Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 28.7% → 54.9%

Time: 39.1s

Alternatives: 38

Speedup: 5.6×

• 89.9% 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: 28.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 54.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y4) - Float64(a * y5))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	t_3 = Float64(Float64(a * b) - Float64(c * i))
	t_4 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * t_3) + Float64(Float64(Float64(b * y0) - Float64(i * y1)) * Float64(Float64(z * k) - Float64(x * j)))) + Float64(Float64(Float64(c * y0) - Float64(a * y1)) * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(t_2 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(t_1 * Float64(Float64(y * y3) - Float64(t * y2)))) + 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(Float64(-t) * fma(t_2, Float64(-j), fma(z, t_3, Float64(y2 * 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[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision] + N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $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[((-t) * N[(t$95$2 * (-j) + N[(z * t$95$3 + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 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. *-lowering-*.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. Simplified 46.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.1%

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

Alternative 2: 43.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y0 - i \cdot y1\\ t_2 := z \cdot \left(k \cdot t\_1 - \mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right)\right)\\ \mathbf{if}\;y1 \leq -9 \cdot 10^{+23}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.34 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.85 \cdot 10^{-223}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq 8.6 \cdot 10^{-55}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(t, i \cdot y5 - b \cdot y4, \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, x \cdot t\_1\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y0) (* i y1)))
        (t_2
         (*
          z
          (-
           (* k t_1)
           (fma y3 (- (* c y0) (* a y1)) (* t (- (* a b) (* c i))))))))
   (if (<= y1 -9e+23)
     (* y1 (fma z (fma y3 a (* i (- k))) (* y4 (fma (- y3) j (* k y2)))))
     (if (<= y1 -1.34e-157)
       (*
        b
        (+
         (fma a (- (* x y) (* z t)) (* y4 (- (* t j) (* y k))))
         (* y0 (- (* z k) (* x j)))))
       (if (<= y1 2.85e-223)
         t_2
         (if (<= y1 8.6e-55)
           (*
            (- j)
            (fma
             t
             (- (* i y5) (* b y4))
             (fma y3 (- (* y1 y4) (* y0 y5)) (* x t_1))))
           (if (<= y1 6e+81)
             t_2
             (*
              y1
              (fma
               a
               (- (* z y3) (* x y2))
               (fma
                y4
                (fma k y2 (* j (- y3)))
                (* i (- (* x j) (* z k)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y0) - (i * y1);
	double t_2 = z * ((k * t_1) - fma(y3, ((c * y0) - (a * y1)), (t * ((a * b) - (c * i)))));
	double tmp;
	if (y1 <= -9e+23) {
		tmp = y1 * fma(z, fma(y3, a, (i * -k)), (y4 * fma(-y3, j, (k * y2))));
	} else if (y1 <= -1.34e-157) {
		tmp = b * (fma(a, ((x * y) - (z * t)), (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 2.85e-223) {
		tmp = t_2;
	} else if (y1 <= 8.6e-55) {
		tmp = -j * fma(t, ((i * y5) - (b * y4)), fma(y3, ((y1 * y4) - (y0 * y5)), (x * t_1)));
	} else if (y1 <= 6e+81) {
		tmp = t_2;
	} else {
		tmp = y1 * fma(a, ((z * y3) - (x * y2)), fma(y4, fma(k, y2, (j * -y3)), (i * ((x * j) - (z * k)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y0) - Float64(i * y1))
	t_2 = Float64(z * Float64(Float64(k * t_1) - fma(y3, Float64(Float64(c * y0) - Float64(a * y1)), Float64(t * Float64(Float64(a * b) - Float64(c * i))))))
	tmp = 0.0
	if (y1 <= -9e+23)
		tmp = Float64(y1 * fma(z, fma(y3, a, Float64(i * Float64(-k))), Float64(y4 * fma(Float64(-y3), j, Float64(k * y2)))));
	elseif (y1 <= -1.34e-157)
		tmp = Float64(b * Float64(fma(a, Float64(Float64(x * y) - Float64(z * t)), Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y1 <= 2.85e-223)
		tmp = t_2;
	elseif (y1 <= 8.6e-55)
		tmp = Float64(Float64(-j) * fma(t, Float64(Float64(i * y5) - Float64(b * y4)), fma(y3, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * t_1))));
	elseif (y1 <= 6e+81)
		tmp = t_2;
	else
		tmp = Float64(y1 * fma(a, Float64(Float64(z * y3) - Float64(x * y2)), fma(y4, fma(k, y2, Float64(j * Float64(-y3))), Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	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 * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(k * t$95$1), $MachinePrecision] - N[(y3 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -9e+23], N[(y1 * N[(z * N[(y3 * a + N[(i * (-k)), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[((-y3) * j + N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.34e-157], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.85e-223], t$95$2, If[LessEqual[y1, 8.6e-55], N[((-j) * N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6e+81], t$95$2, N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + 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]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -8.99999999999999958e23

   1. Initial program 26.5%

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

   3. Taylor expanded in y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 60.5%

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

   6. Taylor expanded in x around 0

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

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

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

      2. associate-+r+ N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-in N/A

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

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

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

   8. Simplified 64.5%

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

   if -8.99999999999999958e23 < y1 < -1.34e-157

   1. Initial program 34.1%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

      14. --lowering--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 64.3

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

   5. Simplified 64.3%

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

   if -1.34e-157 < y1 < 2.8499999999999999e-223 or 8.60000000000000021e-55 < y1 < 5.99999999999999995e81

   1. Initial program 37.5%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 57.3%

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

   if 2.8499999999999999e-223 < y1 < 8.60000000000000021e-55

   1. Initial program 32.6%

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

   3. Taylor expanded in 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. *-lowering-*.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. Simplified 56.9%

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

   if 5.99999999999999995e81 < y1

   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 y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 67.6%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -9 \cdot 10^{+23}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.34 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.85 \cdot 10^{-223}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) - \mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 8.6 \cdot 10^{-55}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(t, i \cdot y5 - b \cdot y4, \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{+81}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) - \mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 41.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;y1 \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{-118}:\\ \;\;\;\;z \cdot \left(\left(-y0\right) \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.95 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{+83}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          b
          (+
           (fma a (- (* x y) (* z t)) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= y1 -3.6e+15)
     (* y1 (fma z (fma y3 a (* i (- k))) (* y4 (fma (- y3) j (* k y2)))))
     (if (<= y1 -3.3e-175)
       t_1
       (if (<= y1 2.6e-118)
         (* z (* (- y0) (fma c y3 (* b (- k)))))
         (if (<= y1 1.95e+49)
           t_1
           (if (<= y1 2e+83)
             (*
              y2
              (fma
               k
               (- (* y1 y4) (* y0 y5))
               (fma (- (* c y0) (* a y1)) x (* t (- (* a y5) (* c y4))))))
             (*
              y1
              (fma
               a
               (- (* z y3) (* x y2))
               (fma
                y4
                (fma k y2 (* j (- y3)))
                (* i (- (* x j) (* z k)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (fma(a, ((x * y) - (z * t)), (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (y1 <= -3.6e+15) {
		tmp = y1 * fma(z, fma(y3, a, (i * -k)), (y4 * fma(-y3, j, (k * y2))));
	} else if (y1 <= -3.3e-175) {
		tmp = t_1;
	} else if (y1 <= 2.6e-118) {
		tmp = z * (-y0 * fma(c, y3, (b * -k)));
	} else if (y1 <= 1.95e+49) {
		tmp = t_1;
	} else if (y1 <= 2e+83) {
		tmp = y2 * fma(k, ((y1 * y4) - (y0 * y5)), fma(((c * y0) - (a * y1)), x, (t * ((a * y5) - (c * y4)))));
	} else {
		tmp = y1 * fma(a, ((z * y3) - (x * y2)), fma(y4, fma(k, y2, (j * -y3)), (i * ((x * j) - (z * k)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(fma(a, Float64(Float64(x * y) - Float64(z * t)), Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (y1 <= -3.6e+15)
		tmp = Float64(y1 * fma(z, fma(y3, a, Float64(i * Float64(-k))), Float64(y4 * fma(Float64(-y3), j, Float64(k * y2)))));
	elseif (y1 <= -3.3e-175)
		tmp = t_1;
	elseif (y1 <= 2.6e-118)
		tmp = Float64(z * Float64(Float64(-y0) * fma(c, y3, Float64(b * Float64(-k)))));
	elseif (y1 <= 1.95e+49)
		tmp = t_1;
	elseif (y1 <= 2e+83)
		tmp = Float64(y2 * fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), fma(Float64(Float64(c * y0) - Float64(a * y1)), x, Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))));
	else
		tmp = Float64(y1 * fma(a, Float64(Float64(z * y3) - Float64(x * y2)), fma(y4, fma(k, y2, Float64(j * Float64(-y3))), Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -3.6e+15], N[(y1 * N[(z * N[(y3 * a + N[(i * (-k)), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[((-y3) * j + N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.3e-175], t$95$1, If[LessEqual[y1, 2.6e-118], N[(z * N[((-y0) * N[(c * y3 + N[(b * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.95e+49], t$95$1, If[LessEqual[y1, 2e+83], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + 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], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + 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]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -3.6e15

   1. Initial program 26.5%

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

   3. Taylor expanded in y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 60.5%

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

   6. Taylor expanded in x around 0

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

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

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

      2. associate-+r+ N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-in N/A

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

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

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

   8. Simplified 64.5%

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

   if -3.6e15 < y1 < -3.29999999999999999e-175 or 2.6e-118 < y1 < 1.95e49

   1. Initial program 34.2%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

      14. --lowering--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 60.4

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

   5. Simplified 60.4%

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

   if -3.29999999999999999e-175 < y1 < 2.6e-118

   1. Initial program 37.8%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 44.4%

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

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{\left(y0 \cdot \left(c \cdot y3 - b \cdot k\right)\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) \]
   7. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. associate-*r* N/A

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

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

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

      7. mul-1-neg N/A

         \[\leadsto \left(y0 \cdot \mathsf{fma}\left(c, y3, \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot k\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. neg-lowering-neg.f64 44.5

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

   8. Simplified 44.5%

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

   if 1.95e49 < y1 < 2.00000000000000006e83

   1. Initial program 27.7%

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

   3. Taylor expanded in y2 around inf

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

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

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

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 81.8%

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

   if 2.00000000000000006e83 < y1

   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 y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 67.6%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{-175}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{-118}:\\ \;\;\;\;z \cdot \left(\left(-y0\right) \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.95 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 2 \cdot 10^{+83}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\\ t_2 := t \cdot j - y \cdot k\\ \mathbf{if}\;y5 \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.55 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3 \cdot 10^{-224}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, t\_1, i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot t\_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, t\_2, \mathsf{fma}\left(y0, t\_1, a \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right) \cdot \left(-y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (fma k y2 (* j (- y3)))) (t_2 (- (* t j) (* y k))))
   (if (<= y5 -1.3e+19)
     (*
      y2
      (fma
       k
       (- (* y1 y4) (* y0 y5))
       (fma (- (* c y0) (* a y1)) x (* t (- (* a y5) (* c y4))))))
     (if (<= y5 -1.55e-150)
       (*
        y
        (fma
         (- (* b y4) (* i y5))
         (- k)
         (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5))))))
       (if (<= y5 3e-224)
         (*
          y1
          (fma a (- (* z y3) (* x y2)) (fma y4 t_1 (* i (- (* x j) (* z k))))))
         (if (<= y5 2e+63)
           (*
            b
            (+
             (fma a (- (* x y) (* z t)) (* y4 t_2))
             (* y0 (- (* z k) (* x j)))))
           (*
            (fma i t_2 (fma y0 t_1 (* a (- (* y y3) (* t y2)))))
            (- y5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = fma(k, y2, (j * -y3));
	double t_2 = (t * j) - (y * k);
	double tmp;
	if (y5 <= -1.3e+19) {
		tmp = y2 * fma(k, ((y1 * y4) - (y0 * y5)), fma(((c * y0) - (a * y1)), x, (t * ((a * y5) - (c * y4)))));
	} else if (y5 <= -1.55e-150) {
		tmp = y * fma(((b * y4) - (i * y5)), -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	} else if (y5 <= 3e-224) {
		tmp = y1 * fma(a, ((z * y3) - (x * y2)), fma(y4, t_1, (i * ((x * j) - (z * k)))));
	} else if (y5 <= 2e+63) {
		tmp = b * (fma(a, ((x * y) - (z * t)), (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else {
		tmp = fma(i, t_2, fma(y0, t_1, (a * ((y * y3) - (t * y2))))) * -y5;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = fma(k, y2, Float64(j * Float64(-y3)))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	tmp = 0.0
	if (y5 <= -1.3e+19)
		tmp = Float64(y2 * fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), fma(Float64(Float64(c * y0) - Float64(a * y1)), x, Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))));
	elseif (y5 <= -1.55e-150)
		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 (y5 <= 3e-224)
		tmp = Float64(y1 * fma(a, Float64(Float64(z * y3) - Float64(x * y2)), fma(y4, t_1, Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (y5 <= 2e+63)
		tmp = Float64(b * Float64(fma(a, Float64(Float64(x * y) - Float64(z * t)), Float64(y4 * t_2)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = Float64(fma(i, t_2, fma(y0, t_1, Float64(a * Float64(Float64(y * y3) - Float64(t * y2))))) * Float64(-y5));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * y2 + N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.3e+19], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + 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[y5, -1.55e-150], 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[y5, 3e-224], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1 + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2e+63], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * t$95$2 + N[(y0 * t$95$1 + N[(a * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-y5)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -1.3e19

