Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.2% → 42.4%

Time: 42.8s

Alternatives: 36

Speedup: 4.8×

• 89.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 42.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := b \cdot y0 - i \cdot y1\\ t_5 := b \cdot y4 - i \cdot y5\\ t_6 := z \cdot y3 - x \cdot y2\\ t_7 := t \cdot y2 - y \cdot y3\\ t_8 := \mathsf{fma}\left(y0, t\_6, \mathsf{fma}\left(i, t\_1, y4 \cdot t\_7\right)\right) \cdot \left(-c\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{+184}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(t, i \cdot y5 - b \cdot y4, \mathsf{fma}\left(y3, t\_3, x \cdot t\_4\right)\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(y2 \cdot t\_2\right)\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-247}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(t\_5, -y, \mathsf{fma}\left(y2, t\_3, z \cdot t\_4\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(t\_5, -j, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(-t\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, t\_6, \mathsf{fma}\left(b, t\_1, y5 \cdot t\_7\right)\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+100}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, t\_3, \mathsf{fma}\left(t\_2, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} \end{array} \]

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 (- (* c y0) (* a y1)))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4 (- (* b y0) (* i y1)))
        (t_5 (- (* b y4) (* i y5)))
        (t_6 (- (* z y3) (* x y2)))
        (t_7 (- (* t y2) (* y y3)))
        (t_8 (* (fma y0 t_6 (fma i t_1 (* y4 t_7))) (- c))))
   (if (<= c -1.5e+184)
     t_8
     (if (<= c -4.2e-17)
       (* (fma t (- (* i y5) (* b y4)) (fma y3 t_3 (* x t_4))) (- j))
       (if (<= c -4.8e-88)
         (* x (* y2 t_2))
         (if (<= c -1.16e-247)
           (* k (fma t_5 (- y) (fma y2 t_3 (* z t_4))))
           (if (<= c 1.15e-272)
             (* (fma t_5 (- j) (* y2 (- (* c y4) (* a y5)))) (- t))
             (if (<= c 1.85e-143)
               (* a (fma y1 t_6 (fma b t_1 (* y5 t_7))))
               (if (<= c 1.9e-46)
                 (* b (* y0 (- (* z k) (* x j))))
                 (if (<= c 3.5e+100)
                   (* y2 (fma k t_3 (fma t_2 x (* t (- (* a y5) (* c y4))))))
                   t_8))))))))))

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 = (c * y0) - (a * y1);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (b * y0) - (i * y1);
	double t_5 = (b * y4) - (i * y5);
	double t_6 = (z * y3) - (x * y2);
	double t_7 = (t * y2) - (y * y3);
	double t_8 = fma(y0, t_6, fma(i, t_1, (y4 * t_7))) * -c;
	double tmp;
	if (c <= -1.5e+184) {
		tmp = t_8;
	} else if (c <= -4.2e-17) {
		tmp = fma(t, ((i * y5) - (b * y4)), fma(y3, t_3, (x * t_4))) * -j;
	} else if (c <= -4.8e-88) {
		tmp = x * (y2 * t_2);
	} else if (c <= -1.16e-247) {
		tmp = k * fma(t_5, -y, fma(y2, t_3, (z * t_4)));
	} else if (c <= 1.15e-272) {
		tmp = fma(t_5, -j, (y2 * ((c * y4) - (a * y5)))) * -t;
	} else if (c <= 1.85e-143) {
		tmp = a * fma(y1, t_6, fma(b, t_1, (y5 * t_7)));
	} else if (c <= 1.9e-46) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (c <= 3.5e+100) {
		tmp = y2 * fma(k, t_3, fma(t_2, x, (t * ((a * y5) - (c * y4)))));
	} else {
		tmp = t_8;
	}
	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(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(Float64(b * y0) - Float64(i * y1))
	t_5 = Float64(Float64(b * y4) - Float64(i * y5))
	t_6 = Float64(Float64(z * y3) - Float64(x * y2))
	t_7 = Float64(Float64(t * y2) - Float64(y * y3))
	t_8 = Float64(fma(y0, t_6, fma(i, t_1, Float64(y4 * t_7))) * Float64(-c))
	tmp = 0.0
	if (c <= -1.5e+184)
		tmp = t_8;
	elseif (c <= -4.2e-17)
		tmp = Float64(fma(t, Float64(Float64(i * y5) - Float64(b * y4)), fma(y3, t_3, Float64(x * t_4))) * Float64(-j));
	elseif (c <= -4.8e-88)
		tmp = Float64(x * Float64(y2 * t_2));
	elseif (c <= -1.16e-247)
		tmp = Float64(k * fma(t_5, Float64(-y), fma(y2, t_3, Float64(z * t_4))));
	elseif (c <= 1.15e-272)
		tmp = Float64(fma(t_5, Float64(-j), Float64(y2 * Float64(Float64(c * y4) - Float64(a * y5)))) * Float64(-t));
	elseif (c <= 1.85e-143)
		tmp = Float64(a * fma(y1, t_6, fma(b, t_1, Float64(y5 * t_7))));
	elseif (c <= 1.9e-46)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (c <= 3.5e+100)
		tmp = Float64(y2 * fma(k, t_3, fma(t_2, x, Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))));
	else
		tmp = t_8;
	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[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(y0 * t$95$6 + N[(i * t$95$1 + N[(y4 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-c)), $MachinePrecision]}, If[LessEqual[c, -1.5e+184], t$95$8, If[LessEqual[c, -4.2e-17], N[(N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$3 + N[(x * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[c, -4.8e-88], N[(x * N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.16e-247], N[(k * N[(t$95$5 * (-y) + N[(y2 * t$95$3 + N[(z * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e-272], N[(N[(t$95$5 * (-j) + N[(y2 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[c, 1.85e-143], N[(a * N[(y1 * t$95$6 + N[(b * t$95$1 + N[(y5 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.9e-46], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.5e+100], N[(y2 * N[(k * t$95$3 + N[(t$95$2 * x + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$8]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if c < -1.49999999999999993e184 or 3.49999999999999976e100 < c

   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 c around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 68.9%

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

   if -1.49999999999999993e184 < c < -4.19999999999999984e-17

   1. Initial program 24.4%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 66.4%

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

   if -4.19999999999999984e-17 < c < -4.7999999999999999e-88

   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 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 57.1

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

   5. Applied rewrites 57.1%

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

   6. Taylor expanded in y2 around inf

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 85.9%

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

   if -4.7999999999999999e-88 < c < -1.16e-247

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 71.4%

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

   if -1.16e-247 < c < 1.14999999999999994e-272

   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 t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 66.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 71.0%

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

   if 1.14999999999999994e-272 < c < 1.85e-143

   1. Initial program 41.7%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 73.3%

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

   if 1.85e-143 < c < 1.8999999999999998e-46

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 52.5

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

   5. Applied rewrites 52.5%

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

   6. Taylor expanded in y0 around inf

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

   8. Applied rewrites 61.1%

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

   if 1.8999999999999998e-46 < c < 3.49999999999999976e100

   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 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. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 71.1%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+184}:\\ \;\;\;\;\mathsf{fma}\left(y0, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(i, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-c\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(t, i \cdot y5 - b \cdot y4, \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-247}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(-t\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+100}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y0, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(i, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(Float64(z * y3) - Float64(x * y2))
	t_4 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * t_2) + Float64(Float64(Float64(b * y0) - Float64(i * y1)) * Float64(Float64(z * k) - Float64(x * j)))) + Float64(t_3 * Float64(Float64(a * y1) - Float64(c * y0)))) + 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(fma(y0, t_3, fma(i, t_2, Float64(y4 * t_1))) * Float64(-c));
	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[(z * y3), $MachinePrecision] - N[(x * y2), $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[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $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[(N[(y0 * t$95$3 + N[(i * t$95$2 + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-c)), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.5%

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

   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 c around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 45.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.0%

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

Alternative 3: 37.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := b \cdot y0 - i \cdot y1\\ t_4 := b \cdot y4 - i \cdot y5\\ t_5 := \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\\ t_6 := z \cdot y3 - x \cdot y2\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{+146}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot t\_5\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(t, i \cdot y5 - b \cdot y4, \mathsf{fma}\left(y3, t\_2, x \cdot t\_3\right)\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(y2 \cdot t\_1\right)\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-247}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(t\_4, -y, \mathsf{fma}\left(y2, t\_2, z \cdot t\_3\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(t\_4, -j, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(-t\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, t\_6, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, t\_2, \mathsf{fma}\left(t\_1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+247}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, t\_6, \mathsf{fma}\left(y4, t\_5, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y0 \cdot \mathsf{fma}\left(c, y2, -b \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* y1 y4) (* y0 y5)))
        (t_3 (- (* b y0) (* i y1)))
        (t_4 (- (* b y4) (* i y5)))
        (t_5 (fma k y2 (* j (- y3))))
        (t_6 (- (* z y3) (* x y2))))
   (if (<= c -5.2e+146)
     (*
      y4
      (+ (fma b (- (* t j) (* y k)) (* y1 t_5)) (* c (- (* y y3) (* t y2)))))
     (if (<= c -4.2e-17)
       (* (fma t (- (* i y5) (* b y4)) (fma y3 t_2 (* x t_3))) (- j))
       (if (<= c -4.8e-88)
         (* x (* y2 t_1))
         (if (<= c -1.16e-247)
           (* k (fma t_4 (- y) (fma y2 t_2 (* z t_3))))
           (if (<= c 1.15e-272)
             (* (fma t_4 (- j) (* y2 (- (* c y4) (* a y5)))) (- t))
             (if (<= c 1.85e-143)
               (*
                a
                (fma
                 y1
                 t_6
                 (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
               (if (<= c 1.9e-46)
                 (* b (* y0 (- (* z k) (* x j))))
                 (if (<= c 5.8e+86)
                   (* y2 (fma k t_2 (fma t_1 x (* t (- (* a y5) (* c y4))))))
                   (if (<= c 8.5e+247)
                     (* y1 (fma a t_6 (fma y4 t_5 (* i (- (* x j) (* z k))))))
                     (* x (* y0 (fma c y2 (- (* b j))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = (b * y0) - (i * y1);
	double t_4 = (b * y4) - (i * y5);
	double t_5 = fma(k, y2, (j * -y3));
	double t_6 = (z * y3) - (x * y2);
	double tmp;
	if (c <= -5.2e+146) {
		tmp = y4 * (fma(b, ((t * j) - (y * k)), (y1 * t_5)) + (c * ((y * y3) - (t * y2))));
	} else if (c <= -4.2e-17) {
		tmp = fma(t, ((i * y5) - (b * y4)), fma(y3, t_2, (x * t_3))) * -j;
	} else if (c <= -4.8e-88) {
		tmp = x * (y2 * t_1);
	} else if (c <= -1.16e-247) {
		tmp = k * fma(t_4, -y, fma(y2, t_2, (z * t_3)));
	} else if (c <= 1.15e-272) {
		tmp = fma(t_4, -j, (y2 * ((c * y4) - (a * y5)))) * -t;
	} else if (c <= 1.85e-143) {
		tmp = a * fma(y1, t_6, fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} else if (c <= 1.9e-46) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (c <= 5.8e+86) {
		tmp = y2 * fma(k, t_2, fma(t_1, x, (t * ((a * y5) - (c * y4)))));
	} else if (c <= 8.5e+247) {
		tmp = y1 * fma(a, t_6, fma(y4, t_5, (i * ((x * j) - (z * k)))));
	} else {
		tmp = x * (y0 * fma(c, y2, -(b * j)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(Float64(b * y0) - Float64(i * y1))
	t_4 = Float64(Float64(b * y4) - Float64(i * y5))
	t_5 = fma(k, y2, Float64(j * Float64(-y3)))
	t_6 = Float64(Float64(z * y3) - Float64(x * y2))
	tmp = 0.0
	if (c <= -5.2e+146)
		tmp = Float64(y4 * Float64(fma(b, Float64(Float64(t * j) - Float64(y * k)), Float64(y1 * t_5)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (c <= -4.2e-17)
		tmp = Float64(fma(t, Float64(Float64(i * y5) - Float64(b * y4)), fma(y3, t_2, Float64(x * t_3))) * Float64(-j));
	elseif (c <= -4.8e-88)
		tmp = Float64(x * Float64(y2 * t_1));
	elseif (c <= -1.16e-247)
		tmp = Float64(k * fma(t_4, Float64(-y), fma(y2, t_2, Float64(z * t_3))));
	elseif (c <= 1.15e-272)
		tmp = Float64(fma(t_4, Float64(-j), Float64(y2 * Float64(Float64(c * y4) - Float64(a * y5)))) * Float64(-t));
	elseif (c <= 1.85e-143)
		tmp = Float64(a * fma(y1, t_6, fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (c <= 1.9e-46)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (c <= 5.8e+86)
		tmp = Float64(y2 * fma(k, t_2, fma(t_1, x, Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))));
	elseif (c <= 8.5e+247)
		tmp = Float64(y1 * fma(a, t_6, fma(y4, t_5, Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	else
		tmp = Float64(x * Float64(y0 * fma(c, y2, Float64(-Float64(b * j)))));
	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[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(k * y2 + N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.2e+146], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.2e-17], N[(N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$2 + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[c, -4.8e-88], N[(x * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.16e-247], N[(k * N[(t$95$4 * (-y) + N[(y2 * t$95$2 + N[(z * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e-272], N[(N[(t$95$4 * (-j) + N[(y2 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[c, 1.85e-143], N[(a * N[(y1 * t$95$6 + 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[c, 1.9e-46], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e+86], N[(y2 * N[(k * t$95$2 + N[(t$95$1 * x + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e+247], N[(y1 * N[(a * t$95$6 + N[(y4 * t$95$5 + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y0 * N[(c * y2 + (-N[(b * j), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if c < -5.20000000000000028e146

   1. Initial program 31.2%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 72.5%

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

   if -5.20000000000000028e146 < c < -4.19999999999999984e-17

   1. Initial program 22.2%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 67.3%

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

   if -4.19999999999999984e-17 < c < -4.7999999999999999e-88

   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 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 57.1

