 * Float64(j * Float64(y0 * y3)));
	elseif (b <= 3e+34)
		tmp = Float64(y0 * Float64(y2 * fma(x, c, Float64(k * Float64(-y5)))));
	elseif (b <= 3.2e+124)
		tmp = Float64(b * Float64(y * fma(a, x, Float64(k * Float64(-y4)))));
	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[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+104], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.45e-43], t$95$1, If[LessEqual[b, -1.7e-292], N[(y2 * N[(t * N[(a * y5 + N[(y4 * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.42e-124], N[(y1 * N[(a * N[((-x) * y2 + N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-82], N[(y5 * N[(j * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+34], N[(y0 * N[(y2 * N[(x * c + N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+124], N[(b * N[(y * N[(a * x + N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -7.20000000000000001e104

   1. Initial program 19.4%

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

   3. Taylor expanded in 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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 64.1

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

   5. Applied rewrites 64.1%

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

   6. Taylor expanded in y4 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. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 56.2

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

   8. Applied rewrites 56.2%

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

   if -7.20000000000000001e104 < b < -3.44999999999999982e-43 or 3.19999999999999993e124 < b

   1. Initial program 17.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. lower-*.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. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. neg-mul-1 N/A

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

      14. lower-neg.f64 N/A

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

      15. sub-neg N/A

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

   5. Applied rewrites 55.0%

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

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 52.6

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

   8. Applied rewrites 52.6%

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

   if -3.44999999999999982e-43 < b < -1.70000000000000009e-292

   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 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. lower-*.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. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 51.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto y2 \cdot \color{blue}{\left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 + \left(\mathsf{neg}\left(c \cdot y4\right)\right)\right)}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(a, y5, \mathsf{neg}\left(c \cdot y4\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \mathsf{neg}\left(\color{blue}{y4 \cdot c}\right)\right)\right) \]

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

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \color{blue}{y4 \cdot \left(\mathsf{neg}\left(c\right)\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \color{blue}{\left(-1 \cdot c\right)}\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \color{blue}{y4 \cdot \left(-1 \cdot c\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \color{blue}{\left(\mathsf{neg}\left(c\right)\right)}\right)\right) \]

      9. lower-neg.f64 53.6

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

   8. Applied rewrites 53.6%

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

   if -1.70000000000000009e-292 < b < 1.42000000000000004e-124

   1. Initial program 45.6%

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

   3. Taylor expanded in y1 around inf

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

      1. lower-*.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. lower-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. Applied rewrites 52.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 53.5

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

   8. Applied rewrites 53.5%

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

   if 1.42000000000000004e-124 < b < 1e-82

   1. Initial program 39.8%

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

   3. Taylor expanded in y5 around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 60.0%

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

   6. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

         \[\leadsto \left(j \cdot \left(i \cdot t + \color{blue}{\left(\mathsf{neg}\left(y0 \cdot y3\right)\right)}\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 40.6

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

   8. Applied rewrites 40.6%

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

   9. Taylor expanded in i around 0

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

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j \cdot \left(y0 \cdot y3\right)\right)\right)} \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

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

          \[\leadsto \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(y0 \cdot y3\right)\right)\right)} \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       3. mul-1-neg N/A

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

       4. lower-*.f64 N/A

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

       5. associate-*r* N/A

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

       6. lower-*.f64 N/A

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

       7. mul-1-neg N/A

          \[\leadsto \left(j \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y3\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       8. lower-neg.f64 70.6

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

   11. Applied rewrites 70.6%

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

   if 1e-82 < b < 3.00000000000000018e34

   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 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. lower-*.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. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 36.6%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\mathsf{fma}\left(x, c, -1 \cdot \left(k \cdot y5\right)\right)} \cdot y2\right) \]

      7. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{\mathsf{neg}\left(k \cdot y5\right)}\right) \cdot y2\right) \]

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

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      9. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      11. mul-1-neg N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      12. lower-neg.f64 43.6

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

   8. Applied rewrites 43.6%

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

   if 3.00000000000000018e34 < b < 3.19999999999999993e124

   1. Initial program 44.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 44.3

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

   5. Applied rewrites 44.3%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(a, x, \color{blue}{\left(\mathsf{neg}\left(k\right)\right)} \cdot y4\right)\right) \]

      7. lower-neg.f64 48.6

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

   8. Applied rewrites 48.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+104}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-292}:\\ \;\;\;\;y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-124}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 10^{-82}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(a, x, k \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+75}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y2 \cdot \mathsf{fma}\left(a, -y1, c \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-292}:\\ \;\;\;\;y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-124}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 10^{-82}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(a, x, k \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -8.2e+75)
   (* (* t b) (- (* j y4) (* z a)))
   (if (<= b -1.2e-24)
     (* x (* y2 (fma a (- y1) (* c y0))))
     (if (<= b -1.7e-292)
       (* y2 (* t (fma a y5 (* y4 (- c)))))
       (if (<= b 1.42e-124)
         (* y1 (* a (fma (- x) y2 (* z y3))))
         (if (<= b 1e-82)
           (* y5 (* j (* y0 y3)))
           (if (<= b 3e+34)
             (* y0 (* y2 (fma x c (* k (- y5)))))
             (if (<= b 3.2e+124)
               (* b (* y (fma a x (* k (- y4)))))
               (* a (* b (- (* x y) (* z t))))))))))))

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 <= -8.2e+75) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (b <= -1.2e-24) {
		tmp = x * (y2 * fma(a, -y1, (c * y0)));
	} else if (b <= -1.7e-292) {
		tmp = y2 * (t * fma(a, y5, (y4 * -c)));
	} else if (b <= 1.42e-124) {
		tmp = y1 * (a * fma(-x, y2, (z * y3)));
	} else if (b <= 1e-82) {
		tmp = y5 * (j * (y0 * y3));
	} else if (b <= 3e+34) {
		tmp = y0 * (y2 * fma(x, c, (k * -y5)));
	} else if (b <= 3.2e+124) {
		tmp = b * (y * fma(a, x, (k * -y4)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	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 <= -8.2e+75)
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * a)));
	elseif (b <= -1.2e-24)
		tmp = Float64(x * Float64(y2 * fma(a, Float64(-y1), Float64(c * y0))));
	elseif (b <= -1.7e-292)
		tmp = Float64(y2 * Float64(t * fma(a, y5, Float64(y4 * Float64(-c)))));
	elseif (b <= 1.42e-124)
		tmp = Float64(y1 * Float64(a * fma(Float64(-x), y2, Float64(z * y3))));
	elseif (b <= 1e-82)
		tmp = Float64(y5 * Float64(j * Float64(y0 * y3)));
	elseif (b <= 3e+34)
		tmp = Float64(y0 * Float64(y2 * fma(x, c, Float64(k * Float64(-y5)))));
	elseif (b <= 3.2e+124)
		tmp = Float64(b * Float64(y * fma(a, x, Float64(k * Float64(-y4)))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	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, -8.2e+75], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-24], N[(x * N[(y2 * N[(a * (-y1) + N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-292], N[(y2 * N[(t * N[(a * y5 + N[(y4 * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.42e-124], N[(y1 * N[(a * N[((-x) * y2 + N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-82], N[(y5 * N[(j * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+34], N[(y0 * N[(y2 * N[(x * c + N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+124], N[(b * N[(y * N[(a * x + N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -8.1999999999999997e75

   1. Initial program 17.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

   6. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 52.0

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

   8. Applied rewrites 52.0%

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

   if -8.1999999999999997e75 < b < -1.1999999999999999e-24

   1. Initial program 23.7%

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

   3. Taylor expanded in 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. lower-*.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. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{\mathsf{fma}\left(a, -1 \cdot y1, c \cdot y0\right)} \cdot y2\right) \]

      9. mul-1-neg N/A

         \[\leadsto x \cdot \left(\mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(y1\right)}, c \cdot y0\right) \cdot y2\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(y1\right)}, c \cdot y0\right) \cdot y2\right) \]

      11. *-commutative N/A

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a, \mathsf{neg}\left(y1\right), \color{blue}{y0 \cdot c}\right) \cdot y2\right) \]

      12. lower-*.f64 48.4

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

   8. Applied rewrites 48.4%

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

   if -1.1999999999999999e-24 < b < -1.70000000000000009e-292

   1. Initial program 29.4%

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

   3. Taylor expanded in 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. lower-*.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. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 45.8%

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

   6. Taylor expanded in t around inf

      \[\leadsto y2 \cdot \color{blue}{\left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 + \left(\mathsf{neg}\left(c \cdot y4\right)\right)\right)}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(a, y5, \mathsf{neg}\left(c \cdot y4\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \mathsf{neg}\left(\color{blue}{y4 \cdot c}\right)\right)\right) \]

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

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \color{blue}{y4 \cdot \left(\mathsf{neg}\left(c\right)\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \color{blue}{\left(-1 \cdot c\right)}\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, \color{blue}{y4 \cdot \left(-1 \cdot c\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \color{blue}{\left(\mathsf{neg}\left(c\right)\right)}\right)\right) \]

      9. lower-neg.f64 48.1

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

   8. Applied rewrites 48.1%

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

   if -1.70000000000000009e-292 < b < 1.42000000000000004e-124

   1. Initial program 45.6%

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

   3. Taylor expanded in y1 around inf

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

      1. lower-*.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. lower-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. Applied rewrites 52.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 53.5

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

   8. Applied rewrites 53.5%

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

   if 1.42000000000000004e-124 < b < 1e-82

   1. Initial program 39.8%

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

   3. Taylor expanded in y5 around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 60.0%

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

   6. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

         \[\leadsto \left(j \cdot \left(i \cdot t + \color{blue}{\left(\mathsf{neg}\left(y0 \cdot y3\right)\right)}\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 40.6