   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 y2 around inf

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

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

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

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 57.7%

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

   if -1.3e19 < y5 < -1.54999999999999999e-150

   1. Initial program 38.0%

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

   3. Taylor expanded in y around inf

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

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

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

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

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

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

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

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

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

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

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

      11. neg-mul-1 N/A

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

      12. neg-lowering-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. Simplified 59.8%

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

   if -1.54999999999999999e-150 < y5 < 2.99999999999999982e-224

   1. Initial program 36.5%

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

   3. Taylor expanded in y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 59.8%

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

   if 2.99999999999999982e-224 < y5 < 2.00000000000000012e63

   1. Initial program 39.8%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

      14. --lowering--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 59.0

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

   5. Simplified 59.0%

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

   if 2.00000000000000012e63 < y5

   1. Initial program 29.3%

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

   3. Taylor expanded in y5 around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 65.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, t \cdot j - k \cdot y, \mathsf{fma}\left(y0, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), \left(t \cdot y2 - y3 \cdot y\right) \cdot \left(-a\right)\right)\right) \cdot \left(-y5\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.55 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3 \cdot 10^{-224}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, t \cdot j - y \cdot k, \mathsf{fma}\left(y0, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), a \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right) \cdot \left(-y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.7 \cdot 10^{+23}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.4 \cdot 10^{-171}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{-106}:\\ \;\;\;\;z \cdot \left(\left(-y0\right) \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 8.8 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.7e+23)
   (* y1 (fma z (fma y3 a (* i (- k))) (* y4 (fma (- y3) j (* k y2)))))
   (if (<= y1 -1.4e-171)
     (*
      b
      (+
       (fma a (- (* x y) (* z t)) (* y4 (- (* t j) (* y k))))
       (* y0 (- (* z k) (* x j)))))
     (if (<= y1 3.4e-106)
       (* z (* (- y0) (fma c y3 (* b (- k)))))
       (if (<= y1 8.8e+79)
         (*
          y
          (fma
           (- (* b y4) (* i y5))
           (- k)
           (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5))))))
         (*
          y1
          (fma
           a
           (- (* z y3) (* x y2))
           (fma y4 (fma k y2 (* j (- y3))) (* i (- (* x j) (* z 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 (y1 <= -1.7e+23) {
		tmp = y1 * fma(z, fma(y3, a, (i * -k)), (y4 * fma(-y3, j, (k * y2))));
	} else if (y1 <= -1.4e-171) {
		tmp = b * (fma(a, ((x * y) - (z * t)), (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 3.4e-106) {
		tmp = z * (-y0 * fma(c, y3, (b * -k)));
	} else if (y1 <= 8.8e+79) {
		tmp = y * fma(((b * y4) - (i * y5)), -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	} else {
		tmp = y1 * fma(a, ((z * y3) - (x * y2)), fma(y4, fma(k, y2, (j * -y3)), (i * ((x * j) - (z * 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 (y1 <= -1.7e+23)
		tmp = Float64(y1 * fma(z, fma(y3, a, Float64(i * Float64(-k))), Float64(y4 * fma(Float64(-y3), j, Float64(k * y2)))));
	elseif (y1 <= -1.4e-171)
		tmp = Float64(b * Float64(fma(a, Float64(Float64(x * y) - Float64(z * t)), Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y1 <= 3.4e-106)
		tmp = Float64(z * Float64(Float64(-y0) * fma(c, y3, Float64(b * Float64(-k)))));
	elseif (y1 <= 8.8e+79)
		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))))));
	else
		tmp = Float64(y1 * fma(a, Float64(Float64(z * y3) - Float64(x * y2)), fma(y4, fma(k, y2, Float64(j * Float64(-y3))), Float64(i * Float64(Float64(x * j) - Float64(z * 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[y1, -1.7e+23], N[(y1 * N[(z * N[(y3 * a + N[(i * (-k)), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[((-y3) * j + N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.4e-171], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.4e-106], N[(z * N[((-y0) * N[(c * y3 + N[(b * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 8.8e+79], 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], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + 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]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -1.69999999999999996e23

   1. Initial program 26.5%

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

   3. Taylor expanded in y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 60.5%

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

   6. Taylor expanded in x around 0

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

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

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

      2. associate-+r+ N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-in N/A

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

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

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

   8. Simplified 64.5%

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

   if -1.69999999999999996e23 < y1 < -1.40000000000000011e-171

   1. Initial program 33.5%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

      14. --lowering--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 65.0

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

   5. Simplified 65.0%

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

   if -1.40000000000000011e-171 < y1 < 3.39999999999999982e-106

   1. Initial program 37.6%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 45.5%

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

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{\left(y0 \cdot \left(c \cdot y3 - b \cdot k\right)\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) \]
   7. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. associate-*r* N/A

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

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

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

      7. mul-1-neg N/A

         \[\leadsto \left(y0 \cdot \mathsf{fma}\left(c, y3, \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot k\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. neg-lowering-neg.f64 44.1

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

   8. Simplified 44.1%

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

   if 3.39999999999999982e-106 < y1 < 8.7999999999999996e79

   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 y around inf

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

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

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

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

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

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

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

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

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

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

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

      11. neg-mul-1 N/A

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

      12. neg-lowering-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. Simplified 52.2%

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

   if 8.7999999999999996e79 < y1

   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 y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 67.6%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.7 \cdot 10^{+23}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.4 \cdot 10^{-171}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.4 \cdot 10^{-106}:\\ \;\;\;\;z \cdot \left(\left(-y0\right) \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 8.8 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ t_2 := b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;y1 \leq -2.3 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -4.1 \cdot 10^{-170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq 1.85 \cdot 10^{-118}:\\ \;\;\;\;z \cdot \left(\left(-y0\right) \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 8.6 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* y1 (fma z (fma y3 a (* i (- k))) (* y4 (fma (- y3) j (* k y2))))))
        (t_2
         (*
          b
          (+
           (fma a (- (* x y) (* z t)) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= y1 -2.3e+21)
     t_1
     (if (<= y1 -4.1e-170)
       t_2
       (if (<= y1 1.85e-118)
         (* z (* (- y0) (fma c y3 (* b (- k)))))
         (if (<= y1 8.6e+66) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * fma(z, fma(y3, a, (i * -k)), (y4 * fma(-y3, j, (k * y2))));
	double t_2 = b * (fma(a, ((x * y) - (z * t)), (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (y1 <= -2.3e+21) {
		tmp = t_1;
	} else if (y1 <= -4.1e-170) {
		tmp = t_2;
	} else if (y1 <= 1.85e-118) {
		tmp = z * (-y0 * fma(c, y3, (b * -k)));
	} else if (y1 <= 8.6e+66) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * fma(z, fma(y3, a, Float64(i * Float64(-k))), Float64(y4 * fma(Float64(-y3), j, Float64(k * y2)))))
	t_2 = Float64(b * Float64(fma(a, Float64(Float64(x * y) - Float64(z * t)), Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (y1 <= -2.3e+21)
		tmp = t_1;
	elseif (y1 <= -4.1e-170)
		tmp = t_2;
	elseif (y1 <= 1.85e-118)
		tmp = Float64(z * Float64(Float64(-y0) * fma(c, y3, Float64(b * Float64(-k)))));
	elseif (y1 <= 8.6e+66)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(z * N[(y3 * a + N[(i * (-k)), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[((-y3) * j + N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -2.3e+21], t$95$1, If[LessEqual[y1, -4.1e-170], t$95$2, If[LessEqual[y1, 1.85e-118], N[(z * N[((-y0) * N[(c * y3 + N[(b * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 8.6e+66], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -2.3e21 or 8.60000000000000054e66 < y1

   1. Initial program 25.5%

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

   3. Taylor expanded in y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 62.1%

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

   6. Taylor expanded in x around 0

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

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

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

      2. associate-+r+ N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-in N/A

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

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

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

   8. Simplified 62.3%

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

   if -2.3e21 < y1 < -4.09999999999999966e-170 or 1.85000000000000007e-118 < y1 < 8.60000000000000054e66

   1. Initial program 34.5%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

      14. --lowering--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 59.3

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

   5. Simplified 59.3%

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

   if -4.09999999999999966e-170 < y1 < 1.85000000000000007e-118

   1. Initial program 37.8%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 44.4%

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

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{\left(y0 \cdot \left(c \cdot y3 - b \cdot k\right)\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) \]
   7. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. associate-*r* N/A

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

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

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

      7. mul-1-neg N/A

         \[\leadsto \left(y0 \cdot \mathsf{fma}\left(c, y3, \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot k\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. neg-lowering-neg.f64 44.5

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

   8. Simplified 44.5%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.3 \cdot 10^{+21}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -4.1 \cdot 10^{-170}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.85 \cdot 10^{-118}:\\ \;\;\;\;z \cdot \left(\left(-y0\right) \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 8.6 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -2.05 \cdot 10^{+20}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -2.25 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 7 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) - \mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -2.05e+20)
   (* y1 (fma z (fma y3 a (* i (- k))) (* y4 (fma (- y3) j (* k y2)))))
   (if (<= y1 -2.25e-157)
     (*
      b
      (+
       (fma a (- (* x y) (* z t)) (* y4 (- (* t j) (* y k))))
       (* y0 (- (* z k) (* x j)))))
     (if (<= y1 7e+79)
       (*
        z
        (-
         (* k (- (* b y0) (* i y1)))
         (fma y3 (- (* c y0) (* a y1)) (* t (- (* a b) (* c i))))))
       (*
        y1
        (fma
         a
         (- (* z y3) (* x y2))
         (fma y4 (fma k y2 (* j (- y3))) (* i (- (* x j) (* z 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 (y1 <= -2.05e+20) {
		tmp = y1 * fma(z, fma(y3, a, (i * -k)), (y4 * fma(-y3, j, (k * y2))));
	} else if (y1 <= -2.25e-157) {
		tmp = b * (fma(a, ((x * y) - (z * t)), (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 7e+79) {
		tmp = z * ((k * ((b * y0) - (i * y1))) - fma(y3, ((c * y0) - (a * y1)), (t * ((a * b) - (c * i)))));
	} else {
		tmp = y1 * fma(a, ((z * y3) - (x * y2)), fma(y4, fma(k, y2, (j * -y3)), (i * ((x * j) - (z * 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 (y1 <= -2.05e+20)
		tmp = Float64(y1 * fma(z, fma(y3, a, Float64(i * Float64(-k))), Float64(y4 * fma(Float64(-y3), j, Float64(k * y2)))));
	elseif (y1 <= -2.25e-157)
		tmp = Float64(b * Float64(fma(a, Float64(Float64(x * y) - Float64(z * t)), Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y1 <= 7e+79)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) - fma(y3, Float64(Float64(c * y0) - Float64(a * y1)), Float64(t * Float64(Float64(a * b) - Float64(c * i))))));
	else
		tmp = Float64(y1 * fma(a, Float64(Float64(z * y3) - Float64(x * y2)), fma(y4, fma(k, y2, Float64(j * Float64(-y3))), Float64(i * Float64(Float64(x * j) - Float64(z * 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[y1, -2.05e+20], N[(y1 * N[(z * N[(y3 * a + N[(i * (-k)), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[((-y3) * j + N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.25e-157], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7e+79], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + 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]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -2.05e20