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

   5. Applied rewrites 57.1%

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

   6. Taylor expanded in y2 around inf

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 85.9%

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

   if -4.7999999999999999e-88 < c < -1.16e-247

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 71.4%

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

   if -1.16e-247 < c < 1.14999999999999994e-272

   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 t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 66.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 71.0%

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

   if 1.14999999999999994e-272 < c < 1.85e-143

   1. Initial program 41.7%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 73.3%

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

   if 1.85e-143 < c < 1.8999999999999998e-46

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 52.5

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

   5. Applied rewrites 52.5%

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

   6. Taylor expanded in y0 around inf

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

   8. Applied rewrites 61.1%

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

   if 1.8999999999999998e-46 < c < 5.79999999999999981e86

   1. Initial program 33.4%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 74.2%

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

   if 5.79999999999999981e86 < c < 8.4999999999999998e247

   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 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 56.3%

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

   if 8.4999999999999998e247 < c

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 33.3

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

   5. Applied rewrites 33.3%

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

   6. Taylor expanded in y0 around inf

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

   8. Applied rewrites 66.7%

      \[\leadsto x \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)}\right) \]
3. Recombined 10 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+146}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(t, i \cdot y5 - b \cdot y4, \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-247}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(-t\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+247}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y0 \cdot \mathsf{fma}\left(c, y2, -b \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y3 - x \cdot y2\\ t_2 := \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\\ t_3 := b \cdot y4 - i \cdot y5\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;c \leq -1.02 \cdot 10^{+120}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot t\_2\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, y2 \cdot t\_4\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-247}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(t\_3, -y, \mathsf{fma}\left(y2, t\_5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, -j, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(-t\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, t\_1, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, t\_5, \mathsf{fma}\left(t\_4, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+247}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, t\_1, \mathsf{fma}\left(y4, t\_2, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y0 \cdot \mathsf{fma}\left(c, y2, -b \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z y3) (* x y2)))
        (t_2 (fma k y2 (* j (- y3))))
        (t_3 (- (* b y4) (* i y5)))
        (t_4 (- (* c y0) (* a y1)))
        (t_5 (- (* y1 y4) (* y0 y5))))
   (if (<= c -1.02e+120)
     (*
      y4
      (+ (fma b (- (* t j) (* y k)) (* y1 t_2)) (* c (- (* y y3) (* t y2)))))
     (if (<= c -2.25e-88)
       (*
        x
        (+ (fma (- (* a b) (* c i)) y (* y2 t_4)) (* j (- (* i y1) (* b y0)))))
       (if (<= c -1.16e-247)
         (* k (fma t_3 (- y) (fma y2 t_5 (* z (- (* b y0) (* i y1))))))
         (if (<= c 1.15e-272)
           (* (fma t_3 (- j) (* y2 (- (* c y4) (* a y5)))) (- t))
           (if (<= c 1.85e-143)
             (*
              a
              (fma
               y1
               t_1
               (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
             (if (<= c 1.9e-46)
               (* b (* y0 (- (* z k) (* x j))))
               (if (<= c 5.8e+86)
                 (* y2 (fma k t_5 (fma t_4 x (* t (- (* a y5) (* c y4))))))
                 (if (<= c 8.5e+247)
                   (* y1 (fma a t_1 (fma y4 t_2 (* i (- (* x j) (* z k))))))
                   (* x (* y0 (fma c y2 (- (* b j)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) - (x * y2);
	double t_2 = fma(k, y2, (j * -y3));
	double t_3 = (b * y4) - (i * y5);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (c <= -1.02e+120) {
		tmp = y4 * (fma(b, ((t * j) - (y * k)), (y1 * t_2)) + (c * ((y * y3) - (t * y2))));
	} else if (c <= -2.25e-88) {
		tmp = x * (fma(((a * b) - (c * i)), y, (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	} else if (c <= -1.16e-247) {
		tmp = k * fma(t_3, -y, fma(y2, t_5, (z * ((b * y0) - (i * y1)))));
	} else if (c <= 1.15e-272) {
		tmp = fma(t_3, -j, (y2 * ((c * y4) - (a * y5)))) * -t;
	} else if (c <= 1.85e-143) {
		tmp = a * fma(y1, t_1, fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} else if (c <= 1.9e-46) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (c <= 5.8e+86) {
		tmp = y2 * fma(k, t_5, fma(t_4, x, (t * ((a * y5) - (c * y4)))));
	} else if (c <= 8.5e+247) {
		tmp = y1 * fma(a, t_1, fma(y4, t_2, (i * ((x * j) - (z * k)))));
	} else {
		tmp = x * (y0 * fma(c, y2, -(b * j)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * y3) - Float64(x * y2))
	t_2 = fma(k, y2, Float64(j * Float64(-y3)))
	t_3 = Float64(Float64(b * y4) - Float64(i * y5))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (c <= -1.02e+120)
		tmp = Float64(y4 * Float64(fma(b, Float64(Float64(t * j) - Float64(y * k)), Float64(y1 * t_2)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (c <= -2.25e-88)
		tmp = Float64(x * Float64(fma(Float64(Float64(a * b) - Float64(c * i)), y, Float64(y2 * t_4)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (c <= -1.16e-247)
		tmp = Float64(k * fma(t_3, Float64(-y), fma(y2, t_5, Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))));
	elseif (c <= 1.15e-272)
		tmp = Float64(fma(t_3, Float64(-j), Float64(y2 * Float64(Float64(c * y4) - Float64(a * y5)))) * Float64(-t));
	elseif (c <= 1.85e-143)
		tmp = Float64(a * fma(y1, t_1, fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (c <= 1.9e-46)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (c <= 5.8e+86)
		tmp = Float64(y2 * fma(k, t_5, fma(t_4, x, Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))));
	elseif (c <= 8.5e+247)
		tmp = Float64(y1 * fma(a, t_1, fma(y4, t_2, Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	else
		tmp = Float64(x * Float64(y0 * fma(c, y2, Float64(-Float64(b * j)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * y2 + N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.02e+120], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.25e-88], N[(x * N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * y + N[(y2 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.16e-247], N[(k * N[(t$95$3 * (-y) + N[(y2 * t$95$5 + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e-272], N[(N[(t$95$3 * (-j) + N[(y2 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[c, 1.85e-143], N[(a * N[(y1 * t$95$1 + 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[c, 1.9e-46], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e+86], N[(y2 * N[(k * t$95$5 + N[(t$95$4 * x + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e+247], N[(y1 * N[(a * t$95$1 + N[(y4 * t$95$2 + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y0 * N[(c * y2 + (-N[(b * j), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if c < -1.01999999999999997e120

   1. Initial program 26.3%

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

   3. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 69.0%

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

   if -1.01999999999999997e120 < c < -2.24999999999999996e-88

   1. Initial program 27.0%

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

   3. Taylor expanded in 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 49.2

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

   5. Applied rewrites 49.2%

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

   if -2.24999999999999996e-88 < c < -1.16e-247

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 71.4%

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

   if -1.16e-247 < c < 1.14999999999999994e-272

   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 t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 66.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 71.0%

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

   if 1.14999999999999994e-272 < c < 1.85e-143

   1. Initial program 41.7%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 73.3%

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

   if 1.85e-143 < c < 1.8999999999999998e-46

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 52.5

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

   5. Applied rewrites 52.5%

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

   6. Taylor expanded in y0 around inf

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

   8. Applied rewrites 61.1%

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

   if 1.8999999999999998e-46 < c < 5.79999999999999981e86

   1. Initial program 33.4%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 74.2%

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

   if 5.79999999999999981e86 < c < 8.4999999999999998e247

   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 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 56.3%

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

   if 8.4999999999999998e247 < c

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 33.3

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

   5. Applied rewrites 33.3%

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

   6. Taylor expanded in y0 around inf

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

   8. Applied rewrites 66.7%

      \[\leadsto x \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)}\right) \]
3. Recombined 9 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.02 \cdot 10^{+120}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - y \cdot k, y1 \cdot \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-247}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(-t\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+247}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y0 \cdot \mathsf{fma}\left(c, y2, -b \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\\ t_2 := z \cdot y3 - x \cdot y2\\ \mathbf{if}\;a \leq -7 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(y1 \cdot t\_2\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+82}:\\ \;\;\;\;a \cdot t\_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+116}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, t\_2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y5 (- (* t y2) (* y y3)))) (t_2 (- (* z y3) (* x y2))))
   (if (<= a -7e+217)
     (* a (* y1 t_2))
     (if (<= a -2e+82)
       (* a t_1)
       (if (<= a 9.5e-21)
         (+
          (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
          (* y0 (* b (* z k))))
         (if (<= a 1.25e+79)
           (* x (* b (- (* y a) (* j y0))))
           (if (<= a 2.3e+116)
             (* b (* t (fma j y4 (* z (- a)))))
             (* a (fma y1 t_2 (fma b (- (* x y) (* z t)) 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 = y5 * ((t * y2) - (y * y3));
	double t_2 = (z * y3) - (x * y2);
	double tmp;
	if (a <= -7e+217) {
		tmp = a * (y1 * t_2);
	} else if (a <= -2e+82) {
		tmp = a * t_1;
	} else if (a <= 9.5e-21) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y0 * (b * (z * k)));
	} else if (a <= 1.25e+79) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (a <= 2.3e+116) {
		tmp = b * (t * fma(j, y4, (z * -a)));
	} else {
		tmp = a * fma(y1, t_2, fma(b, ((x * y) - (z * t)), 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(y5 * Float64(Float64(t * y2) - Float64(y * y3)))
	t_2 = Float64(Float64(z * y3) - Float64(x * y2))
	tmp = 0.0
	if (a <= -7e+217)
		tmp = Float64(a * Float64(y1 * t_2));
	elseif (a <= -2e+82)
		tmp = Float64(a * t_1);
	elseif (a <= 9.5e-21)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y0 * Float64(b * Float64(z * k))));
	elseif (a <= 1.25e+79)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (a <= 2.3e+116)
		tmp = Float64(b * Float64(t * fma(j, y4, Float64(z * Float64(-a)))));
	else
		tmp = Float64(a * fma(y1, t_2, fma(b, Float64(Float64(x * y) - Float64(z * t)), 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[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e+217], N[(a * N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2e+82], N[(a * t$95$1), $MachinePrecision], If[LessEqual[a, 9.5e-21], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+79], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+116], N[(b * N[(t * N[(j * y4 + N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y1 * t$95$2 + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -6.9999999999999996e217

   1. Initial program 22.2%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in y1 around inf

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

   8. Applied rewrites 77.8%

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

   if -6.9999999999999996e217 < a < -1.9999999999999999e82

   1. Initial program 36.6%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 40.7%

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

   6. Taylor expanded in y5 around inf

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

   8. Applied rewrites 50.9%

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

   if -1.9999999999999999e82 < a < 9.4999999999999994e-21

   1. Initial program 31.2%

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

   3. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower--.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. mul-1-neg N/A

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

      11. *-commutative N/A

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

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

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

      13. neg-mul-1 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - k \cdot z\right) \cdot \color{blue}{\left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      14. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right) \cdot \left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      15. lower--.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right)} \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      16. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(\color{blue}{j \cdot x} - k \cdot z\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      17. *-commutative N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      18. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      19. neg-mul-1 N/A

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

      20. lower-neg.f64 50.5

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

   5. Applied rewrites 50.5%

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

   6. Taylor expanded in k around inf

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

   8. Applied rewrites 51.7%

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

   if 9.4999999999999994e-21 < a < 1.25e79

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 61.1

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

   5. Applied rewrites 61.1%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 57.4%

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

   if 1.25e79 < a < 2.29999999999999995e116

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 46.4

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

   5. Applied rewrites 46.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 77.0%

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

   if 2.29999999999999995e116 < a

   1. Initial program 20.1%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 60.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+82}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+116}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y3 - x \cdot y2\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := x \cdot y - z \cdot t\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+170}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, t\_1, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+79}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, t\_2, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot t\_2 + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, t\_3, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, t\_1, \mathsf{fma}\left(b, t\_3, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z y3) (* x y2)))
        (t_2 (- (* y1 y4) (* y0 y5)))
        (t_3 (- (* x y) (* z t))))
   (if (<= a -7.8e+170)
     (*
      y1
      (fma a t_1 (fma y4 (fma k y2 (* j (- y3))) (* i (- (* x j) (* z k))))))
     (if (<= a -5.2e+79)
       (*
        y2
        (fma k t_2 (fma (- (* c y0) (* a y1)) x (* t (- (* a y5) (* c y4))))))
       (if (<= a 9e-21)
         (+ (* (- (* k y2) (* j y3)) t_2) (* y0 (* b (* z k))))
         (if (<= a 2.2e+168)
           (*
            b
            (+
             (fma a t_3 (* y4 (- (* t j) (* y k))))
             (* y0 (- (* z k) (* x j)))))
           (* a (fma y1 t_1 (fma b t_3 (* y5 (- (* t y2) (* y y3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) - (x * y2);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = (x * y) - (z * t);
	double tmp;
	if (a <= -7.8e+170) {
		tmp = y1 * fma(a, t_1, fma(y4, fma(k, y2, (j * -y3)), (i * ((x * j) - (z * k)))));
	} else if (a <= -5.2e+79) {
		tmp = y2 * fma(k, t_2, fma(((c * y0) - (a * y1)), x, (t * ((a * y5) - (c * y4)))));
	} else if (a <= 9e-21) {
		tmp = (((k * y2) - (j * y3)) * t_2) + (y0 * (b * (z * k)));
	} else if (a <= 2.2e+168) {
		tmp = b * (fma(a, t_3, (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = a * fma(y1, t_1, fma(b, t_3, (y5 * ((t * y2) - (y * y3)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * y3) - Float64(x * y2))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (a <= -7.8e+170)
		tmp = Float64(y1 * fma(a, t_1, fma(y4, fma(k, y2, Float64(j * Float64(-y3))), Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (a <= -5.2e+79)
		tmp = Float64(y2 * fma(k, t_2, fma(Float64(Float64(c * y0) - Float64(a * y1)), x, Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))));
	elseif (a <= 9e-21)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_2) + Float64(y0 * Float64(b * Float64(z * k))));
	elseif (a <= 2.2e+168)
		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)))));
	else
		tmp = Float64(a * fma(y1, t_1, fma(b, t_3, Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e+170], N[(y1 * N[(a * t$95$1 + N[(y4 * N[(k * y2 + N[(j * (-y3)), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.2e+79], N[(y2 * N[(k * t$95$2 + N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * x + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-21], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+168], 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], N[(a * N[(y1 * t$95$1 + N[(b * t$95$3 + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.8000000000000005e170