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

   8. Applied rewrites 40.6%

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

   9. Taylor expanded in i around 0

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

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j \cdot \left(y0 \cdot y3\right)\right)\right)} \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

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

          \[\leadsto \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(y0 \cdot y3\right)\right)\right)} \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       3. mul-1-neg N/A

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

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(-1 \cdot \left(y0 \cdot y3\right)\right)\right)} \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \left(j \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot y3\right)}\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       6. lower-*.f64 N/A

          \[\leadsto \left(j \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot y3\right)}\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       7. mul-1-neg N/A

          \[\leadsto \left(j \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y3\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       8. lower-neg.f64 70.6

          \[\leadsto \left(j \cdot \left(\color{blue}{\left(-y0\right)} \cdot y3\right)\right) \cdot \left(-y5\right) \]

   11. Applied rewrites 70.6%

       \[\leadsto \color{blue}{\left(j \cdot \left(\left(-y0\right) \cdot y3\right)\right)} \cdot \left(-y5\right) \]

   if 1e-82 < b < 3.00000000000000018e34

   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 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. lower-*.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. lower--.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(\color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y2 \cdot \left(\left(\color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{t \cdot \left(c \cdot y4 - a \cdot y5\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

   5. Applied rewrites 36.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right) \cdot y2\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right) \cdot y2\right)} \]

      4. +-commutative N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)} \cdot y2\right) \]

      5. *-commutative N/A

         \[\leadsto y0 \cdot \left(\left(\color{blue}{x \cdot c} + -1 \cdot \left(k \cdot y5\right)\right) \cdot y2\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\mathsf{fma}\left(x, c, -1 \cdot \left(k \cdot y5\right)\right)} \cdot y2\right) \]

      7. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{\mathsf{neg}\left(k \cdot y5\right)}\right) \cdot y2\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      9. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      11. mul-1-neg N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      12. lower-neg.f64 43.6

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(-y5\right)}\right) \cdot y2\right) \]

   8. Applied rewrites 43.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right) \cdot y2\right)} \]

   if 3.00000000000000018e34 < b < 3.19999999999999993e124

   1. Initial program 44.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 44.3

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 44.3%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(a, x, -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(a, x, \color{blue}{\left(-1 \cdot k\right) \cdot y4}\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(a, x, \color{blue}{\left(-1 \cdot k\right) \cdot y4}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(a, x, \color{blue}{\left(\mathsf{neg}\left(k\right)\right)} \cdot y4\right)\right) \]

      7. lower-neg.f64 48.6

         \[\leadsto b \cdot \left(y \cdot \mathsf{fma}\left(a, x, \color{blue}{\left(-k\right)} \cdot y4\right)\right) \]

   8. Applied rewrites 48.6%

      \[\leadsto b \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(a, x, \left(-k\right) \cdot y4\right)\right)} \]

   if 3.19999999999999993e124 < b

   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 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 64.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 60.0

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 60.0%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+75}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y2 \cdot \mathsf{fma}\left(a, -y1, c \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-292}:\\ \;\;\;\;y2 \cdot \left(t \cdot \mathsf{fma}\left(a, y5, y4 \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-124}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 10^{-82}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+34}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(a, x, k \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.4% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+162}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(k, -y4, x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-50}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot a\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -8.8e+162)
   (* b (* y (fma k (- y4) (* x a))))
   (if (<= y 1.32e-50)
     (+
      (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
      (* (* t a) (* y2 y5)))
     (* c (* y (fma i (- x) (* y3 y4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -8.8e+162) {
		tmp = b * (y * fma(k, -y4, (x * a)));
	} else if (y <= 1.32e-50) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + ((t * a) * (y2 * y5));
	} else {
		tmp = c * (y * fma(i, -x, (y3 * 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 (y <= -8.8e+162)
		tmp = Float64(b * Float64(y * fma(k, Float64(-y4), Float64(x * a))));
	elseif (y <= 1.32e-50)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(t * a) * Float64(y2 * y5)));
	else
		tmp = Float64(c * Float64(y * fma(i, Float64(-x), Float64(y3 * y4))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -8.8e+162], N[(b * N[(y * N[(k * (-y4) + N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e-50], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(i * (-x) + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.8000000000000007e162

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 77.8%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      4. mul-1-neg N/A

         \[\leadsto b \cdot \left(\left(\color{blue}{\left(\mathsf{neg}\left(k \cdot y4\right)\right)} + a \cdot x\right) \cdot y\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \left(\left(\color{blue}{k \cdot \left(\mathsf{neg}\left(y4\right)\right)} + a \cdot x\right) \cdot y\right) \]

      6. mul-1-neg N/A

         \[\leadsto b \cdot \left(\left(k \cdot \color{blue}{\left(-1 \cdot y4\right)} + a \cdot x\right) \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot y4, a \cdot x\right)} \cdot y\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(k, \color{blue}{\mathsf{neg}\left(y4\right)}, a \cdot x\right) \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{fma}\left(k, \color{blue}{\mathsf{neg}\left(y4\right)}, a \cdot x\right) \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot \left(\mathsf{fma}\left(k, \mathsf{neg}\left(y4\right), \color{blue}{x \cdot a}\right) \cdot y\right) \]

      11. lower-*.f64 61.7

          \[\leadsto b \cdot \left(\mathsf{fma}\left(k, -y4, \color{blue}{x \cdot a}\right) \cdot y\right) \]

   8. Applied rewrites 61.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(k, -y4, x \cdot a\right) \cdot y\right)} \]

   if -8.8000000000000007e162 < y < 1.31999999999999989e-50

   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 y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y5 \cdot \left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. sub-neg N/A

         \[\leadsto y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto y5 \cdot \left(\color{blue}{i \cdot \left(\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(i \cdot \left(\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. remove-double-neg N/A

         \[\leadsto y5 \cdot \left(i \cdot \left(\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)\right) + \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y5 \cdot \color{blue}{\mathsf{fma}\left(i, \mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right), a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)}, a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lower--.f64 N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\color{blue}{\left(j \cdot t - k \cdot y\right)}\right), a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. *-commutative N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(\color{blue}{t \cdot j} - k \cdot y\right)\right), a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      11. lower-*.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(\color{blue}{t \cdot j} - k \cdot y\right)\right), a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - \color{blue}{k \cdot y}\right)\right), a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - k \cdot y\right)\right), \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      14. lower--.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - k \cdot y\right)\right), a \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      15. lower-*.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - k \cdot y\right)\right), a \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      16. *-commutative N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - k \cdot y\right)\right), a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      17. lower-*.f64 44.1

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Applied rewrites 44.1%

      \[\leadsto \color{blue}{y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y2 \cdot y5\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y2 \cdot y5\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot t\right)} \cdot \left(y2 \cdot y5\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-*.f64 45.7

         \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\left(y2 \cdot y5\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   8. Applied rewrites 45.7%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y2 \cdot y5\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if 1.31999999999999989e-50 < y

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 52.0%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right) \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right) \cdot y\right)} \]

      4. mul-1-neg N/A

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(\mathsf{neg}\left(i \cdot x\right)\right)} + y3 \cdot y4\right) \cdot y\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(\mathsf{neg}\left(x\right)\right)} + y3 \cdot y4\right) \cdot y\right) \]

      6. mul-1-neg N/A

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(-1 \cdot x\right)} + y3 \cdot y4\right) \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto c \cdot \left(\color{blue}{\mathsf{fma}\left(i, -1 \cdot x, y3 \cdot y4\right)} \cdot y\right) \]

      8. mul-1-neg N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right) \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right) \cdot y\right) \]

      10. lower-*.f64 48.3

          \[\leadsto c \cdot \left(\mathsf{fma}\left(i, -x, \color{blue}{y3 \cdot y4}\right) \cdot y\right) \]

   8. Applied rewrites 48.3%

      \[\leadsto \color{blue}{c \cdot \left(\mathsf{fma}\left(i, -x, y3 \cdot y4\right) \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+162}:\\ \;\;\;\;b \cdot \left(y \cdot \mathsf{fma}\left(k, -y4, x \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-50}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot a\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.3% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-129}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-303}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, a \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-112}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+168}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (fma i (- x) (* y3 y4))))))
   (if (<= y -1.02e+47)
     t_1
     (if (<= y -4e-129)
       (* y1 (* a (fma (- x) y2 (* z y3))))
       (if (<= y 7.2e-303)
         (* y2 (fma k (- (* y1 y4) (* y0 y5)) (* a (* t y5))))
         (if (<= y 1.25e-112)
           (* y0 (* y2 (fma x c (* k (- y5)))))
           (if (<= y 1.25e+168) (* (* b y4) (- (* t j) (* y 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 = c * (y * fma(i, -x, (y3 * y4)));
	double tmp;
	if (y <= -1.02e+47) {
		tmp = t_1;
	} else if (y <= -4e-129) {
		tmp = y1 * (a * fma(-x, y2, (z * y3)));
	} else if (y <= 7.2e-303) {
		tmp = y2 * fma(k, ((y1 * y4) - (y0 * y5)), (a * (t * y5)));
	} else if (y <= 1.25e-112) {
		tmp = y0 * (y2 * fma(x, c, (k * -y5)));
	} else if (y <= 1.25e+168) {
		tmp = (b * y4) * ((t * j) - (y * 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(c * Float64(y * fma(i, Float64(-x), Float64(y3 * y4))))
	tmp = 0.0
	if (y <= -1.02e+47)
		tmp = t_1;
	elseif (y <= -4e-129)
		tmp = Float64(y1 * Float64(a * fma(Float64(-x), y2, Float64(z * y3))));
	elseif (y <= 7.2e-303)
		tmp = Float64(y2 * fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(a * Float64(t * y5))));
	elseif (y <= 1.25e-112)
		tmp = Float64(y0 * Float64(y2 * fma(x, c, Float64(k * Float64(-y5)))));
	elseif (y <= 1.25e+168)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	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[(c * N[(y * N[(i * (-x) + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+47], t$95$1, If[LessEqual[y, -4e-129], N[(y1 * N[(a * N[((-x) * y2 + N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-303], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-112], N[(y0 * N[(y2 * N[(x * c + N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+168], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.0199999999999999e47 or 1.24999999999999992e168 < y