   1. Initial program 26.5%

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

   3. Taylor expanded in y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 60.5%

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

   6. Taylor expanded in x around 0

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

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

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

      2. associate-+r+ N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-in N/A

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

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

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

   8. Simplified 64.5%

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

   if -2.05e20 < y1 < -2.24999999999999999e-157

   1. Initial program 34.1%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

      14. --lowering--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 64.3

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

   5. Simplified 64.3%

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

   if -2.24999999999999999e-157 < y1 < 6.99999999999999961e79

   1. Initial program 35.6%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 47.2%

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

   if 6.99999999999999961e79 < y1

   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 y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 67.6%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.05 \cdot 10^{+20}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -2.25 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 7 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) - \mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(a, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -140000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(\left(-y0\right) \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* y1 (fma z (fma y3 a (* i (- k))) (* y4 (fma (- y3) j (* k y2)))))))
   (if (<= y1 -140000000000.0)
     t_1
     (if (<= y1 -1.9e-81)
       (*
        a
        (fma
         y1
         (- (* z y3) (* x y2))
         (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
       (if (<= y1 3.2e+58) (* z (* (- y0) (fma c y3 (* b (- k))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * fma(z, fma(y3, a, (i * -k)), (y4 * fma(-y3, j, (k * y2))));
	double tmp;
	if (y1 <= -140000000000.0) {
		tmp = t_1;
	} else if (y1 <= -1.9e-81) {
		tmp = a * fma(y1, ((z * y3) - (x * y2)), fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} else if (y1 <= 3.2e+58) {
		tmp = z * (-y0 * fma(c, y3, (b * -k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * fma(z, fma(y3, a, Float64(i * Float64(-k))), Float64(y4 * fma(Float64(-y3), j, Float64(k * y2)))))
	tmp = 0.0
	if (y1 <= -140000000000.0)
		tmp = t_1;
	elseif (y1 <= -1.9e-81)
		tmp = Float64(a * fma(y1, Float64(Float64(z * y3) - Float64(x * y2)), fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (y1 <= 3.2e+58)
		tmp = Float64(z * Float64(Float64(-y0) * fma(c, y3, Float64(b * Float64(-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[(y1 * N[(z * N[(y3 * a + N[(i * (-k)), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[((-y3) * j + N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -140000000000.0], t$95$1, If[LessEqual[y1, -1.9e-81], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.2e+58], N[(z * N[((-y0) * N[(c * y3 + N[(b * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -1.4e11 or 3.20000000000000015e58 < y1

   1. Initial program 25.1%

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

   3. Taylor expanded in y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 61.9%

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

   6. Taylor expanded in x around 0

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

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

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

      2. associate-+r+ N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-in N/A

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

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

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

   8. Simplified 62.1%

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

   if -1.4e11 < y1 < -1.8999999999999999e-81

   1. Initial program 28.3%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 53.7%

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

   if -1.8999999999999999e-81 < y1 < 3.20000000000000015e58

   1. Initial program 38.5%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 45.0%

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

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{\left(y0 \cdot \left(c \cdot y3 - b \cdot k\right)\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) \]
   7. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

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

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

      5. associate-*r* N/A

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

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

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

      7. mul-1-neg N/A

         \[\leadsto \left(y0 \cdot \mathsf{fma}\left(c, y3, \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot k\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. neg-lowering-neg.f64 41.7

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

   8. Simplified 41.7%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -140000000000:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(\left(-y0\right) \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 31.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-25}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \mathsf{fma}\left(y2, y5, z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-249}:\\ \;\;\;\;y1 \cdot \left(z \cdot \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+42}:\\ \;\;\;\;y4 \cdot \left(y \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, c \cdot \left(-t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (fma b x (* y3 (- y5)))))))
   (if (<= t -1.1e+111)
     (* j (* y4 (fma b t (* y1 (- y3)))))
     (if (<= t -3.8e-25)
       (* (* t a) (fma y2 y5 (* z (- b))))
       (if (<= t -2.4e-191)
         t_1
         (if (<= t 5.8e-249)
           (* y1 (* z (fma y3 a (* i (- k)))))
           (if (<= t 1.05e-85)
             t_1
             (if (<= t 2.4e+42)
               (* y4 (* y (fma c y3 (* b (- k)))))
               (* y2 (* y4 (fma k y1 (* c (- 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 t_1 = a * (y * fma(b, x, (y3 * -y5)));
	double tmp;
	if (t <= -1.1e+111) {
		tmp = j * (y4 * fma(b, t, (y1 * -y3)));
	} else if (t <= -3.8e-25) {
		tmp = (t * a) * fma(y2, y5, (z * -b));
	} else if (t <= -2.4e-191) {
		tmp = t_1;
	} else if (t <= 5.8e-249) {
		tmp = y1 * (z * fma(y3, a, (i * -k)));
	} else if (t <= 1.05e-85) {
		tmp = t_1;
	} else if (t <= 2.4e+42) {
		tmp = y4 * (y * fma(c, y3, (b * -k)));
	} else {
		tmp = y2 * (y4 * fma(k, y1, (c * -t)));
	}
	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(y * fma(b, x, Float64(y3 * Float64(-y5)))))
	tmp = 0.0
	if (t <= -1.1e+111)
		tmp = Float64(j * Float64(y4 * fma(b, t, Float64(y1 * Float64(-y3)))));
	elseif (t <= -3.8e-25)
		tmp = Float64(Float64(t * a) * fma(y2, y5, Float64(z * Float64(-b))));
	elseif (t <= -2.4e-191)
		tmp = t_1;
	elseif (t <= 5.8e-249)
		tmp = Float64(y1 * Float64(z * fma(y3, a, Float64(i * Float64(-k)))));
	elseif (t <= 1.05e-85)
		tmp = t_1;
	elseif (t <= 2.4e+42)
		tmp = Float64(y4 * Float64(y * fma(c, y3, Float64(b * Float64(-k)))));
	else
		tmp = Float64(y2 * Float64(y4 * fma(k, y1, Float64(c * Float64(-t)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[(b * x + N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+111], N[(j * N[(y4 * N[(b * t + N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-25], N[(N[(t * a), $MachinePrecision] * N[(y2 * y5 + N[(z * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.4e-191], t$95$1, If[LessEqual[t, 5.8e-249], N[(y1 * N[(z * N[(y3 * a + N[(i * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-85], t$95$1, If[LessEqual[t, 2.4e+42], N[(y4 * N[(y * N[(c * y3 + N[(b * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(y4 * N[(k * y1 + N[(c * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.09999999999999999e111

   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 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. *-lowering-*.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. Simplified 53.4%

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

   6. Taylor expanded in y4 around -inf

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

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

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

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

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

      3. +-commutative N/A

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

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

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

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

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

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

      8. neg-lowering-neg.f64 59.1

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

   8. Simplified 59.1%

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

   if -1.09999999999999999e111 < t < -3.7999999999999998e-25

   1. Initial program 31.0%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 45.9%

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

   6. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

      6. associate-*r* N/A

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

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

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

      8. mul-1-neg N/A

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

      9. neg-lowering-neg.f64 49.5

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

   8. Simplified 49.5%

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

   if -3.7999999999999998e-25 < t < -2.3999999999999999e-191 or 5.80000000000000044e-249 < t < 1.05e-85

   1. Initial program 34.0%

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

   3. Taylor expanded in a around inf

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

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

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 42.1%

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

   6. Taylor expanded in y around inf

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

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

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

      2. +-commutative N/A

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

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

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

      4. associate-*r* N/A

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

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

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

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 48.1

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

   8. Simplified 48.1%

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

   if -2.3999999999999999e-191 < t < 5.80000000000000044e-249

   1. Initial program 40.1%

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

   3. Taylor expanded in y1 around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

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

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

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

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

   5. Simplified 55.5%

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

   6. Taylor expanded in z around inf

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

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

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 50.6

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

   8. Simplified 50.6%

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

   if 1.05e-85 < t < 2.3999999999999999e42

   1. Initial program 31.8%

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

   3. Taylor expanded in y around inf

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

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

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

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

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

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

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

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

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

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

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

      11. neg-mul-1 N/A

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

      12. neg-lowering-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. Simplified 41.5%

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

   6. Taylor expanded in y4 around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

      9. mul-1-neg N/A

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

      10. *-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. neg-lowering-neg.f64 64.7

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

   8. Simplified 64.7%

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

   if 2.3999999999999999e42 < t

   1. Initial program 21.7%

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

   3. Taylor expanded in y2 around inf

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

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

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

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 55.6%

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

   6. Taylor expanded in y4 around inf

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

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

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

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

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

      3. +-commutative N/A

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

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

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

      5. associate-*r* N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-lowering-neg.f64 48.1

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

   8. Simplified 48.1%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-25}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \mathsf{fma}\left(y2, y5, z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-191}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-249}:\\ \;\;\;\;y1 \cdot \left(z \cdot \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+42}:\\ \;\;\;\;y4 \cdot \left(y \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, c \cdot \left(-t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+100}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-39}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-247}:\\ \;\;\;\;y1 \cdot \left(z \cdot \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.12 \cdot 10^{+42}:\\ \;\;\;\;y4 \cdot \left(y \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, c \cdot \left(-t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (fma b x (* y3 (- y5)))))))
   (if (<= t -6e+100)
     (* j (* y4 (fma b t (* y1 (- y3)))))
     (if (<= t -2.35e-39)
       (* c (* z (fma i t (* y0 (- y3)))))
       (if (<= t -8.5e-190)
         t_1
         (if (<= t 8e-247)
           (* y1 (* z (fma y3 a (* i (- k)))))
           (if (<= t 9.2e-86)
             t_1
             (if (<= t 2.12e+42)
               (* y4 (* y (fma c y3 (* b (- k)))))
               (* y2 (* y4 (fma k y1 (* c (- 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 t_1 = a * (y * fma(b, x, (y3 * -y5)));
	double tmp;
	if (t <= -6e+100) {
		tmp = j * (y4 * fma(b, t, (y1 * -y3)));
	} else if (t <= -2.35e-39) {
		tmp = c * (z * fma(i, t, (y0 * -y3)));
	} else if (t <= -8.5e-190) {
		tmp = t_1;
	} else if (t <= 8e-247) {
		tmp = y1 * (z * fma(y3, a, (i * -k)));
	} else if (t <= 9.2e-86) {
		tmp = t_1;
	} else if (t <= 2.12e+42) {
		tmp = y4 * (y * fma(c, y3, (b * -k)));
	} else {
		tmp = y2 * (y4 * fma(k, y1, (c * -t)));
	}
	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(y * fma(b, x, Float64(y3 * Float64(-y5)))))
	tmp = 0.0
	if (t <= -6e+100)
		tmp = Float64(j * Float64(y4 * fma(b, t, Float64(y1 * Float64(-y3)))));
	elseif (t <= -2.35e-39)
		tmp = Float64(c * Float64(z * fma(i, t, Float64(y0 * Float64(-y3)))));
	elseif (t <= -8.5e-190)
		tmp = t_1;
	elseif (t <= 8e-247)
		tmp = Float64(y1 * Float64(z * fma(y3, a, Float64(i * Float64(-k)))));
	elseif (t <= 9.2e-86)
		tmp = t_1;
	elseif (t <= 2.12e+42)
		tmp = Float64(y4 * Float64(y * fma(c, y3, Float64(b * Float64(-k)))));
	else
		tmp = Float64(y2 * Float64(y4 * fma(k, y1, Float64(c * Float64(-t)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[(b * x + N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+100], N[(j * N[(y4 * N[(b * t + N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.35e-39], N[(c * N[(z * N[(i * t + N[(y0 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.5e-190], t$95$1, If[LessEqual[t, 8e-247], N[(y1 * N[(z * N[(y3 * a + N[(i * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-86], t$95$1, If[LessEqual[t, 2.12e+42], N[(y4 * N[(y * N[(c * y3 + N[(b * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(y4 * N[(k * y1 + N[(c * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.99999999999999971e100