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 64.6%

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

   if -7.8000000000000005e170 < a < -5.20000000000000029e79

   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 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. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 65.5%

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

   if -5.20000000000000029e79 < a < 8.99999999999999936e-21

   1. Initial program 31.2%

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

   3. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower--.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. mul-1-neg N/A

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

      11. *-commutative N/A

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

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

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

      13. neg-mul-1 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - k \cdot z\right) \cdot \color{blue}{\left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      14. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right) \cdot \left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      15. lower--.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right)} \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      16. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(\color{blue}{j \cdot x} - k \cdot z\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      17. *-commutative N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      18. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      19. neg-mul-1 N/A

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

      20. lower-neg.f64 50.5

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

   5. Applied rewrites 50.5%

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

   6. Taylor expanded in k around inf

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

   8. Applied rewrites 51.7%

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

   if 8.99999999999999936e-21 < a < 2.2000000000000002e168

   1. Initial program 29.1%

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

   3. Taylor expanded in 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 54.5

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

   5. Applied rewrites 54.5%

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

   if 2.2000000000000002e168 < a

   1. Initial program 10.8%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 71.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+170}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+79}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := z \cdot y3 - x \cdot y2\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, t\_2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, t\_1, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, t\_2, \mathsf{fma}\left(b, t\_1, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))) (t_2 (- (* z y3) (* x y2))))
   (if (<= a -2.1e+139)
     (*
      y1
      (fma a t_2 (fma y4 (fma k y2 (* j (- y3))) (* i (- (* x j) (* z k))))))
     (if (<= a -7.8e+52)
       (*
        y
        (fma
         (- (* b y4) (* i y5))
         (- k)
         (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5))))))
       (if (<= a 9e-21)
         (+
          (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
          (* y0 (* b (* z k))))
         (if (<= a 2.2e+168)
           (*
            b
            (+
             (fma a t_1 (* y4 (- (* t j) (* y k))))
             (* y0 (- (* z k) (* x j)))))
           (* a (fma y1 t_2 (fma b t_1 (* y5 (- (* t y2) (* y y3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (z * t);
	double t_2 = (z * y3) - (x * y2);
	double tmp;
	if (a <= -2.1e+139) {
		tmp = y1 * fma(a, t_2, fma(y4, fma(k, y2, (j * -y3)), (i * ((x * j) - (z * k)))));
	} else if (a <= -7.8e+52) {
		tmp = y * fma(((b * y4) - (i * y5)), -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	} else if (a <= 9e-21) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y0 * (b * (z * k)));
	} else if (a <= 2.2e+168) {
		tmp = b * (fma(a, t_1, (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = a * fma(y1, t_2, fma(b, t_1, (y5 * ((t * y2) - (y * y3)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	t_2 = Float64(Float64(z * y3) - Float64(x * y2))
	tmp = 0.0
	if (a <= -2.1e+139)
		tmp = Float64(y1 * fma(a, t_2, fma(y4, fma(k, y2, Float64(j * Float64(-y3))), Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (a <= -7.8e+52)
		tmp = 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))))));
	elseif (a <= 9e-21)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y0 * Float64(b * Float64(z * k))));
	elseif (a <= 2.2e+168)
		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)))));
	else
		tmp = Float64(a * fma(y1, t_2, fma(b, t_1, Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+139], N[(y1 * N[(a * t$95$2 + N[(y4 * N[(k * y2 + N[(j * (-y3)), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.8e+52], 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], If[LessEqual[a, 9e-21], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+168], 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], N[(a * N[(y1 * t$95$2 + N[(b * t$95$1 + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.0999999999999999e139

   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 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 60.1%

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

   if -2.0999999999999999e139 < a < -7.7999999999999999e52

   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 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 65.2%

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

   if -7.7999999999999999e52 < a < 8.99999999999999936e-21

   1. Initial program 32.1%

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

   3. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower--.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. mul-1-neg N/A

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

      11. *-commutative N/A

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

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

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

      13. neg-mul-1 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - k \cdot z\right) \cdot \color{blue}{\left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      14. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right) \cdot \left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      15. lower--.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right)} \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      16. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(\color{blue}{j \cdot x} - k \cdot z\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      17. *-commutative N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      18. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      19. neg-mul-1 N/A

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

      20. lower-neg.f64 50.1

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

   5. Applied rewrites 50.1%

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

   6. Taylor expanded in k around inf

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

   8. Applied rewrites 52.1%

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

   if 8.99999999999999936e-21 < a < 2.2000000000000002e168

   1. Initial program 29.1%

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

   3. Taylor expanded in 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 54.5

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

   5. Applied rewrites 54.5%

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

   if 2.2000000000000002e168 < a

   1. Initial program 10.8%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 71.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y3 - x \cdot y2\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;a \leq -1.36 \cdot 10^{+212}:\\ \;\;\;\;a \cdot \left(y1 \cdot t\_1\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, t\_2, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, t\_1, \mathsf{fma}\left(b, t\_2, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z y3) (* x y2))) (t_2 (- (* x y) (* z t))))
   (if (<= a -1.36e+212)
     (* a (* y1 t_1))
     (if (<= a -7.8e+52)
       (*
        x
        (+
         (fma (- (* a b) (* c i)) y (* y2 (- (* c y0) (* a y1))))
         (* j (- (* i y1) (* b y0)))))
       (if (<= a 9e-21)
         (+
          (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
          (* y0 (* b (* z k))))
         (if (<= a 2.2e+168)
           (*
            b
            (+
             (fma a t_2 (* y4 (- (* t j) (* y k))))
             (* y0 (- (* z k) (* x j)))))
           (* a (fma y1 t_1 (fma b t_2 (* y5 (- (* t y2) (* y y3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) - (x * y2);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (a <= -1.36e+212) {
		tmp = a * (y1 * t_1);
	} else if (a <= -7.8e+52) {
		tmp = x * (fma(((a * b) - (c * i)), y, (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (a <= 9e-21) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y0 * (b * (z * k)));
	} else if (a <= 2.2e+168) {
		tmp = b * (fma(a, t_2, (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = a * fma(y1, t_1, fma(b, t_2, (y5 * ((t * y2) - (y * y3)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * y3) - Float64(x * y2))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (a <= -1.36e+212)
		tmp = Float64(a * Float64(y1 * t_1));
	elseif (a <= -7.8e+52)
		tmp = 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)))));
	elseif (a <= 9e-21)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y0 * Float64(b * Float64(z * k))));
	elseif (a <= 2.2e+168)
		tmp = Float64(b * Float64(fma(a, t_2, Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = Float64(a * fma(y1, t_1, fma(b, t_2, Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.36e+212], N[(a * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.8e+52], 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[a, 9e-21], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+168], N[(b * N[(N[(a * t$95$2 + 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], N[(a * N[(y1 * t$95$1 + N[(b * t$95$2 + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.35999999999999996e212

   1. Initial program 21.1%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 52.6%

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

   6. Taylor expanded in y1 around inf

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

   8. Applied rewrites 78.9%

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

   if -1.35999999999999996e212 < a < -7.7999999999999999e52

   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 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 50.5

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

   5. Applied rewrites 50.5%

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

   if -7.7999999999999999e52 < a < 8.99999999999999936e-21

   1. Initial program 32.1%

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

   3. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower--.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. mul-1-neg N/A

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

      11. *-commutative N/A

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

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

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

      13. neg-mul-1 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - k \cdot z\right) \cdot \color{blue}{\left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      14. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right) \cdot \left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      15. lower--.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right)} \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      16. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(\color{blue}{j \cdot x} - k \cdot z\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      17. *-commutative N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      18. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      19. neg-mul-1 N/A

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

      20. lower-neg.f64 50.1

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

   5. Applied rewrites 50.1%

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

   6. Taylor expanded in k around inf

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

   8. Applied rewrites 52.1%

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

   if 8.99999999999999936e-21 < a < 2.2000000000000002e168

   1. Initial program 29.1%

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

   3. Taylor expanded in 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 54.5

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

   5. Applied rewrites 54.5%

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

   if 2.2000000000000002e168 < a

   1. Initial program 10.8%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 71.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.36 \cdot 10^{+212}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 40.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y3 - x \cdot y2\\ t_2 := y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\\ t_3 := x \cdot y - z \cdot t\\ \mathbf{if}\;a \leq -7 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(y1 \cdot t\_1\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+82}:\\ \;\;\;\;a \cdot t\_2\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, t\_3, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, t\_1, \mathsf{fma}\left(b, t\_3, t\_2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z y3) (* x y2)))
        (t_2 (* y5 (- (* t y2) (* y y3))))
        (t_3 (- (* x y) (* z t))))
   (if (<= a -7e+217)
     (* a (* y1 t_1))
     (if (<= a -2e+82)
       (* a t_2)
       (if (<= a 9e-21)
         (+
          (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
          (* y0 (* b (* z k))))
         (if (<= a 2.2e+168)
           (*
            b
            (+
             (fma a t_3 (* y4 (- (* t j) (* y k))))
             (* y0 (- (* z k) (* x j)))))
           (* a (fma y1 t_1 (fma b t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * y3) - (x * y2);
	double t_2 = y5 * ((t * y2) - (y * y3));
	double t_3 = (x * y) - (z * t);
	double tmp;
	if (a <= -7e+217) {
		tmp = a * (y1 * t_1);
	} else if (a <= -2e+82) {
		tmp = a * t_2;
	} else if (a <= 9e-21) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y0 * (b * (z * k)));
	} else if (a <= 2.2e+168) {
		tmp = b * (fma(a, t_3, (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = a * fma(y1, t_1, fma(b, t_3, t_2));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * y3) - Float64(x * y2))
	t_2 = Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (a <= -7e+217)
		tmp = Float64(a * Float64(y1 * t_1));
	elseif (a <= -2e+82)
		tmp = Float64(a * t_2);
	elseif (a <= 9e-21)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y0 * Float64(b * Float64(z * k))));
	elseif (a <= 2.2e+168)
		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)))));
	else
		tmp = Float64(a * fma(y1, t_1, fma(b, t_3, t_2)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e+217], N[(a * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2e+82], N[(a * t$95$2), $MachinePrecision], If[LessEqual[a, 9e-21], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+168], 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], N[(a * N[(y1 * t$95$1 + N[(b * t$95$3 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.9999999999999996e217

   1. Initial program 22.2%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in y1 around inf

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

   8. Applied rewrites 77.8%

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

   if -6.9999999999999996e217 < a < -1.9999999999999999e82

   1. Initial program 36.6%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 40.7%

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

   6. Taylor expanded in y5 around inf

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

   8. Applied rewrites 50.9%

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

   if -1.9999999999999999e82 < a < 8.99999999999999936e-21

   1. Initial program 31.2%

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

   3. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower--.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. mul-1-neg N/A

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

      11. *-commutative N/A

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

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

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

      13. neg-mul-1 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - k \cdot z\right) \cdot \color{blue}{\left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      14. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right) \cdot \left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      15. lower--.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right)} \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      16. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(\color{blue}{j \cdot x} - k \cdot z\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      17. *-commutative N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      18. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      19. neg-mul-1 N/A

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

      20. lower-neg.f64 50.5

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

   5. Applied rewrites 50.5%

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

   6. Taylor expanded in k around inf

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

   8. Applied rewrites 51.7%

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

   if 8.99999999999999936e-21 < a < 2.2000000000000002e168

   1. Initial program 29.1%

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

   3. Taylor expanded in 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 54.5

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

   5. Applied rewrites 54.5%

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

   if 2.2000000000000002e168 < a

   1. Initial program 10.8%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 71.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+82}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+82}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+115}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -7e+217)
   (* a (* y1 (- (* z y3) (* x y2))))
   (if (<= a -2e+82)
     (* a (* y5 (- (* t y2) (* y y3))))
     (if (<= a 9.5e-21)
       (+
        (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
        (* y0 (* b (* z k))))
       (if (<= a 1.25e+79)
         (* x (* b (- (* y a) (* j y0))))
         (if (<= a 5e+115)
           (* b (* t (fma j y4 (* z (- a)))))
           (* x (* y2 (- (* c y0) (* a y1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -7e+217) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (a <= -2e+82) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (a <= 9.5e-21) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y0 * (b * (z * k)));
	} else if (a <= 1.25e+79) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (a <= 5e+115) {
		tmp = b * (t * fma(j, y4, (z * -a)));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (a <= -7e+217)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (a <= -2e+82)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (a <= 9.5e-21)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y0 * Float64(b * Float64(z * k))));
	elseif (a <= 1.25e+79)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (a <= 5e+115)
		tmp = Float64(b * Float64(t * fma(j, y4, Float64(z * Float64(-a)))));
	else
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -7e+217], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2e+82], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-21], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+79], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+115], N[(b * N[(t * N[(j * y4 + N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -6.9999999999999996e217

   1. Initial program 22.2%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in y1 around inf

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

   8. Applied rewrites 77.8%

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

   if -6.9999999999999996e217 < a < -1.9999999999999999e82

   1. Initial program 36.6%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 40.7%

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

   6. Taylor expanded in y5 around inf

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

   8. Applied rewrites 50.9%

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

   if -1.9999999999999999e82 < a < 9.4999999999999994e-21

   1. Initial program 31.2%

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

   3. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower--.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{x \cdot y2 - y3 \cdot z}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, \color{blue}{y2 \cdot x} - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. *-commutative N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - \color{blue}{z \cdot y3}, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. mul-1-neg N/A