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 64.2%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right) \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right) \cdot y\right)} \]

      4. mul-1-neg N/A

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(\mathsf{neg}\left(i \cdot x\right)\right)} + y3 \cdot y4\right) \cdot y\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(\mathsf{neg}\left(x\right)\right)} + y3 \cdot y4\right) \cdot y\right) \]

      6. mul-1-neg N/A

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(-1 \cdot x\right)} + y3 \cdot y4\right) \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto c \cdot \left(\color{blue}{\mathsf{fma}\left(i, -1 \cdot x, y3 \cdot y4\right)} \cdot y\right) \]

      8. mul-1-neg N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right) \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right) \cdot y\right) \]

      10. lower-*.f64 56.0

          \[\leadsto c \cdot \left(\mathsf{fma}\left(i, -x, \color{blue}{y3 \cdot y4}\right) \cdot y\right) \]

   8. Applied rewrites 56.0%

      \[\leadsto \color{blue}{c \cdot \left(\mathsf{fma}\left(i, -x, y3 \cdot y4\right) \cdot y\right)} \]

   if -1.0199999999999999e47 < y < -3.9999999999999997e-129

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. lower-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. Applied rewrites 41.6%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 53.6

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 53.6%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   if -3.9999999999999997e-129 < y < 7.1999999999999996e-303

   1. Initial program 38.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{y5 \cdot \left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y5 \cdot \left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. sub-neg N/A

         \[\leadsto y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot t - k \cdot y\right)\right) + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto y5 \cdot \left(\color{blue}{i \cdot \left(\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. mul-1-neg N/A

         \[\leadsto y5 \cdot \left(i \cdot \left(\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. remove-double-neg N/A

         \[\leadsto y5 \cdot \left(i \cdot \left(\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)\right) + \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y5 \cdot \color{blue}{\mathsf{fma}\left(i, \mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right), a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(\left(j \cdot t - k \cdot y\right)\right)}, a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lower--.f64 N/A

         \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\color{blue}{\left(j \cdot t - k \cdot y\right)}\right), a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. *-commutative N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(\color{blue}{t \cdot j} - k \cdot y\right)\right), a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      11. lower-*.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(\color{blue}{t \cdot j} - k \cdot y\right)\right), a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - \color{blue}{k \cdot y}\right)\right), a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - k \cdot y\right)\right), \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      14. lower--.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - k \cdot y\right)\right), a \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      15. lower-*.f64 N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - k \cdot y\right)\right), a \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      16. *-commutative N/A

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, \mathsf{neg}\left(\left(t \cdot j - k \cdot y\right)\right), a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      17. lower-*.f64 46.9

          \[\leadsto y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), a \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Applied rewrites 46.9%

      \[\leadsto \color{blue}{y5 \cdot \mathsf{fma}\left(i, -\left(t \cdot j - k \cdot y\right), a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(a \cdot \left(t \cdot y5\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(a \cdot \left(t \cdot y5\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + a \cdot \left(t \cdot y5\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, a \cdot \left(t \cdot y5\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, a \cdot \left(t \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4} - y0 \cdot y5, a \cdot \left(t \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, a \cdot \left(t \cdot y5\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{a \cdot \left(t \cdot y5\right)}\right) \]

      8. lower-*.f64 47.6

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, a \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

   8. Applied rewrites 47.6%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, a \cdot \left(t \cdot y5\right)\right)} \]

   if 7.1999999999999996e-303 < y < 1.25000000000000011e-112

   1. Initial program 39.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower--.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(\color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y2 \cdot \left(\left(\color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{t \cdot \left(c \cdot y4 - a \cdot y5\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

   5. Applied rewrites 39.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right) \cdot y2\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right) \cdot y2\right)} \]

      4. +-commutative N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)} \cdot y2\right) \]

      5. *-commutative N/A

         \[\leadsto y0 \cdot \left(\left(\color{blue}{x \cdot c} + -1 \cdot \left(k \cdot y5\right)\right) \cdot y2\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\mathsf{fma}\left(x, c, -1 \cdot \left(k \cdot y5\right)\right)} \cdot y2\right) \]

      7. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{\mathsf{neg}\left(k \cdot y5\right)}\right) \cdot y2\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      9. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      11. mul-1-neg N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      12. lower-neg.f64 44.8

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(-y5\right)}\right) \cdot y2\right) \]

   8. Applied rewrites 44.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right) \cdot y2\right)} \]

   if 1.25000000000000011e-112 < y < 1.24999999999999992e168

   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 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. lower-*.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. lower--.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.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. lower-*.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. lower--.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. lower-*.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. lower-*.f64 44.5

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 44.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot y4\right) \cdot \left(j \cdot t - k \cdot y\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot y4\right) \cdot \left(j \cdot t - k \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot y4\right)} \cdot \left(j \cdot t - k \cdot y\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(b \cdot y4\right) \cdot \left(\color{blue}{j \cdot t} - k \cdot y\right) \]

      6. lower-*.f64 42.9

         \[\leadsto \left(b \cdot y4\right) \cdot \left(j \cdot t - \color{blue}{k \cdot y}\right) \]

   8. Applied rewrites 42.9%

      \[\leadsto \color{blue}{\left(b \cdot y4\right) \cdot \left(j \cdot t - k \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-129}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-303}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, a \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-112}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+168}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.8% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-300}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t)))))
        (t_2 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= t -5e-10)
     t_1
     (if (<= t -2.25e-300)
       (* a (* x (- (* y b) (* y1 y2))))
       (if (<= t 1.65e+78) t_2 (if (<= t 3.6e+257) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (t <= -5e-10) {
		tmp = t_1;
	} else if (t <= -2.25e-300) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (t <= 1.65e+78) {
		tmp = t_2;
	} else if (t <= 3.6e+257) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    t_2 = a * (y5 * ((t * y2) - (y * y3)))
    if (t <= (-5d-10)) then
        tmp = t_1
    else if (t <= (-2.25d-300)) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else if (t <= 1.65d+78) then
        tmp = t_2
    else if (t <= 3.6d+257) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (t <= -5e-10) {
		tmp = t_1;
	} else if (t <= -2.25e-300) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (t <= 1.65e+78) {
		tmp = t_2;
	} else if (t <= 3.6e+257) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	t_2 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if t <= -5e-10:
		tmp = t_1
	elif t <= -2.25e-300:
		tmp = a * (x * ((y * b) - (y1 * y2)))
	elif t <= 1.65e+78:
		tmp = t_2
	elif t <= 3.6e+257:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (t <= -5e-10)
		tmp = t_1;
	elseif (t <= -2.25e-300)
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (t <= 1.65e+78)
		tmp = t_2;
	elseif (t <= 3.6e+257)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	t_2 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (t <= -5e-10)
		tmp = t_1;
	elseif (t <= -2.25e-300)
		tmp = a * (x * ((y * b) - (y1 * y2)));
	elseif (t <= 1.65e+78)
		tmp = t_2;
	elseif (t <= 3.6e+257)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-10], t$95$1, If[LessEqual[t, -2.25e-300], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+78], t$95$2, If[LessEqual[t, 3.6e+257], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.00000000000000031e-10 or 1.65e78 < t < 3.59999999999999984e257

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 45.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 44.8

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 44.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -5.00000000000000031e-10 < t < -2.25e-300

   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 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 43.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(y1 \cdot y2\right) + b \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(y1 \cdot y2\right) + b \cdot y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(x \cdot \color{blue}{\left(b \cdot y + -1 \cdot \left(y1 \cdot y2\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(x \cdot \left(b \cdot y + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y2\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto a \cdot \left(x \cdot \color{blue}{\left(b \cdot y - y1 \cdot y2\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto a \cdot \left(x \cdot \color{blue}{\left(b \cdot y - y1 \cdot y2\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(x \cdot \left(\color{blue}{b \cdot y} - y1 \cdot y2\right)\right) \]

      7. lower-*.f64 39.0

         \[\leadsto a \cdot \left(x \cdot \left(b \cdot y - \color{blue}{y1 \cdot y2}\right)\right) \]

   8. Applied rewrites 39.0%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y - y1 \cdot y2\right)\right)} \]

   if -2.25e-300 < t < 1.65e78 or 3.59999999999999984e257 < t

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 40.9%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   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. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. lower-*.f64 42.5