   1. Initial program 34.1%

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

   3. Taylor expanded in 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. *-lowering-*.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. Simplified 51.0%

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

   6. Taylor expanded in y4 around -inf

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

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

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

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

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

      3. +-commutative N/A

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

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

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

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

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

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

      8. neg-lowering-neg.f64 56.5

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

   8. Simplified 56.5%

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

   if -5.99999999999999971e100 < t < -2.3500000000000001e-39

   1. Initial program 32.8%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 58.0%

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

   6. Taylor expanded in c around -inf

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

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

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

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

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

      3. +-commutative N/A

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

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

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

      5. associate-*r* N/A

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

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

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

      7. mul-1-neg N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 43.5

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

   8. Simplified 43.5%

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

   if -2.3500000000000001e-39 < t < -8.5000000000000003e-190 or 8.0000000000000002e-247 < t < 9.19999999999999985e-86

   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. *-lowering-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 42.4%

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

   6. Taylor expanded in y around inf

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

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

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 48.7

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 48.7%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   if -8.5000000000000003e-190 < t < 8.0000000000000002e-247

   1. Initial program 40.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y1 \cdot \left(\color{blue}{a \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\mathsf{fma}\left(a, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]

   5. Simplified 55.5%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 + -1 \cdot \left(i \cdot k\right)\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(\color{blue}{y3 \cdot a} + -1 \cdot \left(i \cdot k\right)\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(y3, a, -1 \cdot \left(i \cdot k\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(z \cdot \mathsf{fma}\left(y3, a, \color{blue}{\mathsf{neg}\left(i \cdot k\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto y1 \cdot \left(z \cdot \mathsf{fma}\left(y3, a, \color{blue}{i \cdot \left(\mathsf{neg}\left(k\right)\right)}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(z \cdot \mathsf{fma}\left(y3, a, i \cdot \color{blue}{\left(-1 \cdot k\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \mathsf{fma}\left(y3, a, \color{blue}{i \cdot \left(-1 \cdot k\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(z \cdot \mathsf{fma}\left(y3, a, i \cdot \color{blue}{\left(\mathsf{neg}\left(k\right)\right)}\right)\right) \]

      10. neg-lowering-neg.f64 50.6

          \[\leadsto y1 \cdot \left(z \cdot \mathsf{fma}\left(y3, a, i \cdot \color{blue}{\left(-k\right)}\right)\right) \]

   8. Simplified 50.6%

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right)\right)} \]

   if 9.19999999999999985e-86 < t < 2.1199999999999999e42

   1. Initial program 31.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. --lowering--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. neg-lowering-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. Simplified 41.5%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y \cdot \left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right) \cdot y} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right) \cdot y\right)} \]

      3. *-commutative N/A

         \[\leadsto y4 \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(y \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right) \cdot y\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right) \cdot y\right)} \]

      7. +-commutative N/A

         \[\leadsto y4 \cdot \left(\color{blue}{\left(c \cdot y3 + -1 \cdot \left(b \cdot k\right)\right)} \cdot y\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto y4 \cdot \left(\color{blue}{\mathsf{fma}\left(c, y3, -1 \cdot \left(b \cdot k\right)\right)} \cdot y\right) \]

      9. mul-1-neg N/A

         \[\leadsto y4 \cdot \left(\mathsf{fma}\left(c, y3, \color{blue}{\mathsf{neg}\left(b \cdot k\right)}\right) \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(c, y3, \mathsf{neg}\left(\color{blue}{k \cdot b}\right)\right) \cdot y\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(c, y3, \color{blue}{k \cdot \left(\mathsf{neg}\left(b\right)\right)}\right) \cdot y\right) \]

      12. mul-1-neg N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(c, y3, k \cdot \color{blue}{\left(-1 \cdot b\right)}\right) \cdot y\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(c, y3, \color{blue}{k \cdot \left(-1 \cdot b\right)}\right) \cdot y\right) \]

      14. mul-1-neg N/A

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(c, y3, k \cdot \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \cdot y\right) \]

      15. neg-lowering-neg.f64 64.7

          \[\leadsto y4 \cdot \left(\mathsf{fma}\left(c, y3, k \cdot \color{blue}{\left(-b\right)}\right) \cdot y\right) \]

   8. Simplified 64.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(c, y3, k \cdot \left(-b\right)\right) \cdot y\right)} \]

   if 2.1199999999999999e42 < t

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 55.6%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 48.1

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 48.1%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+100}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-39}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-247}:\\ \;\;\;\;y1 \cdot \left(z \cdot \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.12 \cdot 10^{+42}:\\ \;\;\;\;y4 \cdot \left(y \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, c \cdot \left(-t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(c \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ t_2 := a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.28 \cdot 10^{-39}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(t \cdot j\right) \cdot \left(-y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* c (fma i (- x) (* y3 y4)))))
        (t_2 (* a (* y (fma b x (* y3 (- y5)))))))
   (if (<= t -2.15e+96)
     (* j (* y4 (fma b t (* y1 (- y3)))))
     (if (<= t -1.28e-39)
       (* c (* z (fma i t (* y0 (- y3)))))
       (if (<= t -6.6e-180)
         t_2
         (if (<= t 1.76e-224)
           t_1
           (if (<= t 1.25e-73)
             t_2
             (if (<= t 2.15e+164) t_1 (* i (* (* t j) (- y5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (c * fma(i, -x, (y3 * y4)));
	double t_2 = a * (y * fma(b, x, (y3 * -y5)));
	double tmp;
	if (t <= -2.15e+96) {
		tmp = j * (y4 * fma(b, t, (y1 * -y3)));
	} else if (t <= -1.28e-39) {
		tmp = c * (z * fma(i, t, (y0 * -y3)));
	} else if (t <= -6.6e-180) {
		tmp = t_2;
	} else if (t <= 1.76e-224) {
		tmp = t_1;
	} else if (t <= 1.25e-73) {
		tmp = t_2;
	} else if (t <= 2.15e+164) {
		tmp = t_1;
	} else {
		tmp = i * ((t * j) * -y5);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(c * fma(i, Float64(-x), Float64(y3 * y4))))
	t_2 = Float64(a * Float64(y * fma(b, x, Float64(y3 * Float64(-y5)))))
	tmp = 0.0
	if (t <= -2.15e+96)
		tmp = Float64(j * Float64(y4 * fma(b, t, Float64(y1 * Float64(-y3)))));
	elseif (t <= -1.28e-39)
		tmp = Float64(c * Float64(z * fma(i, t, Float64(y0 * Float64(-y3)))));
	elseif (t <= -6.6e-180)
		tmp = t_2;
	elseif (t <= 1.76e-224)
		tmp = t_1;
	elseif (t <= 1.25e-73)
		tmp = t_2;
	elseif (t <= 2.15e+164)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(Float64(t * j) * Float64(-y5)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(c * N[(i * (-x) + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y * N[(b * x + N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e+96], N[(j * N[(y4 * N[(b * t + N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.28e-39], N[(c * N[(z * N[(i * t + N[(y0 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.6e-180], t$95$2, If[LessEqual[t, 1.76e-224], t$95$1, If[LessEqual[t, 1.25e-73], t$95$2, If[LessEqual[t, 2.15e+164], t$95$1, N[(i * N[(N[(t * j), $MachinePrecision] * (-y5)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.15000000000000001e96

   1. Initial program 34.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-lowering-*.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. Simplified 51.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 56.5

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 56.5%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   if -2.15000000000000001e96 < t < -1.28000000000000001e-39

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \color{blue}{\left(-1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-1 \cdot z\right)} \]

   5. Simplified 58.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(i, t, -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 43.5

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-y0\right)} \cdot y3\right)\right) \]

   8. Simplified 43.5%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \left(-y0\right) \cdot y3\right)\right)} \]

   if -1.28000000000000001e-39 < t < -6.59999999999999996e-180 or 1.76e-224 < t < 1.25e-73

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 43.9%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 49.4

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 49.4%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   if -6.59999999999999996e-180 < t < 1.76e-224 or 1.25e-73 < t < 2.15e164

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. --lowering--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. neg-lowering-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. Simplified 44.8%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto y \cdot \left(c \cdot \left(\color{blue}{\left(\mathsf{neg}\left(i \cdot x\right)\right)} + y3 \cdot y4\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(c \cdot \left(\color{blue}{i \cdot \left(\mathsf{neg}\left(x\right)\right)} + y3 \cdot y4\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \left(c \cdot \left(i \cdot \color{blue}{\left(-1 \cdot x\right)} + y3 \cdot y4\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto y \cdot \left(c \cdot \color{blue}{\mathsf{fma}\left(i, -1 \cdot x, y3 \cdot y4\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto y \cdot \left(c \cdot \mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right)\right) \]

      7. neg-lowering-neg.f64 N/A

         \[\leadsto y \cdot \left(c \cdot \mathsf{fma}\left(i, \color{blue}{\mathsf{neg}\left(x\right)}, y3 \cdot y4\right)\right) \]

      8. *-lowering-*.f64 40.7

         \[\leadsto y \cdot \left(c \cdot \mathsf{fma}\left(i, -x, \color{blue}{y3 \cdot y4}\right)\right) \]

   8. Simplified 40.7%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)} \]

   if 2.15e164 < t

   1. Initial program 11.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. *-lowering-*.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. Simplified 52.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right)} \cdot \left(i \cdot y5 - b \cdot y4\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5 - b \cdot y4\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \left(\color{blue}{i \cdot y5} - b \cdot y4\right)\right) \]

      8. *-lowering-*.f64 55.8

         \[\leadsto -\left(j \cdot t\right) \cdot \left(i \cdot y5 - \color{blue}{b \cdot y4}\right) \]

   8. Simplified 55.8%

      \[\leadsto \color{blue}{-\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right)\right) \]

       4. *-lowering-*.f64 49.0

          \[\leadsto -i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 49.0%

       \[\leadsto -\color{blue}{i \cdot \left(j \cdot \left(y5 \cdot t\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot \left(y5 \cdot t\right)\right) \cdot i}\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(y5 \cdot t\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(y5 \cdot t\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y5 \cdot t\right) \cdot j\right)} \cdot \left(\mathsf{neg}\left(i\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \color{blue}{\left(y5 \cdot \left(t \cdot j\right)\right)} \cdot \left(\mathsf{neg}\left(i\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(y5 \cdot \left(t \cdot j\right)\right)} \cdot \left(\mathsf{neg}\left(i\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \left(y5 \cdot \color{blue}{\left(t \cdot j\right)}\right) \cdot \left(\mathsf{neg}\left(i\right)\right) \]

       8. neg-lowering-neg.f64 56.1

          \[\leadsto \left(y5 \cdot \left(t \cdot j\right)\right) \cdot \color{blue}{\left(-i\right)} \]