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

      11. *-commutative N/A

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

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

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

      13. neg-mul-1 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - k \cdot z\right) \cdot \color{blue}{\left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      14. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right) \cdot \left(-1 \cdot b\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      15. lower--.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \color{blue}{\left(j \cdot x - k \cdot z\right)} \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      16. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(\color{blue}{j \cdot x} - k \cdot z\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      17. *-commutative N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      18. lower-*.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(c, y2 \cdot x - z \cdot y3, \left(j \cdot x - \color{blue}{z \cdot k}\right) \cdot \left(-1 \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      19. neg-mul-1 N/A

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

      20. lower-neg.f64 50.5

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

   5. Applied rewrites 50.5%

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

   6. Taylor expanded in k around inf

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

   8. Applied rewrites 51.7%

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

   if 9.4999999999999994e-21 < a < 1.25e79

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 61.1

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

   5. Applied rewrites 61.1%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 57.4%

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

   if 1.25e79 < a < 5.00000000000000008e115

   1. Initial program 24.9%

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

   3. Taylor expanded in 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 50.2

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 75.0%

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

   if 5.00000000000000008e115 < a

   1. Initial program 19.6%

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

   3. Taylor expanded in x around inf

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

      1. 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 31.8

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

   5. Applied rewrites 31.8%

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

   6. Taylor expanded in y2 around inf

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 51.5%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+82}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-21}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+115}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 32.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -2.9 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq -3.2 \cdot 10^{-203}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(-t\right)\\ \mathbf{elif}\;y0 \leq 4 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{-123}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.05 \cdot 10^{+68}:\\ \;\;\;\;\left(-j\right) \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 3.35 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -4.7e+95)
   (* b (* y0 (- (* z k) (* x j))))
   (if (<= y0 -2.9e-66)
     (* j (* y1 (fma (- y3) y4 (* x i))))
     (if (<= y0 -3.2e-203)
       (* (fma (- (* b y4) (* i y5)) (- j) (* y2 (- (* c y4) (* a y5)))) (- t))
       (if (<= y0 4e-200)
         (* a (* y5 (- (* t y2) (* y y3))))
         (if (<= y0 3.5e-123)
           (* y2 (* y4 (- (* k y1) (* t c))))
           (if (<= y0 1.05e+68)
             (* (- j) (* y3 (- (* y1 y4) (* y0 y5))))
             (if (<= y0 3.35e+149)
               (* b (* t (fma j y4 (* z (- a)))))
               (* x (* y2 (- (* c y0) (* a y1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.7e+95) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -2.9e-66) {
		tmp = j * (y1 * fma(-y3, y4, (x * i)));
	} else if (y0 <= -3.2e-203) {
		tmp = fma(((b * y4) - (i * y5)), -j, (y2 * ((c * y4) - (a * y5)))) * -t;
	} else if (y0 <= 4e-200) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y0 <= 3.5e-123) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y0 <= 1.05e+68) {
		tmp = -j * (y3 * ((y1 * y4) - (y0 * y5)));
	} else if (y0 <= 3.35e+149) {
		tmp = b * (t * fma(j, y4, (z * -a)));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -4.7e+95)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -2.9e-66)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))));
	elseif (y0 <= -3.2e-203)
		tmp = Float64(fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(-j), Float64(y2 * Float64(Float64(c * y4) - Float64(a * y5)))) * Float64(-t));
	elseif (y0 <= 4e-200)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y0 <= 3.5e-123)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y0 <= 1.05e+68)
		tmp = Float64(Float64(-j) * Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y0 <= 3.35e+149)
		tmp = Float64(b * Float64(t * fma(j, y4, Float64(z * Float64(-a)))));
	else
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -4.7e+95], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.9e-66], N[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.2e-203], N[(N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * (-j) + N[(y2 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[y0, 4e-200], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.5e-123], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.05e+68], N[((-j) * N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.35e+149], N[(b * N[(t * N[(j * y4 + N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y0 < -4.69999999999999972e95

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in y0 around inf

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

   8. Applied rewrites 55.2%

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

   if -4.69999999999999972e95 < y0 < -2.90000000000000011e-66

   1. Initial program 20.8%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 58.8%

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

   6. Taylor expanded in y1 around -inf

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

   8. Applied rewrites 63.1%

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

   if -2.90000000000000011e-66 < y0 < -3.2e-203

   1. Initial program 54.5%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 68.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 59.7%

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

   if -3.2e-203 < y0 < 3.9999999999999999e-200

   1. Initial program 41.7%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 51.8%

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

   6. Taylor expanded in y5 around inf

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

   8. Applied rewrites 45.2%

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

   if 3.9999999999999999e-200 < y0 < 3.4999999999999999e-123

   1. Initial program 31.7%

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

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 68.5%

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

   6. Taylor expanded in y4 around inf

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

   8. Applied rewrites 60.2%

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

   if 3.4999999999999999e-123 < y0 < 1.05e68

   1. Initial program 29.7%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 46.7%

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

   6. Taylor expanded in y3 around inf

      \[\leadsto \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{j}\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 47.1%

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

   if 1.05e68 < y0 < 3.34999999999999991e149

   1. Initial program 19.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 40.5

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

   5. Applied rewrites 40.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 66.7%

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

   if 3.34999999999999991e149 < y0

   1. Initial program 17.5%

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

   3. Taylor expanded in 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 47.0

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

   5. Applied rewrites 47.0%

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

   6. Taylor expanded in y2 around inf

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 57.2%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
3. Recombined 8 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -2.9 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq -3.2 \cdot 10^{-203}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(-t\right)\\ \mathbf{elif}\;y0 \leq 4 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{-123}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.05 \cdot 10^{+68}:\\ \;\;\;\;\left(-j\right) \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 3.35 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.55 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{-123}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.05 \cdot 10^{+68}:\\ \;\;\;\;\left(-j\right) \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 3.35 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -4.7e+95)
   (* b (* y0 (- (* z k) (* x j))))
   (if (<= y0 -1.55e-202)
     (* j (* y1 (fma (- y3) y4 (* x i))))
     (if (<= y0 4e-200)
       (* a (* y5 (- (* t y2) (* y y3))))
       (if (<= y0 3.5e-123)
         (* y2 (* y4 (- (* k y1) (* t c))))
         (if (<= y0 1.05e+68)
           (* (- j) (* y3 (- (* y1 y4) (* y0 y5))))
           (if (<= y0 3.35e+149)
             (* b (* t (fma j y4 (* z (- a)))))
             (* x (* y2 (- (* c y0) (* a y1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.7e+95) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -1.55e-202) {
		tmp = j * (y1 * fma(-y3, y4, (x * i)));
	} else if (y0 <= 4e-200) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y0 <= 3.5e-123) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y0 <= 1.05e+68) {
		tmp = -j * (y3 * ((y1 * y4) - (y0 * y5)));
	} else if (y0 <= 3.35e+149) {
		tmp = b * (t * fma(j, y4, (z * -a)));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -4.7e+95)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -1.55e-202)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))));
	elseif (y0 <= 4e-200)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y0 <= 3.5e-123)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y0 <= 1.05e+68)
		tmp = Float64(Float64(-j) * Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y0 <= 3.35e+149)
		tmp = Float64(b * Float64(t * fma(j, y4, Float64(z * Float64(-a)))));
	else
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -4.7e+95], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.55e-202], N[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4e-200], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.5e-123], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.05e+68], N[((-j) * N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.35e+149], N[(b * N[(t * N[(j * y4 + N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -4.69999999999999972e95

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in y0 around inf

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

   8. Applied rewrites 55.2%

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

   if -4.69999999999999972e95 < y0 < -1.55e-202

   1. Initial program 36.9%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 55.0%

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

   6. Taylor expanded in y1 around -inf

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

   8. Applied rewrites 50.8%

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

   if -1.55e-202 < y0 < 3.9999999999999999e-200

   1. Initial program 41.7%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 51.8%

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

   6. Taylor expanded in y5 around inf

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

   8. Applied rewrites 45.2%

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

   if 3.9999999999999999e-200 < y0 < 3.4999999999999999e-123

   1. Initial program 31.7%

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

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 68.5%

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

   6. Taylor expanded in y4 around inf

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

   8. Applied rewrites 60.2%

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

   if 3.4999999999999999e-123 < y0 < 1.05e68

   1. Initial program 29.7%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 46.7%

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

   6. Taylor expanded in y3 around inf

      \[\leadsto \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{j}\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 47.1%

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

   if 1.05e68 < y0 < 3.34999999999999991e149

   1. Initial program 19.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 40.5

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

   5. Applied rewrites 40.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 66.7%

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

   if 3.34999999999999991e149 < y0

   1. Initial program 17.5%

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

   3. Taylor expanded in 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 47.0

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

   5. Applied rewrites 47.0%

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

   6. Taylor expanded in y2 around inf

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 57.2%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.55 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{-123}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.05 \cdot 10^{+68}:\\ \;\;\;\;\left(-j\right) \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 3.35 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.55 \cdot 10^{-202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 4 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 1.28 \cdot 10^{-120}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 3.35 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (fma (- y3) y4 (* x i))))))
   (if (<= y0 -4.7e+95)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= y0 -1.55e-202)
       t_1
       (if (<= y0 4e-200)
         (* a (* y5 (- (* t y2) (* y y3))))
         (if (<= y0 1.28e-120)
           (* y2 (* y4 (- (* k y1) (* t c))))
           (if (<= y0 1.5e+97)
             t_1
             (if (<= y0 3.35e+149)
               (* b (* t (fma j y4 (* z (- a)))))
               (* x (* y2 (- (* c y0) (* a y1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y1 * fma(-y3, y4, (x * i)));
	double tmp;
	if (y0 <= -4.7e+95) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -1.55e-202) {
		tmp = t_1;
	} else if (y0 <= 4e-200) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y0 <= 1.28e-120) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y0 <= 1.5e+97) {
		tmp = t_1;
	} else if (y0 <= 3.35e+149) {
		tmp = b * (t * fma(j, y4, (z * -a)));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))))
	tmp = 0.0
	if (y0 <= -4.7e+95)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -1.55e-202)
		tmp = t_1;
	elseif (y0 <= 4e-200)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y0 <= 1.28e-120)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y0 <= 1.5e+97)
		tmp = t_1;
	elseif (y0 <= 3.35e+149)
		tmp = Float64(b * Float64(t * fma(j, y4, Float64(z * Float64(-a)))));
	else
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	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[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -4.7e+95], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.55e-202], t$95$1, If[LessEqual[y0, 4e-200], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.28e-120], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.5e+97], t$95$1, If[LessEqual[y0, 3.35e+149], N[(b * N[(t * N[(j * y4 + N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -4.69999999999999972e95

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in y0 around inf

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

   8. Applied rewrites 55.2%

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

   if -4.69999999999999972e95 < y0 < -1.55e-202 or 1.28000000000000008e-120 < y0 < 1.4999999999999999e97

   1. Initial program 33.7%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 51.9%

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

   6. Taylor expanded in y1 around -inf

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

   8. Applied rewrites 45.1%

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

   if -1.55e-202 < y0 < 3.9999999999999999e-200

   1. Initial program 41.7%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 51.8%

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

   6. Taylor expanded in y5 around inf

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

   8. Applied rewrites 45.2%

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

   if 3.9999999999999999e-200 < y0 < 1.28000000000000008e-120

   1. Initial program 30.4%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 69.9%

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

   6. Taylor expanded in y4 around inf

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

   8. Applied rewrites 61.9%

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

   if 1.4999999999999999e97 < y0 < 3.34999999999999991e149

   1. Initial program 18.0%

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

   3. Taylor expanded in 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 46.1

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

   5. Applied rewrites 46.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 72.8%

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

   if 3.34999999999999991e149 < y0

   1. Initial program 17.5%

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

   3. Taylor expanded in 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 47.0

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

   5. Applied rewrites 47.0%

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

   6. Taylor expanded in y2 around inf

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 57.2%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.55 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 1.28 \cdot 10^{-120}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 3.35 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 5.8 \cdot 10^{-152}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 3.35 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (fma (- y3) y4 (* x i))))))
   (if (<= y0 -4.7e+95)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= y0 -5e-70)
       t_1
       (if (<= y0 4.8e-223)
         (* a (* y3 (fma y1 z (* y (- y5)))))
         (if (<= y0 5.8e-152)
           (* (* t y2) (- (* a y5) (* c y4)))
           (if (<= y0 1.5e+97)
             t_1
             (if (<= y0 3.35e+149)
               (* b (* t (fma j y4 (* z (- a)))))
               (* x (* y2 (- (* c y0) (* a y1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y1 * fma(-y3, y4, (x * i)));
	double tmp;
	if (y0 <= -4.7e+95) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -5e-70) {
		tmp = t_1;
	} else if (y0 <= 4.8e-223) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else if (y0 <= 5.8e-152) {
		tmp = (t * y2) * ((a * y5) - (c * y4));
	} else if (y0 <= 1.5e+97) {
		tmp = t_1;
	} else if (y0 <= 3.35e+149) {
		tmp = b * (t * fma(j, y4, (z * -a)));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))))
	tmp = 0.0
	if (y0 <= -4.7e+95)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -5e-70)
		tmp = t_1;
	elseif (y0 <= 4.8e-223)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	elseif (y0 <= 5.8e-152)
		tmp = Float64(Float64(t * y2) * Float64(Float64(a * y5) - Float64(c * y4)));
	elseif (y0 <= 1.5e+97)
		tmp = t_1;
	elseif (y0 <= 3.35e+149)
		tmp = Float64(b * Float64(t * fma(j, y4, Float64(z * Float64(-a)))));
	else
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	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[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -4.7e+95], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5e-70], t$95$1, If[LessEqual[y0, 4.8e-223], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.8e-152], N[(N[(t * y2), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.5e+97], t$95$1, If[LessEqual[y0, 3.35e+149], N[(b * N[(t * N[(j * y4 + N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -4.69999999999999972e95