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   8. Applied rewrites 42.5%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-300}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+78}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+257}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 22.1% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-39}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-136}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -2.4e+125)
   (* a (* (* x y) b))
   (if (<= y -5.8e-39)
     (* y3 (* j (* y0 y5)))
     (if (<= y -5.4e-136)
       (* y1 (* a (* z y3)))
       (if (<= y 2.25e+35) (* a (* b (* z (- t)))) (* a (* x (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -2.4e+125) {
		tmp = a * ((x * y) * b);
	} else if (y <= -5.8e-39) {
		tmp = y3 * (j * (y0 * y5));
	} else if (y <= -5.4e-136) {
		tmp = y1 * (a * (z * y3));
	} else if (y <= 2.25e+35) {
		tmp = a * (b * (z * -t));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-2.4d+125)) then
        tmp = a * ((x * y) * b)
    else if (y <= (-5.8d-39)) then
        tmp = y3 * (j * (y0 * y5))
    else if (y <= (-5.4d-136)) then
        tmp = y1 * (a * (z * y3))
    else if (y <= 2.25d+35) then
        tmp = a * (b * (z * -t))
    else
        tmp = a * (x * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -2.4e+125) {
		tmp = a * ((x * y) * b);
	} else if (y <= -5.8e-39) {
		tmp = y3 * (j * (y0 * y5));
	} else if (y <= -5.4e-136) {
		tmp = y1 * (a * (z * y3));
	} else if (y <= 2.25e+35) {
		tmp = a * (b * (z * -t));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -2.4e+125:
		tmp = a * ((x * y) * b)
	elif y <= -5.8e-39:
		tmp = y3 * (j * (y0 * y5))
	elif y <= -5.4e-136:
		tmp = y1 * (a * (z * y3))
	elif y <= 2.25e+35:
		tmp = a * (b * (z * -t))
	else:
		tmp = a * (x * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -2.4e+125)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y <= -5.8e-39)
		tmp = Float64(y3 * Float64(j * Float64(y0 * y5)));
	elseif (y <= -5.4e-136)
		tmp = Float64(y1 * Float64(a * Float64(z * y3)));
	elseif (y <= 2.25e+35)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	else
		tmp = Float64(a * Float64(x * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -2.4e+125)
		tmp = a * ((x * y) * b);
	elseif (y <= -5.8e-39)
		tmp = y3 * (j * (y0 * y5));
	elseif (y <= -5.4e-136)
		tmp = y1 * (a * (z * y3));
	elseif (y <= 2.25e+35)
		tmp = a * (b * (z * -t));
	else
		tmp = a * (x * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -2.4e+125], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-39], N[(y3 * N[(j * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.4e-136], N[(y1 * N[(a * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+35], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.4e125

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 48.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 46.2

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 46.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 46.4

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Applied rewrites 46.4%

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   if -2.4e125 < y < -5.79999999999999975e-39

   1. Initial program 15.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y5}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \color{blue}{\left(-1 \cdot y5\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \left(-1 \cdot y5\right)} \]

   5. Applied rewrites 40.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right) \cdot \left(-y5\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \color{blue}{\left(k \cdot y2 + -1 \cdot \left(j \cdot y3\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 + \color{blue}{\left(\mathsf{neg}\left(j \cdot y3\right)\right)}\right)\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 + \left(\mathsf{neg}\left(j \cdot y3\right)\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 + \color{blue}{-1 \cdot \left(j \cdot y3\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right) \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)}\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right)} \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 + -1 \cdot \left(j \cdot y3\right)\right)}\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 + \color{blue}{\left(\mathsf{neg}\left(j \cdot y3\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) \]

      17. lower-*.f64 35.0

          \[\leadsto -\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \]

   8. Applied rewrites 35.0%

      \[\leadsto \color{blue}{-\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   9. Taylor expanded in k around 0

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

       2. *-commutative N/A

          \[\leadsto \left(j \cdot y0\right) \cdot \color{blue}{\left(y5 \cdot y3\right)} \]

       3. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\left(j \cdot y0\right) \cdot y5\right) \cdot y3} \]

       4. associate-*r* N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(y0 \cdot y5\right)\right)} \cdot y3 \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(y0 \cdot y5\right)\right) \cdot y3} \]

       6. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(y0 \cdot y5\right)\right)} \cdot y3 \]

       7. *-commutative N/A

          \[\leadsto \left(j \cdot \color{blue}{\left(y5 \cdot y0\right)}\right) \cdot y3 \]

       8. lower-*.f64 38.3

          \[\leadsto \left(j \cdot \color{blue}{\left(y5 \cdot y0\right)}\right) \cdot y3 \]

   11. Applied rewrites 38.3%

       \[\leadsto \color{blue}{\left(j \cdot \left(y5 \cdot y0\right)\right) \cdot y3} \]

   if -5.79999999999999975e-39 < y < -5.3999999999999997e-136

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower-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. Applied rewrites 34.1%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 67.2

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 67.2%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

       3. lower-*.f64 54.5

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   11. Applied rewrites 54.5%

       \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(z \cdot y3\right)\right)} \]

   if -5.3999999999999997e-136 < y < 2.2499999999999998e35

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 39.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 26.5

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 26.5%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}\right) \]

       4. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \left(t \cdot z\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(\mathsf{neg}\left(t \cdot z\right)\right)}\right) \]

       6. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(t \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}\right) \]

       7. mul-1-neg N/A

          \[\leadsto a \cdot \left(b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

       8. lower-*.f64 N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot z\right)\right)}\right) \]

       9. mul-1-neg N/A

          \[\leadsto a \cdot \left(b \cdot \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right) \]

       10. lower-neg.f64 25.5

           \[\leadsto a \cdot \left(b \cdot \left(t \cdot \color{blue}{\left(-z\right)}\right)\right) \]

   11. Applied rewrites 25.5%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(t \cdot \left(-z\right)\right)\right)} \]

   if 2.2499999999999998e35 < y

   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 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 35.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 23.5

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 23.5%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 22.0

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Applied rewrites 22.0%

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. lower-*.f64 28.6

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied rewrites 28.6%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-39}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-136}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.4% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-289}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-112}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (fma i (- x) (* y3 y4))))))
   (if (<= y -1.02e+47)
     t_1
     (if (<= y -2.1e-289)
       (* y1 (* a (fma (- x) y2 (* z y3))))
       (if (<= y 3.1e-112) (* y0 (* y2 (fma x c (* k (- 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 = c * (y * fma(i, -x, (y3 * y4)));
	double tmp;
	if (y <= -1.02e+47) {
		tmp = t_1;
	} else if (y <= -2.1e-289) {
		tmp = y1 * (a * fma(-x, y2, (z * y3)));
	} else if (y <= 3.1e-112) {
		tmp = y0 * (y2 * fma(x, c, (k * -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(c * Float64(y * fma(i, Float64(-x), Float64(y3 * y4))))
	tmp = 0.0
	if (y <= -1.02e+47)
		tmp = t_1;
	elseif (y <= -2.1e-289)
		tmp = Float64(y1 * Float64(a * fma(Float64(-x), y2, Float64(z * y3))));
	elseif (y <= 3.1e-112)
		tmp = Float64(y0 * Float64(y2 * fma(x, c, Float64(k * Float64(-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[(c * N[(y * N[(i * (-x) + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+47], t$95$1, If[LessEqual[y, -2.1e-289], N[(y1 * N[(a * N[((-x) * y2 + N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-112], N[(y0 * N[(y2 * N[(x * c + N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0199999999999999e47 or 3.0999999999999998e-112 < y

   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 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. lower-*.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 55.4%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right) \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right) \cdot y\right)} \]

      4. mul-1-neg N/A

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(\mathsf{neg}\left(i \cdot x\right)\right)} + y3 \cdot y4\right) \cdot y\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(\mathsf{neg}\left(x\right)\right)} + y3 \cdot y4\right) \cdot y\right) \]

      6. mul-1-neg N/A

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(-1 \cdot x\right)} + y3 \cdot y4\right) \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto c \cdot \left(\color{blue}{\mathsf{fma}\left(i, -1 \cdot x, y3 \cdot y4\right)} \cdot y\right) \]

      8. mul-1-neg N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right) \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right) \cdot y\right) \]

      10. lower-*.f64 47.6

          \[\leadsto c \cdot \left(\mathsf{fma}\left(i, -x, \color{blue}{y3 \cdot y4}\right) \cdot y\right) \]

   8. Applied rewrites 47.6%

      \[\leadsto \color{blue}{c \cdot \left(\mathsf{fma}\left(i, -x, y3 \cdot y4\right) \cdot y\right)} \]

   if -1.0199999999999999e47 < y < -2.0999999999999998e-289

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower-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. Applied rewrites 43.3%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 44.1

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 44.1%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   if -2.0999999999999998e-289 < y < 3.0999999999999998e-112

   1. Initial program 44.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. lower--.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(\color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y2 \cdot \left(\left(\color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{t \cdot \left(c \cdot y4 - a \cdot y5\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

   5. Applied rewrites 39.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right) \cdot y2\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right) \cdot y2\right)} \]

      4. +-commutative N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)} \cdot y2\right) \]

      5. *-commutative N/A

         \[\leadsto y0 \cdot \left(\left(\color{blue}{x \cdot c} + -1 \cdot \left(k \cdot y5\right)\right) \cdot y2\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\mathsf{fma}\left(x, c, -1 \cdot \left(k \cdot y5\right)\right)} \cdot y2\right) \]

      7. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{\mathsf{neg}\left(k \cdot y5\right)}\right) \cdot y2\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      9. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      11. mul-1-neg N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      12. lower-neg.f64 41.5

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(-y5\right)}\right) \cdot y2\right) \]