   13. Applied egg-rr 56.1%

       \[\leadsto \color{blue}{\left(y5 \cdot \left(t \cdot j\right)\right) \cdot \left(-i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.28 \cdot 10^{-39}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \left(c \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+164}:\\ \;\;\;\;y \cdot \left(c \cdot \mathsf{fma}\left(i, -x, y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(t \cdot j\right) \cdot \left(-y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, x \cdot \left(-b\right)\right)\right)\\ \mathbf{if}\;y0 \leq -3 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -3.9 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{-212}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.42 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(y \cdot \mathsf{fma}\left(-c, i, a \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{+151}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y5 \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y0 (fma y3 y5 (* x (- b)))))))
   (if (<= y0 -3e+183)
     t_1
     (if (<= y0 -3.9e-109)
       (* a (* y (fma b x (* y3 (- y5)))))
       (if (<= y0 1.4e-212)
         (* j (* y4 (fma b t (* y1 (- y3)))))
         (if (<= y0 1.35e-52)
           (* a (* y3 (fma y1 z (* y (- y5)))))
           (if (<= y0 1.42e+79)
             (* x (* y (fma (- c) i (* a b))))
             (if (<= y0 7.5e+151) (* y2 (* k (* y5 (- 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 = j * (y0 * fma(y3, y5, (x * -b)));
	double tmp;
	if (y0 <= -3e+183) {
		tmp = t_1;
	} else if (y0 <= -3.9e-109) {
		tmp = a * (y * fma(b, x, (y3 * -y5)));
	} else if (y0 <= 1.4e-212) {
		tmp = j * (y4 * fma(b, t, (y1 * -y3)));
	} else if (y0 <= 1.35e-52) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else if (y0 <= 1.42e+79) {
		tmp = x * (y * fma(-c, i, (a * b)));
	} else if (y0 <= 7.5e+151) {
		tmp = y2 * (k * (y5 * -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(j * Float64(y0 * fma(y3, y5, Float64(x * Float64(-b)))))
	tmp = 0.0
	if (y0 <= -3e+183)
		tmp = t_1;
	elseif (y0 <= -3.9e-109)
		tmp = Float64(a * Float64(y * fma(b, x, Float64(y3 * Float64(-y5)))));
	elseif (y0 <= 1.4e-212)
		tmp = Float64(j * Float64(y4 * fma(b, t, Float64(y1 * Float64(-y3)))));
	elseif (y0 <= 1.35e-52)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	elseif (y0 <= 1.42e+79)
		tmp = Float64(x * Float64(y * fma(Float64(-c), i, Float64(a * b))));
	elseif (y0 <= 7.5e+151)
		tmp = Float64(y2 * Float64(k * Float64(y5 * 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[(j * N[(y0 * N[(y3 * y5 + N[(x * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3e+183], t$95$1, If[LessEqual[y0, -3.9e-109], N[(a * N[(y * N[(b * x + N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.4e-212], N[(j * N[(y4 * N[(b * t + N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.35e-52], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.42e+79], N[(x * N[(y * N[((-c) * i + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7.5e+151], N[(y2 * N[(k * N[(y5 * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -2.99999999999999996e183 or 7.49999999999999977e151 < y0

   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. *-lowering-*.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. Simplified 50.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y0 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(y3, y5, -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(-1 \cdot b\right) \cdot x}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(-1 \cdot b\right) \cdot x}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot x\right)\right) \]

      8. neg-lowering-neg.f64 59.4

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(-b\right)} \cdot x\right)\right) \]

   8. Simplified 59.4%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)} \]

   if -2.99999999999999996e183 < y0 < -3.90000000000000023e-109

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 46.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 35.2

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 35.2%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   if -3.90000000000000023e-109 < y0 < 1.40000000000000007e-212

   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 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. *-lowering-*.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. Simplified 48.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 39.4

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   if 1.40000000000000007e-212 < y0 < 1.35000000000000005e-52

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 50.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\mathsf{neg}\left(y \cdot y5\right)}\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\mathsf{neg}\left(y \cdot y5\right)}\right)\right) \]

      6. *-lowering-*.f64 42.2

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, -\color{blue}{y \cdot y5}\right)\right) \]

   8. Simplified 42.2%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \mathsf{fma}\left(y1, z, -y \cdot y5\right)\right)} \]

   if 1.35000000000000005e-52 < y0 < 1.41999999999999998e79

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. --lowering--.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. *-lowering-*.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. *-lowering-*.f64 38.7

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Simplified 38.7%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\left(a \cdot b + \left(\mathsf{neg}\left(c \cdot i\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot i\right)\right) + a \cdot b\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{-1 \cdot \left(c \cdot i\right)} + a \cdot b\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot c\right) \cdot i} + a \cdot b\right)\right) \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot c, i, a \cdot b\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, i, a \cdot b\right)\right) \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, i, a \cdot b\right)\right) \]

      9. *-lowering-*.f64 54.5

         \[\leadsto x \cdot \left(y \cdot \mathsf{fma}\left(-c, i, \color{blue}{a \cdot b}\right)\right) \]

   8. Simplified 54.5%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(-c, i, a \cdot b\right)\right)} \]

   if 1.41999999999999998e79 < y0 < 7.49999999999999977e151

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 43.7%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(\mathsf{neg}\left(y0 \cdot y5\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\mathsf{fma}\left(y1, y4, \mathsf{neg}\left(y0 \cdot y5\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{-1 \cdot \left(y0 \cdot y5\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 57.7

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-y0\right)} \cdot y5\right)\right) \]

   8. Simplified 57.7%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(\mathsf{neg}\left(y0 \cdot y5\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto y2 \cdot \left(k \cdot \left(\mathsf{neg}\left(\color{blue}{y5 \cdot y0}\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y0\right)\right)\right)}\right) \]

       4. mul-1-neg N/A

          \[\leadsto y2 \cdot \left(k \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot y0\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot y0\right)\right)}\right) \]

       6. mul-1-neg N/A

          \[\leadsto y2 \cdot \left(k \cdot \left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)}\right)\right) \]

       7. neg-lowering-neg.f64 72.0

          \[\leadsto y2 \cdot \left(k \cdot \left(y5 \cdot \color{blue}{\left(-y0\right)}\right)\right) \]

   11. Simplified 72.0%

       \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y5 \cdot \left(-y0\right)\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3 \cdot 10^{+183}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, x \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -3.9 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{-212}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.42 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(y \cdot \mathsf{fma}\left(-c, i, a \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{+151}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y5 \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, x \cdot \left(-b\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -3.55 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 1.4 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(\left(-y0\right) \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* y1 (fma z (fma y3 a (* i (- k))) (* y4 (fma (- y3) j (* k y2)))))))
   (if (<= y1 -3.55e-168)
     t_1
     (if (<= y1 1.4e+58) (* z (* (- y0) (fma c y3 (* b (- k))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * fma(z, fma(y3, a, (i * -k)), (y4 * fma(-y3, j, (k * y2))));
	double tmp;
	if (y1 <= -3.55e-168) {
		tmp = t_1;
	} else if (y1 <= 1.4e+58) {
		tmp = z * (-y0 * fma(c, y3, (b * -k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * fma(z, fma(y3, a, Float64(i * Float64(-k))), Float64(y4 * fma(Float64(-y3), j, Float64(k * y2)))))
	tmp = 0.0
	if (y1 <= -3.55e-168)
		tmp = t_1;
	elseif (y1 <= 1.4e+58)
		tmp = Float64(z * Float64(Float64(-y0) * fma(c, y3, Float64(b * Float64(-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[(y1 * N[(z * N[(y3 * a + N[(i * (-k)), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[((-y3) * j + N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -3.55e-168], t$95$1, If[LessEqual[y1, 1.4e+58], N[(z * N[((-y0) * N[(c * y3 + N[(b * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y1 < -3.55000000000000009e-168 or 1.3999999999999999e58 < y1

   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 y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y1 \cdot \left(\color{blue}{a \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\mathsf{fma}\left(a, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]

   5. Simplified 54.6%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(i \cdot \left(k \cdot z\right)\right) + \left(a \cdot \left(y3 \cdot z\right) + y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(i \cdot \left(k \cdot z\right)\right) + \left(a \cdot \left(y3 \cdot z\right) + y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)\right)} \]

      2. associate-+r+ N/A

         \[\leadsto y1 \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(k \cdot z\right)\right) + a \cdot \left(y3 \cdot z\right)\right) + y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(\left(\color{blue}{\left(\mathsf{neg}\left(i \cdot \left(k \cdot z\right)\right)\right)} + a \cdot \left(y3 \cdot z\right)\right) + y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto y1 \cdot \left(\left(\left(\mathsf{neg}\left(\color{blue}{\left(i \cdot k\right) \cdot z}\right)\right) + a \cdot \left(y3 \cdot z\right)\right) + y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto y1 \cdot \left(\left(\color{blue}{\left(\mathsf{neg}\left(i \cdot k\right)\right) \cdot z} + a \cdot \left(y3 \cdot z\right)\right) + y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(\left(\color{blue}{\left(-1 \cdot \left(i \cdot k\right)\right)} \cdot z + a \cdot \left(y3 \cdot z\right)\right) + y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto y1 \cdot \left(\left(\left(-1 \cdot \left(i \cdot k\right)\right) \cdot z + \color{blue}{\left(a \cdot y3\right) \cdot z}\right) + y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right) \]

      8. distribute-rgt-in N/A

         \[\leadsto y1 \cdot \left(\color{blue}{z \cdot \left(-1 \cdot \left(i \cdot k\right) + a \cdot y3\right)} + y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right) \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\mathsf{fma}\left(z, -1 \cdot \left(i \cdot k\right) + a \cdot y3, y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

   8. Simplified 52.9%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, y2 \cdot k\right)\right)} \]

   if -3.55000000000000009e-168 < y1 < 1.3999999999999999e58

   1. Initial program 37.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \color{blue}{\left(-1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-1 \cdot z\right)} \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{\left(y0 \cdot \left(c \cdot y3 - b \cdot k\right)\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(y0 \cdot \left(c \cdot y3 - b \cdot k\right)\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \left(y0 \cdot \color{blue}{\left(c \cdot y3 + \left(\mathsf{neg}\left(b \cdot k\right)\right)\right)}\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \left(y0 \cdot \left(c \cdot y3 + \color{blue}{-1 \cdot \left(b \cdot k\right)}\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \left(y0 \cdot \color{blue}{\mathsf{fma}\left(c, y3, -1 \cdot \left(b \cdot k\right)\right)}\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(y0 \cdot \mathsf{fma}\left(c, y3, \color{blue}{\left(-1 \cdot b\right) \cdot k}\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(y0 \cdot \mathsf{fma}\left(c, y3, \color{blue}{\left(-1 \cdot b\right) \cdot k}\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \left(y0 \cdot \mathsf{fma}\left(c, y3, \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot k\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. neg-lowering-neg.f64 42.4

         \[\leadsto \left(y0 \cdot \mathsf{fma}\left(c, y3, \color{blue}{\left(-b\right)} \cdot k\right)\right) \cdot \left(-z\right) \]

   8. Simplified 42.4%

      \[\leadsto \color{blue}{\left(y0 \cdot \mathsf{fma}\left(c, y3, \left(-b\right) \cdot k\right)\right)} \cdot \left(-z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.55 \cdot 10^{-168}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 1.4 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(\left(-y0\right) \cdot \mathsf{fma}\left(c, y3, b \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(y3, a, i \cdot \left(-k\right)\right), y4 \cdot \mathsf{fma}\left(-y3, j, k \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.7% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y2 \cdot \mathsf{fma}\left(c, x, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{if}\;y2 \leq -5 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -2.4 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{-256}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.4 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(y \cdot \mathsf{fma}\left(-c, i, a \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y2 (fma c x (* k (- y5)))))))
   (if (<= y2 -5e+127)
     t_1
     (if (<= y2 -2.4e-141)
       (* a (* y3 (fma y1 z (* y (- y5)))))
       (if (<= y2 1.1e-256)
         (* c (* z (fma i t (* y0 (- y3)))))
         (if (<= y2 6.4e+86)
           (* x (* y (fma (- c) i (* a b))))
           (if (<= y2 1.05e+117) (* x (* j (- (* 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 = y0 * (y2 * fma(c, x, (k * -y5)));
	double tmp;
	if (y2 <= -5e+127) {
		tmp = t_1;
	} else if (y2 <= -2.4e-141) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else if (y2 <= 1.1e-256) {
		tmp = c * (z * fma(i, t, (y0 * -y3)));
	} else if (y2 <= 6.4e+86) {
		tmp = x * (y * fma(-c, i, (a * b)));
	} else if (y2 <= 1.05e+117) {
		tmp = x * (j * ((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(y0 * Float64(y2 * fma(c, x, Float64(k * Float64(-y5)))))
	tmp = 0.0
	if (y2 <= -5e+127)
		tmp = t_1;
	elseif (y2 <= -2.4e-141)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	elseif (y2 <= 1.1e-256)
		tmp = Float64(c * Float64(z * fma(i, t, Float64(y0 * Float64(-y3)))));
	elseif (y2 <= 6.4e+86)
		tmp = Float64(x * Float64(y * fma(Float64(-c), i, Float64(a * b))));
	elseif (y2 <= 1.05e+117)
		tmp = Float64(x * Float64(j * Float64(Float64(i * y1) - Float64(b * 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[(y0 * N[(y2 * N[(c * x + N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -5e+127], t$95$1, If[LessEqual[y2, -2.4e-141], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.1e-256], N[(c * N[(z * N[(i * t + N[(y0 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.4e+86], N[(x * N[(y * N[((-c) * i + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.05e+117], N[(x * N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -5.0000000000000004e127 or 1.0500000000000001e117 < y2