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in y0 around inf

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

   8. Applied rewrites 55.2%

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

   if -4.69999999999999972e95 < y0 < -4.9999999999999998e-70 or 5.8000000000000003e-152 < y0 < 1.4999999999999999e97

   1. Initial program 27.6%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 47.9%

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

   6. Taylor expanded in y1 around -inf

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

   8. Applied rewrites 45.6%

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

   if -4.9999999999999998e-70 < y0 < 4.79999999999999971e-223

   1. Initial program 47.3%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 49.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 28.9%

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

   9. Taylor expanded in y3 around inf

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

   11. Applied rewrites 46.2%

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

   if 4.79999999999999971e-223 < y0 < 5.8000000000000003e-152

   1. Initial program 34.7%

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

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 61.4%

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

   6. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

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

   if 1.4999999999999999e97 < y0 < 3.34999999999999991e149

   1. Initial program 18.0%

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

   3. Taylor expanded in 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 46.1

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

   5. Applied rewrites 46.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 72.8%

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

   if 3.34999999999999991e149 < y0

   1. Initial program 17.5%

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

   3. Taylor expanded in 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 47.0

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

   5. Applied rewrites 47.0%

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

   6. Taylor expanded in y2 around inf

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 57.2%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 5.8 \cdot 10^{-152}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 3.35 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.15 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -2.9 \cdot 10^{-172}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-301}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.7 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(c \cdot \mathsf{fma}\left(-i, y, y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 6.2 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y5 \cdot \mathsf{fma}\left(y0, y3, i \cdot \left(-t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -1.15e+123)
   (* a (* y5 (- (* t y2) (* y y3))))
   (if (<= y5 -2.9e-172)
     (* a (* y1 (- (* z y3) (* x y2))))
     (if (<= y5 -1.45e-301)
       (* x (* b (- (* y a) (* j y0))))
       (if (<= y5 1.7e-238)
         (* x (* c (fma (- i) y (* y0 y2))))
         (if (<= y5 6.2e+63)
           (* b (* y0 (- (* z k) (* x j))))
           (* j (* y5 (fma y0 y3 (* i (- 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 (y5 <= -1.15e+123) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y5 <= -2.9e-172) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= -1.45e-301) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (y5 <= 1.7e-238) {
		tmp = x * (c * fma(-i, y, (y0 * y2)));
	} else if (y5 <= 6.2e+63) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = j * (y5 * fma(y0, y3, (i * -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 (y5 <= -1.15e+123)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y5 <= -2.9e-172)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y5 <= -1.45e-301)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y5 <= 1.7e-238)
		tmp = Float64(x * Float64(c * fma(Float64(-i), y, Float64(y0 * y2))));
	elseif (y5 <= 6.2e+63)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = Float64(j * Float64(y5 * fma(y0, y3, Float64(i * Float64(-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[y5, -1.15e+123], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.9e-172], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.45e-301], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.7e-238], N[(x * N[(c * N[((-i) * y + N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6.2e+63], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y5 * N[(y0 * y3 + N[(i * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -1.14999999999999995e123

   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 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. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 48.3%

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

   6. Taylor expanded in y5 around inf

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

   8. Applied rewrites 55.5%

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

   if -1.14999999999999995e123 < y5 < -2.89999999999999997e-172

   1. Initial program 30.1%

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 47.4%

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

   6. Taylor expanded in y1 around inf

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

   8. Applied rewrites 42.6%

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

   if -2.89999999999999997e-172 < y5 < -1.44999999999999992e-301

   1. Initial program 36.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 49.3

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

   5. Applied rewrites 49.3%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 54.2%

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

   if -1.44999999999999992e-301 < y5 < 1.69999999999999992e-238

   1. Initial program 38.7%

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

   3. Taylor expanded in x around inf

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

      1. 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 54.8

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in c around inf

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

   8. Applied rewrites 62.9%

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

   if 1.69999999999999992e-238 < y5 < 6.2000000000000001e63

   1. Initial program 30.5%

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

   3. Taylor expanded in 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 53.4

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

   5. Applied rewrites 53.4%

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

   6. Taylor expanded in y0 around inf

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

   8. Applied rewrites 44.8%

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

   if 6.2000000000000001e63 < y5

   1. Initial program 17.8%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 47.2%

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

   6. Taylor expanded in y5 around -inf

      \[\leadsto \left(-1 \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{j}\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 47.2%

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

   9. Taylor expanded in y5 around -inf

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

   11. Applied rewrites 49.5%

       \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(y0, y3, \left(-i\right) \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.15 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -2.9 \cdot 10^{-172}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-301}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.7 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(c \cdot \mathsf{fma}\left(-i, y, y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 6.2 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y5 \cdot \mathsf{fma}\left(y0, y3, i \cdot \left(-t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 28.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.9 \cdot 10^{+80}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -255000000:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{-259}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{+37}:\\ \;\;\;\;j \cdot \left(x \cdot \mathsf{fma}\left(i, y1, b \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.9e+80)
   (* (- c) (* t (* y2 y4)))
   (if (<= y4 -255000000.0)
     (* a (* b (- (* x y) (* z t))))
     (if (<= y4 -1.02e-259)
       (* a (* y2 (fma (- x) y1 (* t y5))))
       (if (<= y4 1.15e-40)
         (* (fma c y2 (- (* b j))) (* x y0))
         (if (<= y4 7.5e+37)
           (* j (* x (fma i y1 (* b (- y0)))))
           (* (* k y2) (- (* y1 y4) (* y0 y5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.9e+80) {
		tmp = -c * (t * (y2 * y4));
	} else if (y4 <= -255000000.0) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= -1.02e-259) {
		tmp = a * (y2 * fma(-x, y1, (t * y5)));
	} else if (y4 <= 1.15e-40) {
		tmp = fma(c, y2, -(b * j)) * (x * y0);
	} else if (y4 <= 7.5e+37) {
		tmp = j * (x * fma(i, y1, (b * -y0)));
	} else {
		tmp = (k * y2) * ((y1 * y4) - (y0 * y5));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.9e+80)
		tmp = Float64(Float64(-c) * Float64(t * Float64(y2 * y4)));
	elseif (y4 <= -255000000.0)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= -1.02e-259)
		tmp = Float64(a * Float64(y2 * fma(Float64(-x), y1, Float64(t * y5))));
	elseif (y4 <= 1.15e-40)
		tmp = Float64(fma(c, y2, Float64(-Float64(b * j))) * Float64(x * y0));
	elseif (y4 <= 7.5e+37)
		tmp = Float64(j * Float64(x * fma(i, y1, Float64(b * Float64(-y0)))));
	else
		tmp = Float64(Float64(k * y2) * Float64(Float64(y1 * y4) - Float64(y0 * y5)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.9e+80], N[((-c) * N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -255000000.0], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.02e-259], N[(a * N[(y2 * N[((-x) * y1 + N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.15e-40], N[(N[(c * y2 + (-N[(b * j), $MachinePrecision])), $MachinePrecision] * N[(x * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.5e+37], N[(j * N[(x * N[(i * y1 + N[(b * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * y2), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -1.89999999999999999e80

   1. Initial program 29.8%

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

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 48.8%

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

   6. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.2%

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

   9. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 47.1%

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

   if -1.89999999999999999e80 < y4 < -2.55e8

   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 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. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 54.2%

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

   if -2.55e8 < y4 < -1.01999999999999995e-259

   1. Initial program 25.7%

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Applied rewrites 37.8%

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

   6. Taylor expanded in y2 around inf

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

   8. Applied rewrites 37.9%

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

   if -1.01999999999999995e-259 < y4 < 1.15e-40

   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 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 45.4

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

   5. Applied rewrites 45.4%

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

   6. Taylor expanded in y0 around inf

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

   8. Applied rewrites 44.0%

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

   if 1.15e-40 < y4 < 7.5000000000000003e37

   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 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 44.3

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

   5. Applied rewrites 44.3%

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

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 63.0%

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

   if 7.5000000000000003e37 < y4

   1. Initial program 25.6%

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

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Applied rewrites 45.6%

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

   6. Taylor expanded in k around inf

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

   8. Applied rewrites 46.5%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.9 \cdot 10^{+80}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -255000000:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{-259}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{+37}:\\ \;\;\;\;j \cdot \left(x \cdot \mathsf{fma}\left(i, y1, b \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.5% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.1 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-69}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq -1.22 \cdot 10^{-250}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \mathsf{fma}\left(b, j, -c \cdot y2\right)\\ \mathbf{elif}\;y1 \leq 2.15 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(y5 \cdot \mathsf{fma}\left(y0, y3, i \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.6 \cdot 10^{+86}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.1e+38)
   (* j (* y1 (fma (- y3) y4 (* x i))))
   (if (<= y1 -1.9e-69)
     (* a (* b (- (* x y) (* z t))))
     (if (<= y1 -1.22e-250)
       (* (* t y4) (fma b j (- (* c y2))))
       (if (<= y1 2.15e-51)
         (* j (* y5 (fma y0 y3 (* i (- t)))))
         (if (<= y1 1.6e+86)
           (* (* b y4) (- (* t j) (* y k)))
           (* a (* y1 (- (* z y3) (* x y2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -1.1e+38) {
		tmp = j * (y1 * fma(-y3, y4, (x * i)));
	} else if (y1 <= -1.9e-69) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= -1.22e-250) {
		tmp = (t * y4) * fma(b, j, -(c * y2));
	} else if (y1 <= 2.15e-51) {
		tmp = j * (y5 * fma(y0, y3, (i * -t)));
	} else if (y1 <= 1.6e+86) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -1.1e+38)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))));
	elseif (y1 <= -1.9e-69)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= -1.22e-250)
		tmp = Float64(Float64(t * y4) * fma(b, j, Float64(-Float64(c * y2))));
	elseif (y1 <= 2.15e-51)
		tmp = Float64(j * Float64(y5 * fma(y0, y3, Float64(i * Float64(-t)))));
	elseif (y1 <= 1.6e+86)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	else
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -1.1e+38], N[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.9e-69], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.22e-250], N[(N[(t * y4), $MachinePrecision] * N[(b * j + (-N[(c * y2), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.15e-51], N[(j * N[(y5 * N[(y0 * y3 + N[(i * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.6e+86], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -1.10000000000000003e38

   1. Initial program 24.5%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 39.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 41.5%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -1.10000000000000003e38 < y1 < -1.8999999999999999e-69

   1. Initial program 42.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 42.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 48.1%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

   if -1.8999999999999999e-69 < y1 < -1.2200000000000001e-250

   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 t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Applied rewrites 44.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot y2\right) + b \cdot j\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.9%

      \[\leadsto \left(t \cdot y4\right) \cdot \color{blue}{\mathsf{fma}\left(b, j, -c \cdot y2\right)} \]

   if -1.2200000000000001e-250 < y1 < 2.1499999999999999e-51

   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 j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 40.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y5 around -inf

      \[\leadsto \left(-1 \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{j}\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 38.8%

      \[\leadsto \left(\left(-y5\right) \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right) \cdot \left(-\color{blue}{j}\right) \]

   9. Taylor expanded in y5 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 41.0%

       \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(y0, y3, \left(-i\right) \cdot t\right)\right)} \]

   if 2.1499999999999999e-51 < y1 < 1.6e86

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 42.8

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 42.8%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 31.7%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(j, y4, \left(-a\right) \cdot z\right)}\right) \]

   9. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 43.4%

       \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]

   if 1.6e86 < y1

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 50.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z - x \cdot y2\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 54.0%

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z - x \cdot y2\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.1 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-69}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq -1.22 \cdot 10^{-250}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \mathsf{fma}\left(b, j, -c \cdot y2\right)\\ \mathbf{elif}\;y1 \leq 2.15 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(y5 \cdot \mathsf{fma}\left(y0, y3, i \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.6 \cdot 10^{+86}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{if}\;y1 \leq -1.1 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-69}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq -1.22 \cdot 10^{-250}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \mathsf{fma}\left(b, j, -c \cdot y2\right)\\ \mathbf{elif}\;y1 \leq 2.15 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(y5 \cdot \mathsf{fma}\left(y0, y3, i \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (fma (- y3) y4 (* x i))))))
   (if (<= y1 -1.1e+38)
     t_1
     (if (<= y1 -1.9e-69)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y1 -1.22e-250)
         (* (* t y4) (fma b j (- (* c y2))))
         (if (<= y1 2.15e-51)
           (* j (* y5 (fma y0 y3 (* i (- t)))))
           (if (<= y1 3.4e+90) (* (* 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 = j * (y1 * fma(-y3, y4, (x * i)));
	double tmp;
	if (y1 <= -1.1e+38) {
		tmp = t_1;
	} else if (y1 <= -1.9e-69) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= -1.22e-250) {
		tmp = (t * y4) * fma(b, j, -(c * y2));
	} else if (y1 <= 2.15e-51) {
		tmp = j * (y5 * fma(y0, y3, (i * -t)));
	} else if (y1 <= 3.4e+90) {
		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(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))))
	tmp = 0.0
	if (y1 <= -1.1e+38)
		tmp = t_1;
	elseif (y1 <= -1.9e-69)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= -1.22e-250)
		tmp = Float64(Float64(t * y4) * fma(b, j, Float64(-Float64(c * y2))));
	elseif (y1 <= 2.15e-51)
		tmp = Float64(j * Float64(y5 * fma(y0, y3, Float64(i * Float64(-t)))));
	elseif (y1 <= 3.4e+90)
		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[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.1e+38], t$95$1, If[LessEqual[y1, -1.9e-69], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.22e-250], N[(N[(t * y4), $MachinePrecision] * N[(b * j + (-N[(c * y2), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.15e-51], N[(j * N[(y5 * N[(y0 * y3 + N[(i * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.4e+90], 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 y1 < -1.10000000000000003e38 or 3.40000000000000018e90 < y1