   8. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right) \cdot y2\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-289}:\\ \;\;\;\;y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-112}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.1% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-19}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-112}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (fma i (- x) (* y3 y4))))))
   (if (<= y -1e+57)
     t_1
     (if (<= y -1.35e-19)
       (* j (* y1 (fma (- y3) y4 (* x i))))
       (if (<= y 3.1e-112) (* y0 (* y2 (fma x c (* k (- 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 = c * (y * fma(i, -x, (y3 * y4)));
	double tmp;
	if (y <= -1e+57) {
		tmp = t_1;
	} else if (y <= -1.35e-19) {
		tmp = j * (y1 * fma(-y3, y4, (x * i)));
	} else if (y <= 3.1e-112) {
		tmp = y0 * (y2 * fma(x, c, (k * -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(c * Float64(y * fma(i, Float64(-x), Float64(y3 * y4))))
	tmp = 0.0
	if (y <= -1e+57)
		tmp = t_1;
	elseif (y <= -1.35e-19)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))));
	elseif (y <= 3.1e-112)
		tmp = Float64(y0 * Float64(y2 * fma(x, c, Float64(k * Float64(-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[(c * N[(y * N[(i * (-x) + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+57], t$95$1, If[LessEqual[y, -1.35e-19], N[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-112], N[(y0 * N[(y2 * N[(x * c + N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000005e57 or 3.0999999999999998e-112 < y

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 56.1%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right) \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right) \cdot y\right)} \]

      4. mul-1-neg N/A

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(\mathsf{neg}\left(i \cdot x\right)\right)} + y3 \cdot y4\right) \cdot y\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(\mathsf{neg}\left(x\right)\right)} + y3 \cdot y4\right) \cdot y\right) \]

      6. mul-1-neg N/A

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(-1 \cdot x\right)} + y3 \cdot y4\right) \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto c \cdot \left(\color{blue}{\mathsf{fma}\left(i, -1 \cdot x, y3 \cdot y4\right)} \cdot y\right) \]

      8. mul-1-neg N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right) \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right) \cdot y\right) \]

      10. lower-*.f64 47.5

          \[\leadsto c \cdot \left(\mathsf{fma}\left(i, -x, \color{blue}{y3 \cdot y4}\right) \cdot y\right) \]

   8. Applied rewrites 47.5%

      \[\leadsto \color{blue}{c \cdot \left(\mathsf{fma}\left(i, -x, y3 \cdot y4\right) \cdot y\right)} \]

   if -1.00000000000000005e57 < y < -1.35e-19

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. lower-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. Applied rewrites 47.3%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y4} + i \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y4, i \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y4, i \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y4, i \cdot x\right)\right) \]

      7. lower-*.f64 59.5

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, \color{blue}{i \cdot x}\right)\right) \]

   8. Applied rewrites 59.5%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -1.35e-19 < y < 3.0999999999999998e-112

   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 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. lower-*.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. lower--.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(\color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y2 \cdot \left(\left(\color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{t \cdot \left(c \cdot y4 - a \cdot y5\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right) \]

   5. Applied rewrites 44.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right) \cdot y2\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right) \cdot y2\right)} \]

      4. +-commutative N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)} \cdot y2\right) \]

      5. *-commutative N/A

         \[\leadsto y0 \cdot \left(\left(\color{blue}{x \cdot c} + -1 \cdot \left(k \cdot y5\right)\right) \cdot y2\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\mathsf{fma}\left(x, c, -1 \cdot \left(k \cdot y5\right)\right)} \cdot y2\right) \]

      7. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{\mathsf{neg}\left(k \cdot y5\right)}\right) \cdot y2\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      9. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, \color{blue}{k \cdot \left(-1 \cdot y5\right)}\right) \cdot y2\right) \]

      11. mul-1-neg N/A

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y2\right) \]

      12. lower-neg.f64 34.4

          \[\leadsto y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \color{blue}{\left(-y5\right)}\right) \cdot y2\right) \]

   8. Applied rewrites 34.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right) \cdot y2\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+57}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-19}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-112}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(x, c, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 22.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-39}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-134}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -2.4e+125)
   (* a (* (* x y) b))
   (if (<= y -5.8e-39)
     (* y3 (* j (* y0 y5)))
     (if (<= y -1.15e-134)
       (* y1 (* a (* z y3)))
       (if (<= y 5e-25) (* i (* j (* x y1))) (* a (* x (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -2.4e+125) {
		tmp = a * ((x * y) * b);
	} else if (y <= -5.8e-39) {
		tmp = y3 * (j * (y0 * y5));
	} else if (y <= -1.15e-134) {
		tmp = y1 * (a * (z * y3));
	} else if (y <= 5e-25) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-2.4d+125)) then
        tmp = a * ((x * y) * b)
    else if (y <= (-5.8d-39)) then
        tmp = y3 * (j * (y0 * y5))
    else if (y <= (-1.15d-134)) then
        tmp = y1 * (a * (z * y3))
    else if (y <= 5d-25) then
        tmp = i * (j * (x * y1))
    else
        tmp = a * (x * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -2.4e+125) {
		tmp = a * ((x * y) * b);
	} else if (y <= -5.8e-39) {
		tmp = y3 * (j * (y0 * y5));
	} else if (y <= -1.15e-134) {
		tmp = y1 * (a * (z * y3));
	} else if (y <= 5e-25) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -2.4e+125:
		tmp = a * ((x * y) * b)
	elif y <= -5.8e-39:
		tmp = y3 * (j * (y0 * y5))
	elif y <= -1.15e-134:
		tmp = y1 * (a * (z * y3))
	elif y <= 5e-25:
		tmp = i * (j * (x * y1))
	else:
		tmp = a * (x * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -2.4e+125)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y <= -5.8e-39)
		tmp = Float64(y3 * Float64(j * Float64(y0 * y5)));
	elseif (y <= -1.15e-134)
		tmp = Float64(y1 * Float64(a * Float64(z * y3)));
	elseif (y <= 5e-25)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = Float64(a * Float64(x * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -2.4e+125)
		tmp = a * ((x * y) * b);
	elseif (y <= -5.8e-39)
		tmp = y3 * (j * (y0 * y5));
	elseif (y <= -1.15e-134)
		tmp = y1 * (a * (z * y3));
	elseif (y <= 5e-25)
		tmp = i * (j * (x * y1));
	else
		tmp = a * (x * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -2.4e+125], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-39], N[(y3 * N[(j * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-134], N[(y1 * N[(a * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-25], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.4e125

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 48.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 46.2

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 46.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 46.4

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Applied rewrites 46.4%

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   if -2.4e125 < y < -5.79999999999999975e-39

   1. Initial program 15.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y5}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \color{blue}{\left(-1 \cdot y5\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \left(-1 \cdot y5\right)} \]

   5. Applied rewrites 40.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right) \cdot \left(-y5\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \color{blue}{\left(k \cdot y2 + -1 \cdot \left(j \cdot y3\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 + \color{blue}{\left(\mathsf{neg}\left(j \cdot y3\right)\right)}\right)\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 + \left(\mathsf{neg}\left(j \cdot y3\right)\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 + \color{blue}{-1 \cdot \left(j \cdot y3\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right) \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)}\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right)} \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 + -1 \cdot \left(j \cdot y3\right)\right)}\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 + \color{blue}{\left(\mathsf{neg}\left(j \cdot y3\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) \]

      17. lower-*.f64 35.0

          \[\leadsto -\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \]

   8. Applied rewrites 35.0%

      \[\leadsto \color{blue}{-\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   9. Taylor expanded in k around 0

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

       2. *-commutative N/A

          \[\leadsto \left(j \cdot y0\right) \cdot \color{blue}{\left(y5 \cdot y3\right)} \]

       3. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\left(j \cdot y0\right) \cdot y5\right) \cdot y3} \]

       4. associate-*r* N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(y0 \cdot y5\right)\right)} \cdot y3 \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(y0 \cdot y5\right)\right) \cdot y3} \]

       6. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(y0 \cdot y5\right)\right)} \cdot y3 \]

       7. *-commutative N/A

          \[\leadsto \left(j \cdot \color{blue}{\left(y5 \cdot y0\right)}\right) \cdot y3 \]

       8. lower-*.f64 38.3

          \[\leadsto \left(j \cdot \color{blue}{\left(y5 \cdot y0\right)}\right) \cdot y3 \]

   11. Applied rewrites 38.3%

       \[\leadsto \color{blue}{\left(j \cdot \left(y5 \cdot y0\right)\right) \cdot y3} \]

   if -5.79999999999999975e-39 < y < -1.15e-134

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower-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. Applied rewrites 34.1%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 67.2

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 67.2%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

       3. lower-*.f64 54.5

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   11. Applied rewrites 54.5%

       \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(z \cdot y3\right)\right)} \]

   if -1.15e-134 < y < 4.99999999999999962e-25

   1. Initial program 37.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower-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. Applied rewrites 33.1%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y4} + i \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y4, i \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y4, i \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y4, i \cdot x\right)\right) \]

      7. lower-*.f64 26.2

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, \color{blue}{i \cdot x}\right)\right) \]

   8. Applied rewrites 26.2%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in y3 around 0

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)} \]

       3. lower-*.f64 21.4

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(x \cdot y1\right)}\right) \]

   11. Applied rewrites 21.4%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if 4.99999999999999962e-25 < y

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 35.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 24.5

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 24.5%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 20.2