   1. Initial program 17.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 61.6%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(c, x, -1 \cdot \left(k \cdot y5\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(c, x, \color{blue}{\mathsf{neg}\left(k \cdot y5\right)}\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(c, x, \color{blue}{\mathsf{neg}\left(k \cdot y5\right)}\right)\right) \]

      7. *-lowering-*.f64 57.7

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(c, x, -\color{blue}{k \cdot y5}\right)\right) \]

   8. Simplified 57.7%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \mathsf{fma}\left(c, x, -k \cdot y5\right)\right)} \]

   if -5.0000000000000004e127 < y2 < -2.4000000000000001e-141

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 47.9%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\mathsf{neg}\left(y \cdot y5\right)}\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\mathsf{neg}\left(y \cdot y5\right)}\right)\right) \]

      6. *-lowering-*.f64 42.5

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, -\color{blue}{y \cdot y5}\right)\right) \]

   8. Simplified 42.5%

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \mathsf{fma}\left(y1, z, -y \cdot y5\right)\right)} \]

   if -2.4000000000000001e-141 < y2 < 1.10000000000000005e-256

   1. Initial program 44.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \color{blue}{\left(-1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-1 \cdot z\right)} \]

   5. Simplified 40.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(i, t, -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 40.4

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-y0\right)} \cdot y3\right)\right) \]

   8. Simplified 40.4%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \left(-y0\right) \cdot y3\right)\right)} \]

   if 1.10000000000000005e-256 < y2 < 6.4000000000000001e86

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. --lowering--.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. *-lowering-*.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. *-lowering-*.f64 37.9

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Simplified 37.9%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\left(a \cdot b + \left(\mathsf{neg}\left(c \cdot i\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot i\right)\right) + a \cdot b\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{-1 \cdot \left(c \cdot i\right)} + a \cdot b\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot c\right) \cdot i} + a \cdot b\right)\right) \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot c, i, a \cdot b\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, i, a \cdot b\right)\right) \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, i, a \cdot b\right)\right) \]

      9. *-lowering-*.f64 42.6

         \[\leadsto x \cdot \left(y \cdot \mathsf{fma}\left(-c, i, \color{blue}{a \cdot b}\right)\right) \]

   8. Simplified 42.6%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(-c, i, a \cdot b\right)\right)} \]

   if 6.4000000000000001e86 < y2 < 1.0500000000000001e117

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. *-lowering-*.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. --lowering--.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. *-lowering-*.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. *-lowering-*.f64 33.9

          \[\leadsto x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right) \]

   5. Simplified 33.9%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(a \cdot b - c \cdot i, y, \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \left(j \cdot \left(\color{blue}{i \cdot y1} - b \cdot y0\right)\right) \]

      4. *-lowering-*.f64 67.3

         \[\leadsto x \cdot \left(j \cdot \left(i \cdot y1 - \color{blue}{b \cdot y0}\right)\right) \]

   8. Simplified 67.3%

      \[\leadsto x \cdot \color{blue}{\left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5 \cdot 10^{+127}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(c, x, k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.4 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.1 \cdot 10^{-256}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.4 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(y \cdot \mathsf{fma}\left(-c, i, a \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(c, x, k \cdot \left(-y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{if}\;y4 \leq -2.4 \cdot 10^{+212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -5 \cdot 10^{-18}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, x \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.25 \cdot 10^{-100}:\\ \;\;\;\;a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 8 \cdot 10^{+97}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y4 (fma b t (* y1 (- y3)))))))
   (if (<= y4 -2.4e+212)
     t_1
     (if (<= y4 -5e-18)
       (* j (* y0 (fma y3 y5 (* x (- b)))))
       (if (<= y4 -1.25e-100)
         (* a (* y1 (fma y3 z (* y2 (- x)))))
         (if (<= y4 7.5e-206)
           (* a (* y5 (- (* t y2) (* y y3))))
           (if (<= y4 8e+97) (* c (* z (fma i t (* y0 (- 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 = j * (y4 * fma(b, t, (y1 * -y3)));
	double tmp;
	if (y4 <= -2.4e+212) {
		tmp = t_1;
	} else if (y4 <= -5e-18) {
		tmp = j * (y0 * fma(y3, y5, (x * -b)));
	} else if (y4 <= -1.25e-100) {
		tmp = a * (y1 * fma(y3, z, (y2 * -x)));
	} else if (y4 <= 7.5e-206) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y4 <= 8e+97) {
		tmp = c * (z * fma(i, t, (y0 * -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(j * Float64(y4 * fma(b, t, Float64(y1 * Float64(-y3)))))
	tmp = 0.0
	if (y4 <= -2.4e+212)
		tmp = t_1;
	elseif (y4 <= -5e-18)
		tmp = Float64(j * Float64(y0 * fma(y3, y5, Float64(x * Float64(-b)))));
	elseif (y4 <= -1.25e-100)
		tmp = Float64(a * Float64(y1 * fma(y3, z, Float64(y2 * Float64(-x)))));
	elseif (y4 <= 7.5e-206)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y4 <= 8e+97)
		tmp = Float64(c * Float64(z * fma(i, t, Float64(y0 * Float64(-y3)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y4 * N[(b * t + N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.4e+212], t$95$1, If[LessEqual[y4, -5e-18], N[(j * N[(y0 * N[(y3 * y5 + N[(x * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.25e-100], N[(a * N[(y1 * N[(y3 * z + N[(y2 * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.5e-206], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 8e+97], N[(c * N[(z * N[(i * t + N[(y0 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -2.4e212 or 8.0000000000000006e97 < y4

   1. Initial program 23.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-lowering-*.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. Simplified 47.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 54.7

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 54.7%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   if -2.4e212 < y4 < -5.00000000000000036e-18

   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. *-lowering-*.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. Simplified 46.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y0 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(y3, y5, -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(-1 \cdot b\right) \cdot x}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(-1 \cdot b\right) \cdot x}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot x\right)\right) \]

      8. neg-lowering-neg.f64 43.6

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(-b\right)} \cdot x\right)\right) \]

   8. Simplified 43.6%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)} \]

   if -5.00000000000000036e-18 < y4 < -1.25e-100

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 28.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(y3, z, \mathsf{neg}\left(x \cdot y2\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{-1 \cdot \left(x \cdot y2\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-1 \cdot x\right) \cdot y2}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-1 \cdot x\right) \cdot y2}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot y2\right)\right) \]

      8. neg-lowering-neg.f64 40.1

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-x\right)} \cdot y2\right)\right) \]

   8. Simplified 40.1%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if -1.25e-100 < y4 < 7.5e-206

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 41.9%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-lowering-*.f64 38.4

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   8. Simplified 38.4%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 7.5e-206 < y4 < 8.0000000000000006e97

   1. Initial program 40.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \color{blue}{\left(-1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-1 \cdot z\right)} \]

   5. Simplified 52.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(i, t, -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 39.7

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-y0\right)} \cdot y3\right)\right) \]

   8. Simplified 39.7%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \left(-y0\right) \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.4 \cdot 10^{+212}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -5 \cdot 10^{-18}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, x \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.25 \cdot 10^{-100}:\\ \;\;\;\;a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 8 \cdot 10^{+97}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 22.8% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{if}\;y1 \leq -1.95 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -2.36 \cdot 10^{-35}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.25 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq -1.26 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 1.65 \cdot 10^{-119}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 4.9 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (* y4 (* k y1)))))
   (if (<= y1 -1.95e+42)
     t_1
     (if (<= y1 -2.36e-35)
       (* k (* y0 (* y2 (- y5))))
       (if (<= y1 -1.25e-112)
         (* b (* (* x y) a))
         (if (<= y1 -1.26e-250)
           (* a (* y5 (* t y2)))
           (if (<= y1 1.65e-119)
             (* i (* j (* t (- y5))))
             (if (<= y1 4.9e+57) (* b (* j (* t y4))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -1.95e+42) {
		tmp = t_1;
	} else if (y1 <= -2.36e-35) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y1 <= -1.25e-112) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= -1.26e-250) {
		tmp = a * (y5 * (t * y2));
	} else if (y1 <= 1.65e-119) {
		tmp = i * (j * (t * -y5));
	} else if (y1 <= 4.9e+57) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * (y4 * (k * y1))
    if (y1 <= (-1.95d+42)) then
        tmp = t_1
    else if (y1 <= (-2.36d-35)) then
        tmp = k * (y0 * (y2 * -y5))
    else if (y1 <= (-1.25d-112)) then
        tmp = b * ((x * y) * a)
    else if (y1 <= (-1.26d-250)) then
        tmp = a * (y5 * (t * y2))
    else if (y1 <= 1.65d-119) then
        tmp = i * (j * (t * -y5))
    else if (y1 <= 4.9d+57) then
        tmp = b * (j * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -1.95e+42) {
		tmp = t_1;
	} else if (y1 <= -2.36e-35) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y1 <= -1.25e-112) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= -1.26e-250) {
		tmp = a * (y5 * (t * y2));
	} else if (y1 <= 1.65e-119) {
		tmp = i * (j * (t * -y5));
	} else if (y1 <= 4.9e+57) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (y4 * (k * y1))
	tmp = 0
	if y1 <= -1.95e+42:
		tmp = t_1
	elif y1 <= -2.36e-35:
		tmp = k * (y0 * (y2 * -y5))
	elif y1 <= -1.25e-112:
		tmp = b * ((x * y) * a)
	elif y1 <= -1.26e-250:
		tmp = a * (y5 * (t * y2))
	elif y1 <= 1.65e-119:
		tmp = i * (j * (t * -y5))
	elif y1 <= 4.9e+57:
		tmp = b * (j * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(y4 * Float64(k * y1)))
	tmp = 0.0
	if (y1 <= -1.95e+42)
		tmp = t_1;
	elseif (y1 <= -2.36e-35)
		tmp = Float64(k * Float64(y0 * Float64(y2 * Float64(-y5))));
	elseif (y1 <= -1.25e-112)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (y1 <= -1.26e-250)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y1 <= 1.65e-119)
		tmp = Float64(i * Float64(j * Float64(t * Float64(-y5))));
	elseif (y1 <= 4.9e+57)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (y4 * (k * y1));
	tmp = 0.0;
	if (y1 <= -1.95e+42)
		tmp = t_1;
	elseif (y1 <= -2.36e-35)
		tmp = k * (y0 * (y2 * -y5));
	elseif (y1 <= -1.25e-112)
		tmp = b * ((x * y) * a);
	elseif (y1 <= -1.26e-250)
		tmp = a * (y5 * (t * y2));
	elseif (y1 <= 1.65e-119)
		tmp = i * (j * (t * -y5));
	elseif (y1 <= 4.9e+57)
		tmp = b * (j * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.95e+42], t$95$1, If[LessEqual[y1, -2.36e-35], N[(k * N[(y0 * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.25e-112], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.26e-250], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.65e-119], N[(i * N[(j * N[(t * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.9e+57], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -1.94999999999999985e42 or 4.8999999999999999e57 < y1

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 46.4%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 48.2

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 48.2%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 43.2

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 43.2%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   if -1.94999999999999985e42 < y1 < -2.35999999999999998e-35

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 44.2%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(\mathsf{neg}\left(y0 \cdot y5\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\mathsf{fma}\left(y1, y4, \mathsf{neg}\left(y0 \cdot y5\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{-1 \cdot \left(y0 \cdot y5\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 40.2

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-y0\right)} \cdot y5\right)\right) \]

   8. Simplified 40.2%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       2. neg-lowering-neg.f64 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot y0\right)\right) \]

       7. *-lowering-*.f64 35.9

          \[\leadsto -k \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot y0\right) \]

   11. Simplified 35.9%

       \[\leadsto \color{blue}{-k \cdot \left(\left(y5 \cdot y2\right) \cdot y0\right)} \]

   if -2.35999999999999998e-35 < y1 < -1.25000000000000011e-112

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 38.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 38.3

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 38.3%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 42.8

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 42.8%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \cdot b \]