   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 j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 45.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.1%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -1.10000000000000003e38 < y1 < -1.8999999999999999e-69

   1. Initial program 42.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 42.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 48.1%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right) \]

   if -1.8999999999999999e-69 < y1 < -1.2200000000000001e-250

   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 t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Applied rewrites 44.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot y2\right) + b \cdot j\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.9%

      \[\leadsto \left(t \cdot y4\right) \cdot \color{blue}{\mathsf{fma}\left(b, j, -c \cdot y2\right)} \]

   if -1.2200000000000001e-250 < y1 < 2.1499999999999999e-51

   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 j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 40.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y5 around -inf

      \[\leadsto \left(-1 \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{j}\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 38.8%

      \[\leadsto \left(\left(-y5\right) \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right) \cdot \left(-\color{blue}{j}\right) \]

   9. Taylor expanded in y5 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 41.0%

       \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(y0, y3, \left(-i\right) \cdot t\right)\right)} \]

   if 2.1499999999999999e-51 < y1 < 3.40000000000000018e90

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 39.8

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 39.8%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 33.0%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(j, y4, \left(-a\right) \cdot z\right)}\right) \]

   9. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 40.4%

       \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.1 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-69}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq -1.22 \cdot 10^{-250}:\\ \;\;\;\;\left(t \cdot y4\right) \cdot \mathsf{fma}\left(b, j, -c \cdot y2\right)\\ \mathbf{elif}\;y1 \leq 2.15 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(y5 \cdot \mathsf{fma}\left(y0, y3, i \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.7% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.7 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 3.35 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -4.7e+95)
   (* b (* y0 (- (* z k) (* x j))))
   (if (<= y0 -5e-70)
     (* j (* y1 (fma (- y3) y4 (* x i))))
     (if (<= y0 4.7e+58)
       (* a (* y3 (fma y1 z (* y (- y5)))))
       (if (<= y0 3.35e+149)
         (* b (* t (fma j y4 (* z (- a)))))
         (* x (* y2 (- (* c y0) (* a y1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.7e+95) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -5e-70) {
		tmp = j * (y1 * fma(-y3, y4, (x * i)));
	} else if (y0 <= 4.7e+58) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else if (y0 <= 3.35e+149) {
		tmp = b * (t * fma(j, y4, (z * -a)));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -4.7e+95)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -5e-70)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))));
	elseif (y0 <= 4.7e+58)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	elseif (y0 <= 3.35e+149)
		tmp = Float64(b * Float64(t * fma(j, y4, Float64(z * Float64(-a)))));
	else
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -4.7e+95], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5e-70], N[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.7e+58], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.35e+149], N[(b * N[(t * N[(j * y4 + N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -4.69999999999999972e95

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 55.4

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 55.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z - j \cdot x\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 55.2%

      \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z - j \cdot x\right)}\right) \]

   if -4.69999999999999972e95 < y0 < -4.9999999999999998e-70

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 56.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.7%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -4.9999999999999998e-70 < y0 < 4.69999999999999972e58

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 46.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 28.1%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-y3, y5, b \cdot x\right)}\right) \]

   9. Taylor expanded in y3 around inf

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 38.9%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -y \cdot y5\right)}\right) \]

   if 4.69999999999999972e58 < y0 < 3.34999999999999991e149

   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 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 40.7

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 40.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 50.6%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(j, y4, \left(-a\right) \cdot z\right)}\right) \]

   if 3.34999999999999991e149 < y0

   1. Initial program 17.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 47.0

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Applied rewrites 47.0%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 57.2%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.7 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 3.35 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(t \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.4% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{if}\;y1 \leq -650000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -1.35 \cdot 10^{-213}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(t \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.15 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(y5 \cdot \mathsf{fma}\left(y0, y3, i \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (fma (- y3) y4 (* x i))))))
   (if (<= y1 -650000000000.0)
     t_1
     (if (<= y1 -1.35e-213)
       (* (* c y4) (* t (- y2)))
       (if (<= y1 2.15e-51)
         (* j (* y5 (fma y0 y3 (* i (- t)))))
         (if (<= y1 3.4e+90) (* (* 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 = j * (y1 * fma(-y3, y4, (x * i)));
	double tmp;
	if (y1 <= -650000000000.0) {
		tmp = t_1;
	} else if (y1 <= -1.35e-213) {
		tmp = (c * y4) * (t * -y2);
	} else if (y1 <= 2.15e-51) {
		tmp = j * (y5 * fma(y0, y3, (i * -t)));
	} else if (y1 <= 3.4e+90) {
		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(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))))
	tmp = 0.0
	if (y1 <= -650000000000.0)
		tmp = t_1;
	elseif (y1 <= -1.35e-213)
		tmp = Float64(Float64(c * y4) * Float64(t * Float64(-y2)));
	elseif (y1 <= 2.15e-51)
		tmp = Float64(j * Float64(y5 * fma(y0, y3, Float64(i * Float64(-t)))));
	elseif (y1 <= 3.4e+90)
		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[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -650000000000.0], t$95$1, If[LessEqual[y1, -1.35e-213], N[(N[(c * y4), $MachinePrecision] * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.15e-51], N[(j * N[(y5 * N[(y0 * y3 + N[(i * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.4e+90], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -6.5e11 or 3.40000000000000018e90 < y1

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 43.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 46.6%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -6.5e11 < y1 < -1.35e-213

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. associate--l+ N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4} - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \mathsf{neg}\left(\color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot t}\right)\right)\right) \]

   5. Applied rewrites 51.8%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 43.2%

      \[\leadsto -\left(t \cdot y2\right) \cdot \left(c \cdot y4 - a \cdot y5\right) \]

   9. Taylor expanded in c around inf

      \[\leadsto \mathsf{neg}\left(\left(t \cdot y2\right) \cdot \left(c \cdot y4\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 41.4%

       \[\leadsto -\left(t \cdot y2\right) \cdot \left(c \cdot y4\right) \]

   if -1.35e-213 < y1 < 2.1499999999999999e-51

   1. Initial program 40.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 39.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y5 around -inf

      \[\leadsto \left(-1 \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{j}\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 35.6%

      \[\leadsto \left(\left(-y5\right) \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right) \cdot \left(-\color{blue}{j}\right) \]

   9. Taylor expanded in y5 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 37.4%

       \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(y0, y3, \left(-i\right) \cdot t\right)\right)} \]

   if 2.1499999999999999e-51 < y1 < 3.40000000000000018e90

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 39.8

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 39.8%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 33.0%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(j, y4, \left(-a\right) \cdot z\right)}\right) \]

   9. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 40.4%

       \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -650000000000:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.35 \cdot 10^{-213}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(t \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.15 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(y5 \cdot \mathsf{fma}\left(y0, y3, i \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.3% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{if}\;y1 \leq -650000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -1.55 \cdot 10^{-207}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(t \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.6 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (fma (- y3) y4 (* x i))))))
   (if (<= y1 -650000000000.0)
     t_1
     (if (<= y1 -1.55e-207)
       (* (* c y4) (* t (- y2)))
       (if (<= y1 5.6e-53)
         (* (fma c y2 (- (* b j))) (* x y0))
         (if (<= y1 3.4e+90) (* (* 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 = j * (y1 * fma(-y3, y4, (x * i)));
	double tmp;
	if (y1 <= -650000000000.0) {
		tmp = t_1;
	} else if (y1 <= -1.55e-207) {
		tmp = (c * y4) * (t * -y2);
	} else if (y1 <= 5.6e-53) {
		tmp = fma(c, y2, -(b * j)) * (x * y0);
	} else if (y1 <= 3.4e+90) {
		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(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))))
	tmp = 0.0
	if (y1 <= -650000000000.0)
		tmp = t_1;
	elseif (y1 <= -1.55e-207)
		tmp = Float64(Float64(c * y4) * Float64(t * Float64(-y2)));
	elseif (y1 <= 5.6e-53)
		tmp = Float64(fma(c, y2, Float64(-Float64(b * j))) * Float64(x * y0));
	elseif (y1 <= 3.4e+90)
		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[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -650000000000.0], t$95$1, If[LessEqual[y1, -1.55e-207], N[(N[(c * y4), $MachinePrecision] * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.6e-53], N[(N[(c * y2 + (-N[(b * j), $MachinePrecision])), $MachinePrecision] * N[(x * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.4e+90], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -6.5e11 or 3.40000000000000018e90 < y1

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 43.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 46.6%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -6.5e11 < y1 < -1.5500000000000001e-207

   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. associate--l+ N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4} - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \mathsf{neg}\left(\color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot t}\right)\right)\right) \]

   5. Applied rewrites 51.8%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.9%

      \[\leadsto -\left(t \cdot y2\right) \cdot \left(c \cdot y4 - a \cdot y5\right) \]

   9. Taylor expanded in c around inf

      \[\leadsto \mathsf{neg}\left(\left(t \cdot y2\right) \cdot \left(c \cdot y4\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 41.0%

       \[\leadsto -\left(t \cdot y2\right) \cdot \left(c \cdot y4\right) \]

   if -1.5500000000000001e-207 < y1 < 5.59999999999999971e-53

   1. Initial program 41.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. 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 42.2

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Applied rewrites 42.2%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.9%

      \[\leadsto \left(x \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)} \]

   if 5.59999999999999971e-53 < y1 < 3.40000000000000018e90

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 38.4

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 38.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 31.8%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(j, y4, \left(-a\right) \cdot z\right)}\right) \]

   9. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 39.1%

       \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -650000000000:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.55 \cdot 10^{-207}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(t \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.6 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 32.8% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.45 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y0 \cdot \mathsf{fma}\left(c, y2, -b \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -4.7e+95)
   (* b (* y0 (- (* z k) (* x j))))
   (if (<= y0 -5e-70)
     (* j (* y1 (fma (- y3) y4 (* x i))))
     (if (<= y0 4.45e+58)
       (* a (* y3 (fma y1 z (* y (- y5)))))
       (* x (* y0 (fma c y2 (- (* b j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.7e+95) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -5e-70) {
		tmp = j * (y1 * fma(-y3, y4, (x * i)));
	} else if (y0 <= 4.45e+58) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else {
		tmp = x * (y0 * fma(c, y2, -(b * j)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -4.7e+95)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -5e-70)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))));
	elseif (y0 <= 4.45e+58)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	else
		tmp = Float64(x * Float64(y0 * fma(c, y2, Float64(-Float64(b * j)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -4.7e+95], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5e-70], N[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.45e+58], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y0 * N[(c * y2 + (-N[(b * j), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -4.69999999999999972e95

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 55.4

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 55.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z - j \cdot x\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 55.2%

      \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z - j \cdot x\right)}\right) \]

   if -4.69999999999999972e95 < y0 < -4.9999999999999998e-70

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 56.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.7%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -4.9999999999999998e-70 < y0 < 4.45e58

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 46.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 28.1%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-y3, y5, b \cdot x\right)}\right) \]

   9. Taylor expanded in y3 around inf

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 38.9%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -y \cdot y5\right)}\right) \]

   if 4.45e58 < y0

   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 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 41.8

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Applied rewrites 41.8%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto x \cdot \left(y0 \cdot \color{blue}{\left(c \cdot y2 - b \cdot j\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.45 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y0 \cdot \mathsf{fma}\left(c, y2, -b \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 32.4% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.45 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -4.7e+95)
   (* b (* y0 (- (* z k) (* x j))))
   (if (<= y0 -5e-70)
     (* j (* y1 (fma (- y3) y4 (* x i))))
     (if (<= y0 4.45e+58)
       (* a (* y3 (fma y1 z (* y (- y5)))))
       (* (fma c y2 (- (* b j))) (* x y0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.7e+95) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -5e-70) {
		tmp = j * (y1 * fma(-y3, y4, (x * i)));
	} else if (y0 <= 4.45e+58) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else {
		tmp = fma(c, y2, -(b * j)) * (x * y0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -4.7e+95)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -5e-70)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))));
	elseif (y0 <= 4.45e+58)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	else
		tmp = Float64(fma(c, y2, Float64(-Float64(b * j))) * Float64(x * y0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -4.7e+95], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5e-70], N[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.45e+58], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * y2 + (-N[(b * j), $MachinePrecision])), $MachinePrecision] * N[(x * y0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -4.69999999999999972e95

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 55.4

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 55.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z - j \cdot x\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 55.2%

      \[\leadsto b \cdot \left(y0 \cdot \color{blue}{\left(k \cdot z - j \cdot x\right)}\right) \]

   if -4.69999999999999972e95 < y0 < -4.9999999999999998e-70

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 56.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.7%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -4.9999999999999998e-70 < y0 < 4.45e58

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 46.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 28.1%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-y3, y5, b \cdot x\right)}\right) \]

   9. Taylor expanded in y3 around inf

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 38.9%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -y \cdot y5\right)}\right) \]

   if 4.45e58 < y0

   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 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 41.8

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Applied rewrites 41.8%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.9%

      \[\leadsto \left(x \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.45 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 31.1% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -7.6 \cdot 10^{+99}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.45 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -7.6e+99)
   (* b (* x (- (* y a) (* j y0))))
   (if (<= y0 -5e-70)
     (* j (* y1 (fma (- y3) y4 (* x i))))
     (if (<= y0 4.45e+58)
       (* a (* y3 (fma y1 z (* y (- y5)))))
       (* (fma c y2 (- (* b j))) (* x y0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -7.6e+99) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y0 <= -5e-70) {
		tmp = j * (y1 * fma(-y3, y4, (x * i)));
	} else if (y0 <= 4.45e+58) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else {
		tmp = fma(c, y2, -(b * j)) * (x * y0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -7.6e+99)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y0 <= -5e-70)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))));
	elseif (y0 <= 4.45e+58)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	else
		tmp = Float64(fma(c, y2, Float64(-Float64(b * j))) * Float64(x * y0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -7.6e+99], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5e-70], N[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.45e+58], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * y2 + (-N[(b * j), $MachinePrecision])), $MachinePrecision] * N[(x * y0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -7.6e99