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Applied rewrites 20.2%

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. lower-*.f64 26.2

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied rewrites 26.2%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-39}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-134}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 20.6% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-96}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+188}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -4.3e-12)
   (* a (* b (* z (- t))))
   (if (<= t 1.36e-96)
     (* y1 (* a (* y2 (- x))))
     (if (<= t 9.4e+188) (* k (* y0 (* y2 (- y5)))) (* a (* z (* y1 y3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -4.3e-12) {
		tmp = a * (b * (z * -t));
	} else if (t <= 1.36e-96) {
		tmp = y1 * (a * (y2 * -x));
	} else if (t <= 9.4e+188) {
		tmp = k * (y0 * (y2 * -y5));
	} else {
		tmp = a * (z * (y1 * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (t <= (-4.3d-12)) then
        tmp = a * (b * (z * -t))
    else if (t <= 1.36d-96) then
        tmp = y1 * (a * (y2 * -x))
    else if (t <= 9.4d+188) then
        tmp = k * (y0 * (y2 * -y5))
    else
        tmp = a * (z * (y1 * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -4.3e-12) {
		tmp = a * (b * (z * -t));
	} else if (t <= 1.36e-96) {
		tmp = y1 * (a * (y2 * -x));
	} else if (t <= 9.4e+188) {
		tmp = k * (y0 * (y2 * -y5));
	} else {
		tmp = a * (z * (y1 * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -4.3e-12:
		tmp = a * (b * (z * -t))
	elif t <= 1.36e-96:
		tmp = y1 * (a * (y2 * -x))
	elif t <= 9.4e+188:
		tmp = k * (y0 * (y2 * -y5))
	else:
		tmp = a * (z * (y1 * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -4.3e-12)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (t <= 1.36e-96)
		tmp = Float64(y1 * Float64(a * Float64(y2 * Float64(-x))));
	elseif (t <= 9.4e+188)
		tmp = Float64(k * Float64(y0 * Float64(y2 * Float64(-y5))));
	else
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -4.3e-12)
		tmp = a * (b * (z * -t));
	elseif (t <= 1.36e-96)
		tmp = y1 * (a * (y2 * -x));
	elseif (t <= 9.4e+188)
		tmp = k * (y0 * (y2 * -y5));
	else
		tmp = a * (z * (y1 * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -4.3e-12], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.36e-96], N[(y1 * N[(a * N[(y2 * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.4e+188], N[(k * N[(y0 * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.29999999999999985e-12

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 51.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 48.5

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 48.5%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}\right) \]

       4. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \left(t \cdot z\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(\mathsf{neg}\left(t \cdot z\right)\right)}\right) \]

       6. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(t \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}\right) \]

       7. mul-1-neg N/A

          \[\leadsto a \cdot \left(b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

       8. lower-*.f64 N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(t \cdot \left(-1 \cdot z\right)\right)}\right) \]

       9. mul-1-neg N/A

          \[\leadsto a \cdot \left(b \cdot \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right) \]

       10. lower-neg.f64 42.9

           \[\leadsto a \cdot \left(b \cdot \left(t \cdot \color{blue}{\left(-z\right)}\right)\right) \]

   11. Applied rewrites 42.9%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(t \cdot \left(-z\right)\right)\right)} \]

   if -4.29999999999999985e-12 < t < 1.36e-96

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower-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. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 33.0

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 33.0%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(-1 \cdot \left(x \cdot y2\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(x \cdot y2\right)\right)}\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(x \cdot \left(\mathsf{neg}\left(y2\right)\right)\right)}\right) \]

       3. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(a \cdot \left(x \cdot \color{blue}{\left(-1 \cdot y2\right)}\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(x \cdot \left(-1 \cdot y2\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(a \cdot \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(y2\right)\right)}\right)\right) \]

       6. lower-neg.f64 27.4

          \[\leadsto y1 \cdot \left(a \cdot \left(x \cdot \color{blue}{\left(-y2\right)}\right)\right) \]

   11. Applied rewrites 27.4%

       \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(x \cdot \left(-y2\right)\right)}\right) \]

   if 1.36e-96 < t < 9.3999999999999995e188

   1. Initial program 35.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y5}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \color{blue}{\left(-1 \cdot y5\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \left(-1 \cdot y5\right)} \]

   5. Applied rewrites 42.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right) \cdot \left(-y5\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \color{blue}{\left(k \cdot y2 + -1 \cdot \left(j \cdot y3\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 + \color{blue}{\left(\mathsf{neg}\left(j \cdot y3\right)\right)}\right)\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 + \left(\mathsf{neg}\left(j \cdot y3\right)\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 + \color{blue}{-1 \cdot \left(j \cdot y3\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right) \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)}\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right)} \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 + -1 \cdot \left(j \cdot y3\right)\right)}\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 + \color{blue}{\left(\mathsf{neg}\left(j \cdot y3\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) \]

      17. lower-*.f64 28.0

          \[\leadsto -\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \]

   8. Applied rewrites 28.0%

      \[\leadsto \color{blue}{-\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{neg}\left(\color{blue}{k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot y2\right)}\right)\right) \]

       4. lower-*.f64 24.5

          \[\leadsto -k \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Applied rewrites 24.5%

       \[\leadsto -\color{blue}{k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)} \]

   if 9.3999999999999995e188 < t

   1. Initial program 14.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. lower-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. Applied rewrites 45.8%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 37.8

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 37.8%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

       4. lower-*.f64 41.8

          \[\leadsto a \cdot \left(\color{blue}{\left(y1 \cdot y3\right)} \cdot z\right) \]

   11. Applied rewrites 41.8%

       \[\leadsto \color{blue}{a \cdot \left(\left(y1 \cdot y3\right) \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-96}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+188}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 21.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.2 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 7 \cdot 10^{-211}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 7.2 \cdot 10^{+176}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -1.2e-81)
   (* a (* z (* y1 y3)))
   (if (<= y3 7e-211)
     (* y (* x (* a b)))
     (if (<= y3 7.2e+176) (* k (* y0 (* y2 (- y5)))) (* y1 (* a (* z y3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -1.2e-81) {
		tmp = a * (z * (y1 * y3));
	} else if (y3 <= 7e-211) {
		tmp = y * (x * (a * b));
	} else if (y3 <= 7.2e+176) {
		tmp = k * (y0 * (y2 * -y5));
	} else {
		tmp = y1 * (a * (z * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-1.2d-81)) then
        tmp = a * (z * (y1 * y3))
    else if (y3 <= 7d-211) then
        tmp = y * (x * (a * b))
    else if (y3 <= 7.2d+176) then
        tmp = k * (y0 * (y2 * -y5))
    else
        tmp = y1 * (a * (z * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -1.2e-81) {
		tmp = a * (z * (y1 * y3));
	} else if (y3 <= 7e-211) {
		tmp = y * (x * (a * b));
	} else if (y3 <= 7.2e+176) {
		tmp = k * (y0 * (y2 * -y5));
	} else {
		tmp = y1 * (a * (z * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -1.2e-81:
		tmp = a * (z * (y1 * y3))
	elif y3 <= 7e-211:
		tmp = y * (x * (a * b))
	elif y3 <= 7.2e+176:
		tmp = k * (y0 * (y2 * -y5))
	else:
		tmp = y1 * (a * (z * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -1.2e-81)
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	elseif (y3 <= 7e-211)
		tmp = Float64(y * Float64(x * Float64(a * b)));
	elseif (y3 <= 7.2e+176)
		tmp = Float64(k * Float64(y0 * Float64(y2 * Float64(-y5))));
	else
		tmp = Float64(y1 * Float64(a * Float64(z * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -1.2e-81)
		tmp = a * (z * (y1 * y3));
	elseif (y3 <= 7e-211)
		tmp = y * (x * (a * b));
	elseif (y3 <= 7.2e+176)
		tmp = k * (y0 * (y2 * -y5));
	else
		tmp = y1 * (a * (z * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -1.2e-81], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 7e-211], N[(y * N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 7.2e+176], N[(k * N[(y0 * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(a * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -1.2e-81

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. lower-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. Applied rewrites 33.8%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 34.3

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 34.3%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

       4. lower-*.f64 31.7

          \[\leadsto a \cdot \left(\color{blue}{\left(y1 \cdot y3\right)} \cdot z\right) \]

   11. Applied rewrites 31.7%

       \[\leadsto \color{blue}{a \cdot \left(\left(y1 \cdot y3\right) \cdot z\right)} \]

   if -1.2e-81 < y3 < 7e-211

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 42.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 29.9

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 29.9%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 18.7

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Applied rewrites 18.7%

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot \left(x \cdot y\right)} \]

       3. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot b\right)} \cdot \left(x \cdot y\right) \]

       4. lift-*.f64 N/A

          \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{\left(x \cdot y\right)} \]

       5. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\left(a \cdot b\right) \cdot x\right) \cdot y} \]

       6. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(a \cdot b\right) \cdot x\right) \cdot y} \]

       7. lower-*.f64 26.3

          \[\leadsto \color{blue}{\left(\left(a \cdot b\right) \cdot x\right)} \cdot y \]

       8. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{\left(a \cdot b\right)} \cdot x\right) \cdot y \]

       9. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(b \cdot a\right)} \cdot x\right) \cdot y \]

       10. lower-*.f64 26.3

           \[\leadsto \left(\color{blue}{\left(b \cdot a\right)} \cdot x\right) \cdot y \]

   13. Applied rewrites 26.3%

       \[\leadsto \color{blue}{\left(\left(b \cdot a\right) \cdot x\right) \cdot y} \]

   if 7e-211 < y3 < 7.19999999999999983e176

   1. Initial program 34.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y5}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \color{blue}{\left(-1 \cdot y5\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \left(-1 \cdot y5\right)} \]