       5. *-lowering-*.f64 42.9

          \[\leadsto \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot b \]

   13. Applied egg-rr 42.9%

       \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

   if -1.25000000000000011e-112 < y1 < -1.26e-250

   1. Initial program 47.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 48.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-lowering-*.f64 44.2

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   8. Simplified 44.2%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 35.7

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   11. Simplified 35.7%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   if -1.26e-250 < y1 < 1.65000000000000004e-119

   1. Initial program 39.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 51.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right)} \cdot \left(i \cdot y5 - b \cdot y4\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5 - b \cdot y4\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \left(\color{blue}{i \cdot y5} - b \cdot y4\right)\right) \]

      8. *-lowering-*.f64 25.2

         \[\leadsto -\left(j \cdot t\right) \cdot \left(i \cdot y5 - \color{blue}{b \cdot y4}\right) \]

   8. Simplified 25.2%

      \[\leadsto \color{blue}{-\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right)\right) \]

       4. *-lowering-*.f64 25.2

          \[\leadsto -i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 25.2%

       \[\leadsto -\color{blue}{i \cdot \left(j \cdot \left(y5 \cdot t\right)\right)} \]

   if 1.65000000000000004e-119 < y1 < 4.8999999999999999e57

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 38.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 25.2

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 25.2%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 27.7

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 27.7%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.95 \cdot 10^{+42}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -2.36 \cdot 10^{-35}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.25 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq -1.26 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 1.65 \cdot 10^{-119}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 4.9 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 23.3% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.8 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -9 \cdot 10^{-43}:\\ \;\;\;\;-y \cdot \left(y3 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -9 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.1 \cdot 10^{-120}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 4.3 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.8e+34)
   (* j (* y4 (* y1 (- y3))))
   (if (<= y1 -9e-43)
     (- (* y (* y3 (* a y5))))
     (if (<= y1 -9e-113)
       (* a (* x (* y b)))
       (if (<= y1 4.1e-120)
         (* y5 (* t (* i (- j))))
         (if (<= y1 4.3e+52) (* b (* j (* t y4))) (* y2 (* y4 (* k 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 <= -1.8e+34) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (y1 <= -9e-43) {
		tmp = -(y * (y3 * (a * y5)));
	} else if (y1 <= -9e-113) {
		tmp = a * (x * (y * b));
	} else if (y1 <= 4.1e-120) {
		tmp = y5 * (t * (i * -j));
	} else if (y1 <= 4.3e+52) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = y2 * (y4 * (k * 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 <= (-1.8d+34)) then
        tmp = j * (y4 * (y1 * -y3))
    else if (y1 <= (-9d-43)) then
        tmp = -(y * (y3 * (a * y5)))
    else if (y1 <= (-9d-113)) then
        tmp = a * (x * (y * b))
    else if (y1 <= 4.1d-120) then
        tmp = y5 * (t * (i * -j))
    else if (y1 <= 4.3d+52) then
        tmp = b * (j * (t * y4))
    else
        tmp = y2 * (y4 * (k * 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 <= -1.8e+34) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (y1 <= -9e-43) {
		tmp = -(y * (y3 * (a * y5)));
	} else if (y1 <= -9e-113) {
		tmp = a * (x * (y * b));
	} else if (y1 <= 4.1e-120) {
		tmp = y5 * (t * (i * -j));
	} else if (y1 <= 4.3e+52) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = y2 * (y4 * (k * 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 <= -1.8e+34:
		tmp = j * (y4 * (y1 * -y3))
	elif y1 <= -9e-43:
		tmp = -(y * (y3 * (a * y5)))
	elif y1 <= -9e-113:
		tmp = a * (x * (y * b))
	elif y1 <= 4.1e-120:
		tmp = y5 * (t * (i * -j))
	elif y1 <= 4.3e+52:
		tmp = b * (j * (t * y4))
	else:
		tmp = y2 * (y4 * (k * 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 <= -1.8e+34)
		tmp = Float64(j * Float64(y4 * Float64(y1 * Float64(-y3))));
	elseif (y1 <= -9e-43)
		tmp = Float64(-Float64(y * Float64(y3 * Float64(a * y5))));
	elseif (y1 <= -9e-113)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y1 <= 4.1e-120)
		tmp = Float64(y5 * Float64(t * Float64(i * Float64(-j))));
	elseif (y1 <= 4.3e+52)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = Float64(y2 * Float64(y4 * Float64(k * 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 <= -1.8e+34)
		tmp = j * (y4 * (y1 * -y3));
	elseif (y1 <= -9e-43)
		tmp = -(y * (y3 * (a * y5)));
	elseif (y1 <= -9e-113)
		tmp = a * (x * (y * b));
	elseif (y1 <= 4.1e-120)
		tmp = y5 * (t * (i * -j));
	elseif (y1 <= 4.3e+52)
		tmp = b * (j * (t * y4));
	else
		tmp = y2 * (y4 * (k * 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, -1.8e+34], N[(j * N[(y4 * N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -9e-43], (-N[(y * N[(y3 * N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[y1, -9e-113], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.1e-120], N[(y5 * N[(t * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.3e+52], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -1.8e34

   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 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. *-lowering-*.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. Simplified 41.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 45.6

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 45.6%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto j \cdot \left(y4 \cdot \left(\mathsf{neg}\left(\color{blue}{y3 \cdot y1}\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot \left(\mathsf{neg}\left(y1\right)\right)\right)}\right) \]

       4. mul-1-neg N/A

          \[\leadsto j \cdot \left(y4 \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot y1\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot y1\right)\right)}\right) \]

       6. mul-1-neg N/A

          \[\leadsto j \cdot \left(y4 \cdot \left(y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)}\right)\right) \]

       7. neg-lowering-neg.f64 41.9

          \[\leadsto j \cdot \left(y4 \cdot \left(y3 \cdot \color{blue}{\left(-y1\right)}\right)\right) \]

   11. Simplified 41.9%

       \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot \left(-y1\right)\right)}\right) \]

   if -1.8e34 < y1 < -9.0000000000000005e-43

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 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

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-lowering-*.f64 48.9

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   8. Simplified 48.9%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y\right)} \]

       3. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y} \]

       4. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)\right)} \cdot y \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)\right) \cdot y} \]

       6. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(y3 \cdot y5\right)\right)} \cdot y \]

       7. *-commutative N/A

          \[\leadsto \left(\left(-1 \cdot a\right) \cdot \color{blue}{\left(y5 \cdot y3\right)}\right) \cdot y \]

       8. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\left(\left(-1 \cdot a\right) \cdot y5\right) \cdot y3\right)} \cdot y \]

       9. neg-mul-1 N/A

          \[\leadsto \left(\left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot y5\right) \cdot y3\right) \cdot y \]

       10. distribute-lft-neg-in N/A

           \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a \cdot y5\right)\right)} \cdot y3\right) \cdot y \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(a \cdot y5\right)\right) \cdot y3\right)} \cdot y \]

       12. distribute-rgt-neg-in N/A

           \[\leadsto \left(\color{blue}{\left(a \cdot \left(\mathsf{neg}\left(y5\right)\right)\right)} \cdot y3\right) \cdot y \]

       13. mul-1-neg N/A

           \[\leadsto \left(\left(a \cdot \color{blue}{\left(-1 \cdot y5\right)}\right) \cdot y3\right) \cdot y \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \left(\color{blue}{\left(a \cdot \left(-1 \cdot y5\right)\right)} \cdot y3\right) \cdot y \]

       15. mul-1-neg N/A

           \[\leadsto \left(\left(a \cdot \color{blue}{\left(\mathsf{neg}\left(y5\right)\right)}\right) \cdot y3\right) \cdot y \]

       16. neg-lowering-neg.f64 48.7

           \[\leadsto \left(\left(a \cdot \color{blue}{\left(-y5\right)}\right) \cdot y3\right) \cdot y \]

   11. Simplified 48.7%

       \[\leadsto \color{blue}{\left(\left(a \cdot \left(-y5\right)\right) \cdot y3\right) \cdot y} \]

   if -9.0000000000000005e-43 < y1 < -9.0000000000000002e-113

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 41.2%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 37.0

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 37.0%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 46.3

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 46.3%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. *-lowering-*.f64 46.3

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied egg-rr 46.3%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

   if -9.0000000000000002e-113 < y1 < 4.10000000000000034e-120

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 52.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right)} \cdot \left(i \cdot y5 - b \cdot y4\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5 - b \cdot y4\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \left(\color{blue}{i \cdot y5} - b \cdot y4\right)\right) \]

      8. *-lowering-*.f64 31.2

         \[\leadsto -\left(j \cdot t\right) \cdot \left(i \cdot y5 - \color{blue}{b \cdot y4}\right) \]

   8. Simplified 31.2%

      \[\leadsto \color{blue}{-\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right)\right) \]

       4. *-lowering-*.f64 22.0

          \[\leadsto -i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 22.0%

       \[\leadsto -\color{blue}{i \cdot \left(j \cdot \left(y5 \cdot t\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(i \cdot j\right) \cdot \left(y5 \cdot t\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(i \cdot j\right) \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right)} \cdot y5\right) \]

       6. *-lowering-*.f64 27.1

          \[\leadsto -\left(\color{blue}{\left(i \cdot j\right)} \cdot t\right) \cdot y5 \]

   13. Applied egg-rr 27.1%

       \[\leadsto -\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5} \]

   if 4.10000000000000034e-120 < y1 < 4.3e52

   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 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. *-lowering-*.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. Simplified 39.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 23.2

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 23.2%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 28.4

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 28.4%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if 4.3e52 < y1

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 52.7%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 48.0

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 48.0%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 42.6

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 42.6%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.8 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -9 \cdot 10^{-43}:\\ \;\;\;\;-y \cdot \left(y3 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -9 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.1 \cdot 10^{-120}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 4.3 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 23.2% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -3.35 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -6.7 \cdot 10^{-46}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -8.6 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 1.16 \cdot 10^{-119}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -3.35e+34)
   (* j (* y4 (* y1 (- y3))))
   (if (<= y1 -6.7e-46)
     (* (- a) (* y3 (* y y5)))
     (if (<= y1 -8.6e-113)
       (* a (* x (* y b)))
       (if (<= y1 1.16e-119)
         (* y5 (* t (* i (- j))))
         (if (<= y1 3e+56) (* b (* j (* t y4))) (* y2 (* y4 (* k 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 <= -3.35e+34) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (y1 <= -6.7e-46) {
		tmp = -a * (y3 * (y * y5));
	} else if (y1 <= -8.6e-113) {
		tmp = a * (x * (y * b));
	} else if (y1 <= 1.16e-119) {
		tmp = y5 * (t * (i * -j));
	} else if (y1 <= 3e+56) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = y2 * (y4 * (k * 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 <= (-3.35d+34)) then
        tmp = j * (y4 * (y1 * -y3))
    else if (y1 <= (-6.7d-46)) then
        tmp = -a * (y3 * (y * y5))
    else if (y1 <= (-8.6d-113)) then
        tmp = a * (x * (y * b))
    else if (y1 <= 1.16d-119) then
        tmp = y5 * (t * (i * -j))
    else if (y1 <= 3d+56) then
        tmp = b * (j * (t * y4))
    else
        tmp = y2 * (y4 * (k * 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 <= -3.35e+34) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (y1 <= -6.7e-46) {
		tmp = -a * (y3 * (y * y5));
	} else if (y1 <= -8.6e-113) {
		tmp = a * (x * (y * b));
	} else if (y1 <= 1.16e-119) {
		tmp = y5 * (t * (i * -j));
	} else if (y1 <= 3e+56) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = y2 * (y4 * (k * 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 <= -3.35e+34:
		tmp = j * (y4 * (y1 * -y3))
	elif y1 <= -6.7e-46:
		tmp = -a * (y3 * (y * y5))
	elif y1 <= -8.6e-113:
		tmp = a * (x * (y * b))
	elif y1 <= 1.16e-119:
		tmp = y5 * (t * (i * -j))
	elif y1 <= 3e+56:
		tmp = b * (j * (t * y4))
	else:
		tmp = y2 * (y4 * (k * 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 <= -3.35e+34)
		tmp = Float64(j * Float64(y4 * Float64(y1 * Float64(-y3))));
	elseif (y1 <= -6.7e-46)
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	elseif (y1 <= -8.6e-113)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y1 <= 1.16e-119)
		tmp = Float64(y5 * Float64(t * Float64(i * Float64(-j))));
	elseif (y1 <= 3e+56)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = Float64(y2 * Float64(y4 * Float64(k * 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 <= -3.35e+34)
		tmp = j * (y4 * (y1 * -y3));
	elseif (y1 <= -6.7e-46)
		tmp = -a * (y3 * (y * y5));
	elseif (y1 <= -8.6e-113)
		tmp = a * (x * (y * b));
	elseif (y1 <= 1.16e-119)
		tmp = y5 * (t * (i * -j));
	elseif (y1 <= 3e+56)
		tmp = b * (j * (t * y4));
	else
		tmp = y2 * (y4 * (k * 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, -3.35e+34], N[(j * N[(y4 * N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -6.7e-46], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -8.6e-113], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.16e-119], N[(y5 * N[(t * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3e+56], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -3.3500000000000001e34