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 56.4

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 56.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 49.0%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   if -7.6e99 < y0 < -4.9999999999999998e-70

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 54.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 58.4%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -4.9999999999999998e-70 < y0 < 4.45e58

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 46.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 28.1%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-y3, y5, b \cdot x\right)}\right) \]

   9. Taylor expanded in y3 around inf

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 38.9%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -y \cdot y5\right)}\right) \]

   if 4.45e58 < y0

   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 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 41.8

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Applied rewrites 41.8%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.9%

      \[\leadsto \left(x \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -7.6 \cdot 10^{+99}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.45 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 31.0% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -8 \cdot 10^{+99}:\\ \;\;\;\;\left(b \cdot j\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.45 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -8e+99)
   (* (* b j) (fma (- x) y0 (* t y4)))
   (if (<= y0 -5e-70)
     (* j (* y1 (fma (- y3) y4 (* x i))))
     (if (<= y0 4.45e+58)
       (* a (* y3 (fma y1 z (* y (- y5)))))
       (* (fma c y2 (- (* b j))) (* x y0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -8e+99) {
		tmp = (b * j) * fma(-x, y0, (t * y4));
	} else if (y0 <= -5e-70) {
		tmp = j * (y1 * fma(-y3, y4, (x * i)));
	} else if (y0 <= 4.45e+58) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else {
		tmp = fma(c, y2, -(b * j)) * (x * y0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -8e+99)
		tmp = Float64(Float64(b * j) * fma(Float64(-x), y0, Float64(t * y4)));
	elseif (y0 <= -5e-70)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))));
	elseif (y0 <= 4.45e+58)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	else
		tmp = Float64(fma(c, y2, Float64(-Float64(b * j))) * Float64(x * y0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -8e+99], N[(N[(b * j), $MachinePrecision] * N[((-x) * y0 + N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5e-70], N[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.45e+58], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * y2 + (-N[(b * j), $MachinePrecision])), $MachinePrecision] * N[(x * y0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -7.9999999999999997e99

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 48.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.7%

      \[\leadsto \left(b \cdot j\right) \cdot \color{blue}{\mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   if -7.9999999999999997e99 < y0 < -4.9999999999999998e-70

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 54.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 58.4%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -4.9999999999999998e-70 < y0 < 4.45e58

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 46.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 28.1%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-y3, y5, b \cdot x\right)}\right) \]

   9. Taylor expanded in y3 around inf

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 38.9%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -y \cdot y5\right)}\right) \]

   if 4.45e58 < y0

   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 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 41.8

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Applied rewrites 41.8%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.9%

      \[\leadsto \left(x \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -8 \cdot 10^{+99}:\\ \;\;\;\;\left(b \cdot j\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.45 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 28.8% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -8 \cdot 10^{+99}:\\ \;\;\;\;\left(b \cdot j\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{-273}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 1.36 \cdot 10^{-36}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -8e+99)
   (* (* b j) (fma (- x) y0 (* t y4)))
   (if (<= y0 9e-273)
     (* j (* y1 (fma (- y3) y4 (* x i))))
     (if (<= y0 1.36e-36)
       (* (* k y2) (- (* y1 y4) (* y0 y5)))
       (* (fma c y2 (- (* b j))) (* x y0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -8e+99) {
		tmp = (b * j) * fma(-x, y0, (t * y4));
	} else if (y0 <= 9e-273) {
		tmp = j * (y1 * fma(-y3, y4, (x * i)));
	} else if (y0 <= 1.36e-36) {
		tmp = (k * y2) * ((y1 * y4) - (y0 * y5));
	} else {
		tmp = fma(c, y2, -(b * j)) * (x * y0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -8e+99)
		tmp = Float64(Float64(b * j) * fma(Float64(-x), y0, Float64(t * y4)));
	elseif (y0 <= 9e-273)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(x * i))));
	elseif (y0 <= 1.36e-36)
		tmp = Float64(Float64(k * y2) * Float64(Float64(y1 * y4) - Float64(y0 * y5)));
	else
		tmp = Float64(fma(c, y2, Float64(-Float64(b * j))) * Float64(x * y0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -8e+99], N[(N[(b * j), $MachinePrecision] * N[((-x) * y0 + N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9e-273], N[(j * N[(y1 * N[((-y3) * y4 + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.36e-36], N[(N[(k * y2), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * y2 + (-N[(b * j), $MachinePrecision])), $MachinePrecision] * N[(x * y0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -7.9999999999999997e99

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 48.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.7%

      \[\leadsto \left(b \cdot j\right) \cdot \color{blue}{\mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   if -7.9999999999999997e99 < y0 < 8.99999999999999921e-273

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Applied rewrites 46.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.0%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if 8.99999999999999921e-273 < y0 < 1.36000000000000007e-36

   1. Initial program 27.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. associate--l+ N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4} - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \mathsf{neg}\left(\color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot t}\right)\right)\right) \]

   5. Applied rewrites 46.7%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.2%

      \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   if 1.36000000000000007e-36 < y0

   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 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 41.7

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Applied rewrites 41.7%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 40.2%

      \[\leadsto \left(x \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -8 \cdot 10^{+99}:\\ \;\;\;\;\left(b \cdot j\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{-273}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, x \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 1.36 \cdot 10^{-36}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, y2, -b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 27.3% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1 \cdot 10^{-153}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{+37}:\\ \;\;\;\;j \cdot \left(x \cdot \mathsf{fma}\left(i, y1, b \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -2.4e+55)
   (* (- c) (* t (* y2 y4)))
   (if (<= y4 -1e-153)
     (* (* b y4) (- (* t j) (* y k)))
     (if (<= y4 7.5e+37)
       (* j (* x (fma i y1 (* b (- y0)))))
       (* (* k y2) (- (* y1 y4) (* y0 y5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -2.4e+55) {
		tmp = -c * (t * (y2 * y4));
	} else if (y4 <= -1e-153) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= 7.5e+37) {
		tmp = j * (x * fma(i, y1, (b * -y0)));
	} else {
		tmp = (k * y2) * ((y1 * y4) - (y0 * y5));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -2.4e+55)
		tmp = Float64(Float64(-c) * Float64(t * Float64(y2 * y4)));
	elseif (y4 <= -1e-153)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	elseif (y4 <= 7.5e+37)
		tmp = Float64(j * Float64(x * fma(i, y1, Float64(b * Float64(-y0)))));
	else
		tmp = Float64(Float64(k * y2) * Float64(Float64(y1 * y4) - Float64(y0 * y5)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -2.4e+55], N[((-c) * N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1e-153], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.5e+37], N[(j * N[(x * N[(i * y1 + N[(b * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * y2), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -2.3999999999999999e55

   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 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. associate--l+ N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4} - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \mathsf{neg}\left(\color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot t}\right)\right)\right) \]

   5. Applied rewrites 48.1%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.4%

      \[\leadsto -\left(t \cdot y2\right) \cdot \left(c \cdot y4 - a \cdot y5\right) \]

   9. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 43.5%

       \[\leadsto \left(-c\right) \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y4\right)}\right) \]

   if -2.3999999999999999e55 < y4 < -1.00000000000000004e-153

   1. Initial program 33.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 56.6

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 56.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 25.0%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(j, y4, \left(-a\right) \cdot z\right)}\right) \]

   9. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 29.4%

       \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]

   if -1.00000000000000004e-153 < y4 < 7.5000000000000003e37

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 42.7

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Applied rewrites 42.7%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 40.9%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \mathsf{fma}\left(i, y1, \left(-b\right) \cdot y0\right)\right)} \]

   if 7.5000000000000003e37 < y4

   1. Initial program 25.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. associate--l+ N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4} - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \mathsf{neg}\left(\color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot t}\right)\right)\right) \]

   5. Applied rewrites 45.6%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 46.5%

      \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1 \cdot 10^{-153}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{+37}:\\ \;\;\;\;j \cdot \left(x \cdot \mathsf{fma}\left(i, y1, b \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 28.0% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{if}\;y4 \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(x \cdot \mathsf{fma}\left(i, y1, b \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* b y4) (- (* t j) (* y k)))))
   (if (<= y4 -2.4e+55)
     (* (- c) (* t (* y2 y4)))
     (if (<= y4 -1e-153)
       t_1
       (if (<= y4 1.35e+41) (* j (* x (fma i y1 (* b (- y0))))) 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 * y4) * ((t * j) - (y * k));
	double tmp;
	if (y4 <= -2.4e+55) {
		tmp = -c * (t * (y2 * y4));
	} else if (y4 <= -1e-153) {
		tmp = t_1;
	} else if (y4 <= 1.35e+41) {
		tmp = j * (x * fma(i, y1, (b * -y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)))
	tmp = 0.0
	if (y4 <= -2.4e+55)
		tmp = Float64(Float64(-c) * Float64(t * Float64(y2 * y4)));
	elseif (y4 <= -1e-153)
		tmp = t_1;
	elseif (y4 <= 1.35e+41)
		tmp = Float64(j * Float64(x * fma(i, y1, Float64(b * Float64(-y0)))));
	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[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.4e+55], N[((-c) * N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1e-153], t$95$1, If[LessEqual[y4, 1.35e+41], N[(j * N[(x * N[(i * y1 + N[(b * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -2.3999999999999999e55

   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 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. associate--l+ N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4} - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \mathsf{neg}\left(\color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot t}\right)\right)\right) \]

   5. Applied rewrites 48.1%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.4%

      \[\leadsto -\left(t \cdot y2\right) \cdot \left(c \cdot y4 - a \cdot y5\right) \]

   9. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 43.5%

       \[\leadsto \left(-c\right) \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y4\right)}\right) \]

   if -2.3999999999999999e55 < y4 < -1.00000000000000004e-153 or 1.35e41 < y4

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 49.2

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 49.2%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 29.4%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(j, y4, \left(-a\right) \cdot z\right)}\right) \]

   9. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 35.4%

       \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]

   if -1.00000000000000004e-153 < y4 < 1.35e41

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 42.7

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Applied rewrites 42.7%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 40.9%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \mathsf{fma}\left(i, y1, \left(-b\right) \cdot y0\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1 \cdot 10^{-153}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(x \cdot \mathsf{fma}\left(i, y1, b \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 21.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.8 \cdot 10^{+80}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 3.2 \cdot 10^{-209}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{+117}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(t \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.8e+80)
   (* (- c) (* t (* y2 y4)))
   (if (<= y4 3.2e-209)
     (* y3 (* z (* a y1)))
     (if (<= y4 2.5e+117) (* (* z a) (* t (- b))) (* b (* j (* t y4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.8e+80) {
		tmp = -c * (t * (y2 * y4));
	} else if (y4 <= 3.2e-209) {
		tmp = y3 * (z * (a * y1));
	} else if (y4 <= 2.5e+117) {
		tmp = (z * a) * (t * -b);
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1.8d+80)) then
        tmp = -c * (t * (y2 * y4))
    else if (y4 <= 3.2d-209) then
        tmp = y3 * (z * (a * y1))
    else if (y4 <= 2.5d+117) then
        tmp = (z * a) * (t * -b)
    else
        tmp = b * (j * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.8e+80) {
		tmp = -c * (t * (y2 * y4));
	} else if (y4 <= 3.2e-209) {
		tmp = y3 * (z * (a * y1));
	} else if (y4 <= 2.5e+117) {
		tmp = (z * a) * (t * -b);
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1.8e+80:
		tmp = -c * (t * (y2 * y4))
	elif y4 <= 3.2e-209:
		tmp = y3 * (z * (a * y1))
	elif y4 <= 2.5e+117:
		tmp = (z * a) * (t * -b)
	else:
		tmp = b * (j * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.8e+80)
		tmp = Float64(Float64(-c) * Float64(t * Float64(y2 * y4)));
	elseif (y4 <= 3.2e-209)
		tmp = Float64(y3 * Float64(z * Float64(a * y1)));
	elseif (y4 <= 2.5e+117)
		tmp = Float64(Float64(z * a) * Float64(t * Float64(-b)));
	else
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1.8e+80)
		tmp = -c * (t * (y2 * y4));
	elseif (y4 <= 3.2e-209)
		tmp = y3 * (z * (a * y1));
	elseif (y4 <= 2.5e+117)
		tmp = (z * a) * (t * -b);
	else
		tmp = b * (j * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.8e+80], N[((-c) * N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.2e-209], N[(y3 * N[(z * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.5e+117], N[(N[(z * a), $MachinePrecision] * N[(t * (-b)), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -1.79999999999999997e80

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. associate--l+ N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4} - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \mathsf{neg}\left(\color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot t}\right)\right)\right) \]

   5. Applied rewrites 48.8%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.2%

      \[\leadsto -\left(t \cdot y2\right) \cdot \left(c \cdot y4 - a \cdot y5\right) \]

   9. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 47.1%

       \[\leadsto \left(-c\right) \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y4\right)}\right) \]

   if -1.79999999999999997e80 < y4 < 3.2000000000000001e-209

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 41.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 23.6%

      \[\leadsto \left(a \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-b, t, y1 \cdot y3\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 16.5%

       \[\leadsto \left(a \cdot y1\right) \cdot \left(y3 \cdot \color{blue}{z}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 19.9%

       \[\leadsto \left(\left(a \cdot y1\right) \cdot z\right) \cdot y3 \]

   if 3.2000000000000001e-209 < y4 < 2.49999999999999992e117

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 47.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 40.7%

      \[\leadsto \left(a \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-b, t, y1 \cdot y3\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \left(a \cdot z\right) \cdot \left(-1 \cdot \left(b \cdot \color{blue}{t}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 36.2%

       \[\leadsto \left(a \cdot z\right) \cdot \left(\left(-b\right) \cdot t\right) \]

   if 2.49999999999999992e117 < y4

   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 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 35.7

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 35.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 33.5%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(j, y4, \left(-a\right) \cdot z\right)}\right) \]