   5. Applied rewrites 45.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right) \cdot \left(-y5\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \color{blue}{\left(k \cdot y2 + -1 \cdot \left(j \cdot y3\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 + \color{blue}{\left(\mathsf{neg}\left(j \cdot y3\right)\right)}\right)\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(y0 \cdot \left(y5 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 + \left(\mathsf{neg}\left(j \cdot y3\right)\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 + \color{blue}{-1 \cdot \left(j \cdot y3\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right) \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)}\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(y0 \cdot y5\right)} \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 + -1 \cdot \left(j \cdot y3\right)\right)}\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 + \color{blue}{\left(\mathsf{neg}\left(j \cdot y3\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\left(y0 \cdot y5\right) \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right) \]

      17. lower-*.f64 25.3

          \[\leadsto -\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \]

   8. Applied rewrites 25.3%

      \[\leadsto \color{blue}{-\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{neg}\left(\color{blue}{k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot y2\right)}\right)\right) \]

       4. lower-*.f64 24.2

          \[\leadsto -k \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Applied rewrites 24.2%

       \[\leadsto -\color{blue}{k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)} \]

   if 7.19999999999999983e176 < y3

   1. Initial program 17.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower-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. Applied rewrites 48.9%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 46.6

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 46.6%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

       3. lower-*.f64 43.8

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   11. Applied rewrites 43.8%

       \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(z \cdot y3\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.2 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 7 \cdot 10^{-211}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq 7.2 \cdot 10^{+176}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -2.9 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(y2 \cdot \left(-x\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -2.9e-113)
   (* a (* x (- (* y b) (* y1 y2))))
   (if (<= y2 7.5e+164)
     (* a (* b (- (* x y) (* z t))))
     (* y1 (* a (* y2 (- x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -2.9e-113) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (y2 <= 7.5e+164) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = y1 * (a * (y2 * -x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-2.9d-113)) then
        tmp = a * (x * ((y * b) - (y1 * y2)))
    else if (y2 <= 7.5d+164) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = y1 * (a * (y2 * -x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -2.9e-113) {
		tmp = a * (x * ((y * b) - (y1 * y2)));
	} else if (y2 <= 7.5e+164) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = y1 * (a * (y2 * -x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -2.9e-113:
		tmp = a * (x * ((y * b) - (y1 * y2)))
	elif y2 <= 7.5e+164:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = y1 * (a * (y2 * -x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -2.9e-113)
		tmp = Float64(a * Float64(x * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y2 <= 7.5e+164)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(y1 * Float64(a * Float64(y2 * Float64(-x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -2.9e-113)
		tmp = a * (x * ((y * b) - (y1 * y2)));
	elseif (y2 <= 7.5e+164)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = y1 * (a * (y2 * -x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -2.9e-113], N[(a * N[(x * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.5e+164], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(a * N[(y2 * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -2.90000000000000004e-113

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 42.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(y1 \cdot y2\right) + b \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(y1 \cdot y2\right) + b \cdot y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(x \cdot \color{blue}{\left(b \cdot y + -1 \cdot \left(y1 \cdot y2\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(x \cdot \left(b \cdot y + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y2\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto a \cdot \left(x \cdot \color{blue}{\left(b \cdot y - y1 \cdot y2\right)}\right) \]

      5. lower--.f64 N/A

         \[\leadsto a \cdot \left(x \cdot \color{blue}{\left(b \cdot y - y1 \cdot y2\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(x \cdot \left(\color{blue}{b \cdot y} - y1 \cdot y2\right)\right) \]

      7. lower-*.f64 35.7

         \[\leadsto a \cdot \left(x \cdot \left(b \cdot y - \color{blue}{y1 \cdot y2}\right)\right) \]

   8. Applied rewrites 35.7%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(b \cdot y - y1 \cdot y2\right)\right)} \]

   if -2.90000000000000004e-113 < y2 < 7.49999999999999976e164

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 43.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 36.0

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 36.0%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 7.49999999999999976e164 < y2

   1. Initial program 18.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.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. lower-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. Applied rewrites 22.5%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 41.8

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 41.8%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(-1 \cdot \left(x \cdot y2\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(x \cdot y2\right)\right)}\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(x \cdot \left(\mathsf{neg}\left(y2\right)\right)\right)}\right) \]

       3. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(a \cdot \left(x \cdot \color{blue}{\left(-1 \cdot y2\right)}\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(x \cdot \left(-1 \cdot y2\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(a \cdot \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(y2\right)\right)}\right)\right) \]

       6. lower-neg.f64 42.0

          \[\leadsto y1 \cdot \left(a \cdot \left(x \cdot \color{blue}{\left(-y2\right)}\right)\right) \]

   11. Applied rewrites 42.0%

       \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(x \cdot \left(-y2\right)\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.9 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(y2 \cdot \left(-x\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.6% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -4.8 \cdot 10^{+179}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -4.8e+179)
   (* y5 (* j (* y0 y3)))
   (if (<= y3 1.25e+95)
     (* a (* b (- (* x y) (* z t))))
     (* y1 (* a (* z y3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -4.8e+179) {
		tmp = y5 * (j * (y0 * y3));
	} else if (y3 <= 1.25e+95) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = y1 * (a * (z * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-4.8d+179)) then
        tmp = y5 * (j * (y0 * y3))
    else if (y3 <= 1.25d+95) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = y1 * (a * (z * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -4.8e+179) {
		tmp = y5 * (j * (y0 * y3));
	} else if (y3 <= 1.25e+95) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = y1 * (a * (z * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -4.8e+179:
		tmp = y5 * (j * (y0 * y3))
	elif y3 <= 1.25e+95:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = y1 * (a * (z * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -4.8e+179)
		tmp = Float64(y5 * Float64(j * Float64(y0 * y3)));
	elseif (y3 <= 1.25e+95)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(y1 * Float64(a * Float64(z * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -4.8e+179)
		tmp = y5 * (j * (y0 * y3));
	elseif (y3 <= 1.25e+95)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = y1 * (a * (z * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -4.8e+179], N[(y5 * N[(j * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.25e+95], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(a * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y3 < -4.80000000000000025e179

   1. Initial program 39.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y5}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \color{blue}{\left(-1 \cdot y5\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot \left(-1 \cdot y5\right)} \]

   5. Applied rewrites 35.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(i, t \cdot j - k \cdot y, y0 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right) \cdot \left(-y5\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{\left(j \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \cdot \left(\mathsf{neg}\left(y5\right)\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(j \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \left(j \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \left(j \cdot \left(i \cdot t + \color{blue}{\left(\mathsf{neg}\left(y0 \cdot y3\right)\right)}\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \left(j \cdot \color{blue}{\left(i \cdot t - y0 \cdot y3\right)}\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto \left(j \cdot \color{blue}{\left(i \cdot t - y0 \cdot y3\right)}\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \left(j \cdot \left(\color{blue}{i \cdot t} - y0 \cdot y3\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

      7. lower-*.f64 40.6

         \[\leadsto \left(j \cdot \left(i \cdot t - \color{blue}{y0 \cdot y3}\right)\right) \cdot \left(-y5\right) \]

   8. Applied rewrites 40.6%

      \[\leadsto \color{blue}{\left(j \cdot \left(i \cdot t - y0 \cdot y3\right)\right)} \cdot \left(-y5\right) \]

   9. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right)\right)} \cdot \left(\mathsf{neg}\left(y5\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j \cdot \left(y0 \cdot y3\right)\right)\right)} \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(y0 \cdot y3\right)\right)\right)} \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \left(j \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y3\right)\right)}\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(-1 \cdot \left(y0 \cdot y3\right)\right)\right)} \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \left(j \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot y3\right)}\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       6. lower-*.f64 N/A

          \[\leadsto \left(j \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot y3\right)}\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       7. mul-1-neg N/A

          \[\leadsto \left(j \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y3\right)\right) \cdot \left(\mathsf{neg}\left(y5\right)\right) \]

       8. lower-neg.f64 45.0

          \[\leadsto \left(j \cdot \left(\color{blue}{\left(-y0\right)} \cdot y3\right)\right) \cdot \left(-y5\right) \]

   11. Applied rewrites 45.0%

       \[\leadsto \color{blue}{\left(j \cdot \left(\left(-y0\right) \cdot y3\right)\right)} \cdot \left(-y5\right) \]

   if -4.80000000000000025e179 < y3 < 1.25000000000000006e95

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 42.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 34.1

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 34.1%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 1.25000000000000006e95 < y3

   1. Initial program 14.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.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. lower-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. Applied rewrites 44.3%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 44.6

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 44.6%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

       3. lower-*.f64 36.5

          \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   11. Applied rewrites 36.5%

       \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(z \cdot y3\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -4.8 \cdot 10^{+179}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.7% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-134}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -9.5e+124)
   (* a (* (* x y) b))
   (if (<= y -1.15e-134)
     (* a (* z (* y1 y3)))
     (if (<= y 5e-25) (* i (* j (* x y1))) (* a (* x (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -9.5e+124) {
		tmp = a * ((x * y) * b);
	} else if (y <= -1.15e-134) {
		tmp = a * (z * (y1 * y3));
	} else if (y <= 5e-25) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-9.5d+124)) then
        tmp = a * ((x * y) * b)
    else if (y <= (-1.15d-134)) then
        tmp = a * (z * (y1 * y3))
    else if (y <= 5d-25) then
        tmp = i * (j * (x * y1))
    else
        tmp = a * (x * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -9.5e+124) {
		tmp = a * ((x * y) * b);
	} else if (y <= -1.15e-134) {
		tmp = a * (z * (y1 * y3));
	} else if (y <= 5e-25) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -9.5e+124:
		tmp = a * ((x * y) * b)
	elif y <= -1.15e-134:
		tmp = a * (z * (y1 * y3))
	elif y <= 5e-25:
		tmp = i * (j * (x * y1))
	else:
		tmp = a * (x * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -9.5e+124)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y <= -1.15e-134)
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	elseif (y <= 5e-25)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = Float64(a * Float64(x * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -9.5e+124)
		tmp = a * ((x * y) * b);
	elseif (y <= -1.15e-134)
		tmp = a * (z * (y1 * y3));
	elseif (y <= 5e-25)
		tmp = i * (j * (x * y1));
	else
		tmp = a * (x * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -9.5e+124], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-134], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-25], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.50000000000000004e124