   9. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot \color{blue}{y4}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 36.2%

       \[\leadsto b \cdot \left(j \cdot \left(t \cdot \color{blue}{y4}\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.8 \cdot 10^{+80}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 3.2 \cdot 10^{-209}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{+117}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(t \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 28.6% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.9 \cdot 10^{+80}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 2.4 \cdot 10^{+66}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \mathsf{fma}\left(-b, t, y1 \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.9e+80)
   (* (- c) (* t (* y2 y4)))
   (if (<= y4 2.4e+66)
     (* (* z a) (fma (- b) t (* y1 y3)))
     (* (* b y4) (- (* t j) (* y k))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.9e+80) {
		tmp = -c * (t * (y2 * y4));
	} else if (y4 <= 2.4e+66) {
		tmp = (z * a) * fma(-b, t, (y1 * y3));
	} else {
		tmp = (b * y4) * ((t * j) - (y * k));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.9e+80)
		tmp = Float64(Float64(-c) * Float64(t * Float64(y2 * y4)));
	elseif (y4 <= 2.4e+66)
		tmp = Float64(Float64(z * a) * fma(Float64(-b), t, Float64(y1 * y3)));
	else
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.9e+80], N[((-c) * N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.4e+66], N[(N[(z * a), $MachinePrecision] * N[((-b) * t + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -1.89999999999999999e80

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. associate--l+ N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4} - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \mathsf{neg}\left(\color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot t}\right)\right)\right) \]

   5. Applied rewrites 48.8%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.2%

      \[\leadsto -\left(t \cdot y2\right) \cdot \left(c \cdot y4 - a \cdot y5\right) \]

   9. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 47.1%

       \[\leadsto \left(-c\right) \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y4\right)}\right) \]

   if -1.89999999999999999e80 < y4 < 2.4000000000000002e66

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 43.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 30.5%

      \[\leadsto \left(a \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-b, t, y1 \cdot y3\right)} \]

   if 2.4000000000000002e66 < y4

   1. Initial program 19.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 36.0

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 36.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 29.9%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(j, y4, \left(-a\right) \cdot z\right)}\right) \]

   9. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 41.1%

       \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.9 \cdot 10^{+80}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 2.4 \cdot 10^{+66}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \mathsf{fma}\left(-b, t, y1 \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 27.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.9 \cdot 10^{+80}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 9 \cdot 10^{+160}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \mathsf{fma}\left(-b, t, y1 \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.9e+80)
   (* (- c) (* t (* y2 y4)))
   (if (<= y4 9e+160)
     (* (* z a) (fma (- b) t (* y1 y3)))
     (* b (* j (* t y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.9e+80) {
		tmp = -c * (t * (y2 * y4));
	} else if (y4 <= 9e+160) {
		tmp = (z * a) * fma(-b, t, (y1 * y3));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.9e+80)
		tmp = Float64(Float64(-c) * Float64(t * Float64(y2 * y4)));
	elseif (y4 <= 9e+160)
		tmp = Float64(Float64(z * a) * fma(Float64(-b), t, Float64(y1 * y3)));
	else
		tmp = Float64(b * Float64(j * Float64(t * 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[y4, -1.9e+80], N[((-c) * N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 9e+160], N[(N[(z * a), $MachinePrecision] * N[((-b) * t + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -1.89999999999999999e80

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. associate--l+ N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4} - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \mathsf{neg}\left(\color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot t}\right)\right)\right) \]

   5. Applied rewrites 48.8%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.2%

      \[\leadsto -\left(t \cdot y2\right) \cdot \left(c \cdot y4 - a \cdot y5\right) \]

   9. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 47.1%

       \[\leadsto \left(-c\right) \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y4\right)}\right) \]

   if -1.89999999999999999e80 < y4 < 8.99999999999999959e160

   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 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 42.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 29.4%

      \[\leadsto \left(a \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-b, t, y1 \cdot y3\right)} \]

   if 8.99999999999999959e160 < y4

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 32.5

          \[\leadsto b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Applied rewrites 32.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 37.1%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(j, y4, \left(-a\right) \cdot z\right)}\right) \]

   9. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot \color{blue}{y4}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 40.9%

       \[\leadsto b \cdot \left(j \cdot \left(t \cdot \color{blue}{y4}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.9 \cdot 10^{+80}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 9 \cdot 10^{+160}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \mathsf{fma}\left(-b, t, y1 \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 19.5% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -7.2 \cdot 10^{-269}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y1 \leq 5.8 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -7.2e-269)
   (* (* a b) (* z (- t)))
   (if (<= y1 5.8e+99) (* a (* (* x y) b)) (* y3 (* z (* a y1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -7.2e-269) {
		tmp = (a * b) * (z * -t);
	} else if (y1 <= 5.8e+99) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = y3 * (z * (a * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-7.2d-269)) then
        tmp = (a * b) * (z * -t)
    else if (y1 <= 5.8d+99) then
        tmp = a * ((x * y) * b)
    else
        tmp = y3 * (z * (a * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -7.2e-269) {
		tmp = (a * b) * (z * -t);
	} else if (y1 <= 5.8e+99) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = y3 * (z * (a * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -7.2e-269:
		tmp = (a * b) * (z * -t)
	elif y1 <= 5.8e+99:
		tmp = a * ((x * y) * b)
	else:
		tmp = y3 * (z * (a * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -7.2e-269)
		tmp = Float64(Float64(a * b) * Float64(z * Float64(-t)));
	elseif (y1 <= 5.8e+99)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = Float64(y3 * Float64(z * Float64(a * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -7.2e-269)
		tmp = (a * b) * (z * -t);
	elseif (y1 <= 5.8e+99)
		tmp = a * ((x * y) * b);
	else
		tmp = y3 * (z * (a * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -7.2e-269], N[(N[(a * b), $MachinePrecision] * N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.8e+99], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(z * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -7.19999999999999996e-269

   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 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 35.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 22.2%

      \[\leadsto \left(a \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-b, t, y1 \cdot y3\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 11.8%

       \[\leadsto \left(a \cdot y1\right) \cdot \left(y3 \cdot \color{blue}{z}\right) \]

   12. Taylor expanded in b around inf

       \[\leadsto -1 \cdot \left(a \cdot \color{blue}{\left(b \cdot \left(t \cdot z\right)\right)}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 21.8%

       \[\leadsto -\left(a \cdot b\right) \cdot \left(t \cdot z\right) \]

   if -7.19999999999999996e-269 < y1 < 5.8000000000000004e99

   1. Initial program 27.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 35.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 31.8%

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-y3, y5, b \cdot x\right)}\right) \]

   9. Taylor expanded in y3 around 0

      \[\leadsto a \cdot \left(b \cdot \left(x \cdot \color{blue}{y}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 21.7%

       \[\leadsto a \cdot \left(b \cdot \left(x \cdot \color{blue}{y}\right)\right) \]

   if 5.8000000000000004e99 < y1

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 53.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.3%

      \[\leadsto \left(a \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-b, t, y1 \cdot y3\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 37.5%

       \[\leadsto \left(a \cdot y1\right) \cdot \left(y3 \cdot \color{blue}{z}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 44.5%

       \[\leadsto \left(\left(a \cdot y1\right) \cdot z\right) \cdot y3 \]
3. Recombined 3 regimes into one program.

4. Final simplification 26.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -7.2 \cdot 10^{-269}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y1 \leq 5.8 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 22.3% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -2.05 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 2.55 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))))
   (if (<= y5 -2.05e+124)
     t_1
     (if (<= y5 2.55e+33) (* a (* y1 (* z 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 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -2.05e+124) {
		tmp = t_1;
	} else if (y5 <= 2.55e+33) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (y2 * y5))
    if (y5 <= (-2.05d+124)) then
        tmp = t_1
    else if (y5 <= 2.55d+33) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (t * (y2 * y5));
	double tmp;
	if (y5 <= -2.05e+124) {
		tmp = t_1;
	} else if (y5 <= 2.55e+33) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (t * (y2 * y5))
	tmp = 0
	if y5 <= -2.05e+124:
		tmp = t_1
	elif y5 <= 2.55e+33:
		tmp = a * (y1 * (z * 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(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (y5 <= -2.05e+124)
		tmp = t_1;
	elseif (y5 <= 2.55e+33)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (y5 <= -2.05e+124)
		tmp = t_1;
	elseif (y5 <= 2.55e+33)
		tmp = a * (y1 * (z * y3));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.05e+124], t$95$1, If[LessEqual[y5, 2.55e+33], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y5 < -2.05000000000000001e124 or 2.5499999999999999e33 < y5

   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 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. associate--l+ N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, \color{blue}{y1 \cdot y4} - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x} + \left(\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x + \color{blue}{-1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)}\right) \]

      11. lower--.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0 - a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      12. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(\color{blue}{c \cdot y0} - a \cdot y1, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - \color{blue}{a \cdot y1}, x, -1 \cdot \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \color{blue}{\mathsf{neg}\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \mathsf{neg}\left(\color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot t}\right)\right)\right) \]

   5. Applied rewrites 40.0%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 34.8%

      \[\leadsto -\left(t \cdot y2\right) \cdot \left(c \cdot y4 - a \cdot y5\right) \]

   9. Taylor expanded in c around 0

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 33.9%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \]

   if -2.05000000000000001e124 < y5 < 2.5499999999999999e33

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 38.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 29.7%

      \[\leadsto \left(a \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-b, t, y1 \cdot y3\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 17.9%

       \[\leadsto \left(a \cdot y1\right) \cdot \left(y3 \cdot \color{blue}{z}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 21.3%

       \[\leadsto \left(y1 \cdot \left(z \cdot y3\right)\right) \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.05 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 2.55 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 18.3% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq 2.3 \cdot 10^{-43}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 2.3e-43) (* y3 (* z (* a y1))) (* a (* y1 (* 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 <= 2.3e-43) {
		tmp = y3 * (z * (a * y1));
	} else {
		tmp = a * (y1 * (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 <= 2.3d-43) then
        tmp = y3 * (z * (a * y1))
    else
        tmp = a * (y1 * (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 <= 2.3e-43) {
		tmp = y3 * (z * (a * y1));
	} else {
		tmp = a * (y1 * (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 <= 2.3e-43:
		tmp = y3 * (z * (a * y1))
	else:
		tmp = a * (y1 * (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 <= 2.3e-43)
		tmp = Float64(y3 * Float64(z * Float64(a * y1)));
	else
		tmp = Float64(a * Float64(y1 * 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 <= 2.3e-43)
		tmp = y3 * (z * (a * y1));
	else
		tmp = a * (y1 * (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, 2.3e-43], N[(y3 * N[(z * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y3 < 2.2999999999999999e-43

   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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 41.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 24.6%

      \[\leadsto \left(a \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-b, t, y1 \cdot y3\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 13.0%

       \[\leadsto \left(a \cdot y1\right) \cdot \left(y3 \cdot \color{blue}{z}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 16.0%

       \[\leadsto \left(\left(a \cdot y1\right) \cdot z\right) \cdot y3 \]

   if 2.2999999999999999e-43 < y3

   1. Initial program 18.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Applied rewrites 31.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 27.8%

      \[\leadsto \left(a \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-b, t, y1 \cdot y3\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 23.9%

       \[\leadsto \left(a \cdot y1\right) \cdot \left(y3 \cdot \color{blue}{z}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 29.3%

       \[\leadsto \left(y1 \cdot \left(z \cdot y3\right)\right) \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 19.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq 2.3 \cdot 10^{-43}:\\ \;\;\;\;y3 \cdot \left(z \cdot \left(a \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 17.0% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y1 (* 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) {
	return a * (y1 * (z * y3));
}

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 * (y1 * (z * y3))
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 * (y1 * (z * y3));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y1 * (z * y3))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y1 * Float64(z * y3)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y1 * (z * y3));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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 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. distribute-rgt-neg-in N/A

      \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   5. lower-fma.f64 N/A

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. lower-neg.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   7. lower--.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. *-commutative N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   9. lower-*.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   11. lower-*.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   12. sub-neg N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

5. Applied rewrites 39.0%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in z around inf

   \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
7. Step-by-step derivation

8. Applied rewrites 25.5%

   \[\leadsto \left(a \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-b, t, y1 \cdot y3\right)} \]

9. Taylor expanded in b around 0

   \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
10. Step-by-step derivation

11. Applied rewrites 16.0%

    \[\leadsto \left(a \cdot y1\right) \cdot \left(y3 \cdot \color{blue}{z}\right) \]
12. Step-by-step derivation

13. Applied rewrites 17.5%

    \[\leadsto \left(y1 \cdot \left(z \cdot y3\right)\right) \cdot a \]

14. Final simplification 17.5%

    \[\leadsto a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \]
15. Add Preprocessing

Alternative 36: 16.7% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \left(a \cdot y1\right) \cdot \left(z \cdot y3\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* (* a y1) (* 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) {
	return (a * y1) * (z * y3);
}

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 * y1) * (z * y3)
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 * y1) * (z * y3);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return (a * y1) * (z * y3)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(Float64(a * y1) * Float64(z * y3))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = (a * y1) * (z * y3);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(N[(a * y1), $MachinePrecision] * N[(z * y3), $MachinePrecision]), $MachinePrecision]

Derivation

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 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. distribute-rgt-neg-in N/A

      \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   5. lower-fma.f64 N/A

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. lower-neg.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   7. lower--.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. *-commutative N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   9. lower-*.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   11. lower-*.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   12. sub-neg N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

5. Applied rewrites 39.0%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in z around inf

   \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
7. Step-by-step derivation

8. Applied rewrites 25.5%

   \[\leadsto \left(a \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-b, t, y1 \cdot y3\right)} \]

9. Taylor expanded in b around 0

   \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
10. Step-by-step derivation

11. Applied rewrites 16.0%

    \[\leadsto \left(a \cdot y1\right) \cdot \left(y3 \cdot \color{blue}{z}\right) \]

12. Final simplification 16.0%

    \[\leadsto \left(a \cdot y1\right) \cdot \left(z \cdot y3\right) \]
13. Add Preprocessing

Developer Target 1: 27.4% 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 2024233 
(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)))))