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 48.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 46.2

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 46.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 46.4

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Applied rewrites 46.4%

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   if -9.50000000000000004e124 < y < -1.15e-134

   1. Initial program 19.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. lower-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. Applied rewrites 36.7%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 43.6

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 43.6%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

       4. lower-*.f64 33.2

          \[\leadsto a \cdot \left(\color{blue}{\left(y1 \cdot y3\right)} \cdot z\right) \]

   11. Applied rewrites 33.2%

       \[\leadsto \color{blue}{a \cdot \left(\left(y1 \cdot y3\right) \cdot z\right)} \]

   if -1.15e-134 < y < 4.99999999999999962e-25

   1. Initial program 37.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower-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. Applied rewrites 33.1%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y4} + i \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y4, i \cdot x\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y4, i \cdot x\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y4, i \cdot x\right)\right) \]

      7. lower-*.f64 26.2

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, \color{blue}{i \cdot x}\right)\right) \]

   8. Applied rewrites 26.2%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   9. Taylor expanded in y3 around 0

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)} \]

       3. lower-*.f64 21.4

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(x \cdot y1\right)}\right) \]

   11. Applied rewrites 21.4%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if 4.99999999999999962e-25 < y

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 35.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 24.5

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 24.5%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 20.2

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Applied rewrites 20.2%

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. lower-*.f64 26.2

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied rewrites 26.2%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-134}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 26.9% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8.2 \cdot 10^{-248}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z 8.2e-248)
   (* c (* y (fma i (- x) (* y3 y4))))
   (* a (* b (- (* x y) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= 8.2e-248) {
		tmp = c * (y * fma(i, -x, (y3 * y4)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= 8.2e-248)
		tmp = Float64(c * Float64(y * fma(i, Float64(-x), Float64(y3 * y4))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, 8.2e-248], N[(c * N[(y * N[(i * (-x) + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.20000000000000067e-248

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. lower-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. lower--.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. lower-*.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. lower-*.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. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 44.1%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right) \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right) \cdot y\right)} \]

      4. mul-1-neg N/A

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(\mathsf{neg}\left(i \cdot x\right)\right)} + y3 \cdot y4\right) \cdot y\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(\mathsf{neg}\left(x\right)\right)} + y3 \cdot y4\right) \cdot y\right) \]

      6. mul-1-neg N/A

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(-1 \cdot x\right)} + y3 \cdot y4\right) \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto c \cdot \left(\color{blue}{\mathsf{fma}\left(i, -1 \cdot x, y3 \cdot y4\right)} \cdot y\right) \]

      8. mul-1-neg N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right) \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto c \cdot \left(\mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right) \cdot y\right) \]

      10. lower-*.f64 40.6

          \[\leadsto c \cdot \left(\mathsf{fma}\left(i, -x, \color{blue}{y3 \cdot y4}\right) \cdot y\right) \]

   8. Applied rewrites 40.6%

      \[\leadsto \color{blue}{c \cdot \left(\mathsf{fma}\left(i, -x, y3 \cdot y4\right) \cdot y\right)} \]

   if 8.20000000000000067e-248 < z

   1. Initial program 30.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 47.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 38.5

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 38.5%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.2 \cdot 10^{-248}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 23.0% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -9.5e+124)
   (* a (* (* x y) b))
   (if (<= y 2.15e+36) (* a (* z (* y1 y3))) (* a (* x (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -9.5e+124) {
		tmp = a * ((x * y) * b);
	} else if (y <= 2.15e+36) {
		tmp = a * (z * (y1 * y3));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-9.5d+124)) then
        tmp = a * ((x * y) * b)
    else if (y <= 2.15d+36) then
        tmp = a * (z * (y1 * y3))
    else
        tmp = a * (x * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -9.5e+124) {
		tmp = a * ((x * y) * b);
	} else if (y <= 2.15e+36) {
		tmp = a * (z * (y1 * y3));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -9.5e+124:
		tmp = a * ((x * y) * b)
	elif y <= 2.15e+36:
		tmp = a * (z * (y1 * y3))
	else:
		tmp = a * (x * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -9.5e+124)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y <= 2.15e+36)
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	else
		tmp = Float64(a * Float64(x * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -9.5e+124)
		tmp = a * ((x * y) * b);
	elseif (y <= 2.15e+36)
		tmp = a * (z * (y1 * y3));
	else
		tmp = a * (x * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -9.5e+124], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+36], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000004e124

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 48.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 46.2

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 46.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 46.4

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Applied rewrites 46.4%

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   if -9.50000000000000004e124 < y < 2.15000000000000002e36

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. lower-*.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. lower-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. Applied rewrites 33.4%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot y2\right)\right) + y3 \cdot z\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{-1 \cdot \left(x \cdot y2\right)} + y3 \cdot z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y1 \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y2} + y3 \cdot z\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y2, y3 \cdot z\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y2, y3 \cdot z\right)\right) \]

      9. lower-*.f64 31.6

         \[\leadsto y1 \cdot \left(a \cdot \mathsf{fma}\left(-x, y2, \color{blue}{y3 \cdot z}\right)\right) \]

   8. Applied rewrites 31.6%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-x, y2, y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

       4. lower-*.f64 20.2

          \[\leadsto a \cdot \left(\color{blue}{\left(y1 \cdot y3\right)} \cdot z\right) \]

   11. Applied rewrites 20.2%

       \[\leadsto \color{blue}{a \cdot \left(\left(y1 \cdot y3\right) \cdot z\right)} \]

   if 2.15000000000000002e36 < y

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. lower-*.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. *-commutative N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      14. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 35.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. lower-*.f64 23.9

         \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

   8. Applied rewrites 23.9%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 22.4

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Applied rewrites 22.4%

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. lower-*.f64 29.1

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied rewrites 29.1%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 26.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 16.9% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(x \cdot \left(y \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* x (* y b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (x * (y * b));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (x * (y * b))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (x * (y * b));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (x * (y * b))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(x * Float64(y * b)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (x * (y * b));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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. lower-*.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. *-commutative N/A

      \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   5. distribute-rgt-neg-in N/A

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   6. neg-mul-1 N/A

      \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   7. lower-fma.f64 N/A

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   8. lower--.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   9. *-commutative N/A

      \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   10. lower-*.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   11. *-commutative N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   12. lower-*.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   13. neg-mul-1 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   14. lower-neg.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   15. sub-neg N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

5. Applied rewrites 43.3%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in b around inf

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
7. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   2. lower--.f64 N/A

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

   4. lower-*.f64 29.6

      \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

8. Applied rewrites 29.6%

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

9. Taylor expanded in x around inf

   \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
10. Step-by-step derivation

    1. lower-*.f64 17.5

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

11. Applied rewrites 17.5%

    \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
12. Step-by-step derivation

    1. *-commutative N/A

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

    2. associate-*r* N/A

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

    3. lower-*.f64 N/A

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

    4. lower-*.f64 17.8

       \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

13. Applied rewrites 17.8%

    \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

14. Final simplification 17.8%

    \[\leadsto a \cdot \left(x \cdot \left(y \cdot b\right)\right) \]
15. Add Preprocessing

Alternative 28: 17.1% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 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. lower-*.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. *-commutative N/A

      \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot y1}\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   5. distribute-rgt-neg-in N/A

      \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right) \cdot \left(\mathsf{neg}\left(y1\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   6. neg-mul-1 N/A

      \[\leadsto a \cdot \left(\left(x \cdot y2 - y3 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot y1\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   7. lower-fma.f64 N/A

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(x \cdot y2 - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   8. lower--.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   9. *-commutative N/A

      \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   10. lower-*.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(\color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   11. *-commutative N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   12. lower-*.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot y1, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   13. neg-mul-1 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   14. lower-neg.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \color{blue}{\mathsf{neg}\left(y1\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   15. sub-neg N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, \mathsf{neg}\left(y1\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

5. Applied rewrites 43.3%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y2 \cdot x - z \cdot y3, -y1, \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in b around inf

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
7. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   2. lower--.f64 N/A

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

   4. lower-*.f64 29.6

      \[\leadsto a \cdot \left(b \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right) \]

8. Applied rewrites 29.6%

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

9. Taylor expanded in x around inf

   \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]
10. Step-by-step derivation

    1. lower-*.f64 17.5

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

11. Applied rewrites 17.5%

    \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

12. Final simplification 17.5%

    \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
13. Add Preprocessing

Developer Target 1: 27.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t\_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t\_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t\_9\\ t_11 := t\_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t\_4 \cdot t\_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t\_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t\_3 \cdot t\_1 - t\_14\right)\right) + \left(t\_8 - \left(t\_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t\_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t\_13\right)\right) + \left(t\_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t\_10 - \left(y \cdot x - z \cdot t\right) \cdot t\_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t\_8 - \left(t\_11 - t\_6\right)\right) - \left(\frac{t\_3}{\frac{1}{t\_1}} - t\_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t\_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t\_2 - \left(t\_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t\_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t\_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t\_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t\_5\right) - t\_17 \cdot t\_1\right) + t\_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024219 
(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)))))