   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 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. *-lowering-*.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. Simplified 41.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 45.6

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 45.6%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto j \cdot \left(y4 \cdot \left(\mathsf{neg}\left(\color{blue}{y3 \cdot y1}\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot \left(\mathsf{neg}\left(y1\right)\right)\right)}\right) \]

       4. mul-1-neg N/A

          \[\leadsto j \cdot \left(y4 \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot y1\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot y1\right)\right)}\right) \]

       6. mul-1-neg N/A

          \[\leadsto j \cdot \left(y4 \cdot \left(y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)}\right)\right) \]

       7. neg-lowering-neg.f64 41.9

          \[\leadsto j \cdot \left(y4 \cdot \left(y3 \cdot \color{blue}{\left(-y1\right)}\right)\right) \]

   11. Simplified 41.9%

       \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot \left(-y1\right)\right)}\right) \]

   if -3.3500000000000001e34 < y1 < -6.7000000000000001e-46

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 50.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-lowering-*.f64 51.2

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   8. Simplified 51.2%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y3 \cdot y5\right) \cdot y}\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{y3 \cdot \left(y5 \cdot y\right)}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(y3 \cdot \color{blue}{\left(y \cdot y5\right)}\right)\right) \]

       5. distribute-rgt-neg-out N/A

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(\mathsf{neg}\left(y \cdot y5\right)\right)\right)} \]

       6. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right)\right)\right)} \]

       8. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot y5\right)\right)}\right) \]

       9. *-commutative N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(\mathsf{neg}\left(\color{blue}{y5 \cdot y}\right)\right)\right) \]

       10. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}\right) \]

       11. mul-1-neg N/A

           \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot y\right)}\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot y\right)\right)}\right) \]

       13. mul-1-neg N/A

           \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

       14. neg-lowering-neg.f64 42.4

           \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-y\right)}\right)\right) \]

   11. Simplified 42.4%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot \left(-y\right)\right)\right)} \]

   if -6.7000000000000001e-46 < y1 < -8.6000000000000001e-113

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 38.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 38.6

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 38.6%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 43.7

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 43.7%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. *-lowering-*.f64 48.4

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied egg-rr 48.4%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

   if -8.6000000000000001e-113 < y1 < 1.16e-119

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 52.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right)} \cdot \left(i \cdot y5 - b \cdot y4\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5 - b \cdot y4\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \left(\color{blue}{i \cdot y5} - b \cdot y4\right)\right) \]

      8. *-lowering-*.f64 31.2

         \[\leadsto -\left(j \cdot t\right) \cdot \left(i \cdot y5 - \color{blue}{b \cdot y4}\right) \]

   8. Simplified 31.2%

      \[\leadsto \color{blue}{-\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right)\right) \]

       4. *-lowering-*.f64 22.0

          \[\leadsto -i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 22.0%

       \[\leadsto -\color{blue}{i \cdot \left(j \cdot \left(y5 \cdot t\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(i \cdot j\right) \cdot \left(y5 \cdot t\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(i \cdot j\right) \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right)} \cdot y5\right) \]

       6. *-lowering-*.f64 27.1

          \[\leadsto -\left(\color{blue}{\left(i \cdot j\right)} \cdot t\right) \cdot y5 \]

   13. Applied egg-rr 27.1%

       \[\leadsto -\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5} \]

   if 1.16e-119 < y1 < 3.00000000000000006e56

   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 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. *-lowering-*.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. Simplified 39.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 23.2

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 23.2%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 28.4

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 28.4%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if 3.00000000000000006e56 < y1

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 52.7%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 48.0

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 48.0%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 42.6

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 42.6%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.35 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -6.7 \cdot 10^{-46}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -8.6 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 1.16 \cdot 10^{-119}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 22.9% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{if}\;y1 \leq -2.6 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{-46}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -4.8 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 1.35 \cdot 10^{-119}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.85 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (* y4 (* k y1)))))
   (if (<= y1 -2.6e+38)
     t_1
     (if (<= y1 -3.3e-46)
       (* (- a) (* y3 (* y y5)))
       (if (<= y1 -4.8e-112)
         (* a (* x (* y b)))
         (if (<= y1 1.35e-119)
           (* y5 (* t (* i (- j))))
           (if (<= y1 1.85e+54) (* b (* j (* t y4))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -2.6e+38) {
		tmp = t_1;
	} else if (y1 <= -3.3e-46) {
		tmp = -a * (y3 * (y * y5));
	} else if (y1 <= -4.8e-112) {
		tmp = a * (x * (y * b));
	} else if (y1 <= 1.35e-119) {
		tmp = y5 * (t * (i * -j));
	} else if (y1 <= 1.85e+54) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * (y4 * (k * y1))
    if (y1 <= (-2.6d+38)) then
        tmp = t_1
    else if (y1 <= (-3.3d-46)) then
        tmp = -a * (y3 * (y * y5))
    else if (y1 <= (-4.8d-112)) then
        tmp = a * (x * (y * b))
    else if (y1 <= 1.35d-119) then
        tmp = y5 * (t * (i * -j))
    else if (y1 <= 1.85d+54) then
        tmp = b * (j * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -2.6e+38) {
		tmp = t_1;
	} else if (y1 <= -3.3e-46) {
		tmp = -a * (y3 * (y * y5));
	} else if (y1 <= -4.8e-112) {
		tmp = a * (x * (y * b));
	} else if (y1 <= 1.35e-119) {
		tmp = y5 * (t * (i * -j));
	} else if (y1 <= 1.85e+54) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (y4 * (k * y1))
	tmp = 0
	if y1 <= -2.6e+38:
		tmp = t_1
	elif y1 <= -3.3e-46:
		tmp = -a * (y3 * (y * y5))
	elif y1 <= -4.8e-112:
		tmp = a * (x * (y * b))
	elif y1 <= 1.35e-119:
		tmp = y5 * (t * (i * -j))
	elif y1 <= 1.85e+54:
		tmp = b * (j * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(y4 * Float64(k * y1)))
	tmp = 0.0
	if (y1 <= -2.6e+38)
		tmp = t_1;
	elseif (y1 <= -3.3e-46)
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	elseif (y1 <= -4.8e-112)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y1 <= 1.35e-119)
		tmp = Float64(y5 * Float64(t * Float64(i * Float64(-j))));
	elseif (y1 <= 1.85e+54)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (y4 * (k * y1));
	tmp = 0.0;
	if (y1 <= -2.6e+38)
		tmp = t_1;
	elseif (y1 <= -3.3e-46)
		tmp = -a * (y3 * (y * y5));
	elseif (y1 <= -4.8e-112)
		tmp = a * (x * (y * b));
	elseif (y1 <= 1.35e-119)
		tmp = y5 * (t * (i * -j));
	elseif (y1 <= 1.85e+54)
		tmp = b * (j * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -2.6e+38], t$95$1, If[LessEqual[y1, -3.3e-46], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -4.8e-112], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.35e-119], N[(y5 * N[(t * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.85e+54], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -2.5999999999999999e38 or 1.8500000000000001e54 < y1

   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 y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 46.5%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 48.3

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 48.3%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 42.3

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 42.3%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   if -2.5999999999999999e38 < y1 < -3.30000000000000013e-46

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 45.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-lowering-*.f64 49.4

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   8. Simplified 49.4%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y3 \cdot y5\right) \cdot y}\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{y3 \cdot \left(y5 \cdot y\right)}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(y3 \cdot \color{blue}{\left(y \cdot y5\right)}\right)\right) \]

       5. distribute-rgt-neg-out N/A

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(\mathsf{neg}\left(y \cdot y5\right)\right)\right)} \]

       6. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right)\right)\right)} \]

       8. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot y5\right)\right)}\right) \]

       9. *-commutative N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(\mathsf{neg}\left(\color{blue}{y5 \cdot y}\right)\right)\right) \]

       10. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}\right) \]

       11. mul-1-neg N/A

           \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot y\right)}\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot y\right)\right)}\right) \]

       13. mul-1-neg N/A

           \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

       14. neg-lowering-neg.f64 41.6

           \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-y\right)}\right)\right) \]

   11. Simplified 41.6%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot \left(-y\right)\right)\right)} \]

   if -3.30000000000000013e-46 < y1 < -4.8000000000000001e-112

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 38.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 38.6

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 38.6%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 43.7

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 43.7%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. *-lowering-*.f64 48.4

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied egg-rr 48.4%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

   if -4.8000000000000001e-112 < y1 < 1.35000000000000013e-119

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 52.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right)} \cdot \left(i \cdot y5 - b \cdot y4\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5 - b \cdot y4\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \left(\color{blue}{i \cdot y5} - b \cdot y4\right)\right) \]

      8. *-lowering-*.f64 31.2

         \[\leadsto -\left(j \cdot t\right) \cdot \left(i \cdot y5 - \color{blue}{b \cdot y4}\right) \]

   8. Simplified 31.2%

      \[\leadsto \color{blue}{-\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right)\right) \]

       4. *-lowering-*.f64 22.0

          \[\leadsto -i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 22.0%

       \[\leadsto -\color{blue}{i \cdot \left(j \cdot \left(y5 \cdot t\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(i \cdot j\right) \cdot \left(y5 \cdot t\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(i \cdot j\right) \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right)} \cdot y5\right) \]

       6. *-lowering-*.f64 27.1

          \[\leadsto -\left(\color{blue}{\left(i \cdot j\right)} \cdot t\right) \cdot y5 \]

   13. Applied egg-rr 27.1%

       \[\leadsto -\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5} \]

   if 1.35000000000000013e-119 < y1 < 1.8500000000000001e54

   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 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. *-lowering-*.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. Simplified 39.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 23.2

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 23.2%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 28.4

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 28.4%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.6 \cdot 10^{+38}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{-46}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -4.8 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 1.35 \cdot 10^{-119}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.85 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 22.8% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{if}\;y1 \leq -9.2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -2.45 \cdot 10^{-46}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{-120}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.45 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (* y4 (* k y1)))))
   (if (<= y1 -9.2e+44)
     t_1
     (if (<= y1 -2.45e-46)
       (* (- a) (* y (* y3 y5)))
       (if (<= y1 -2.4e-112)
         (* a (* x (* y b)))
         (if (<= y1 6e-120)
           (* y5 (* t (* i (- j))))
           (if (<= y1 1.45e+55) (* b (* j (* t y4))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -9.2e+44) {
		tmp = t_1;
	} else if (y1 <= -2.45e-46) {
		tmp = -a * (y * (y3 * y5));
	} else if (y1 <= -2.4e-112) {
		tmp = a * (x * (y * b));
	} else if (y1 <= 6e-120) {
		tmp = y5 * (t * (i * -j));
	} else if (y1 <= 1.45e+55) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * (y4 * (k * y1))
    if (y1 <= (-9.2d+44)) then
        tmp = t_1
    else if (y1 <= (-2.45d-46)) then
        tmp = -a * (y * (y3 * y5))
    else if (y1 <= (-2.4d-112)) then
        tmp = a * (x * (y * b))
    else if (y1 <= 6d-120) then
        tmp = y5 * (t * (i * -j))
    else if (y1 <= 1.45d+55) then
        tmp = b * (j * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -9.2e+44) {
		tmp = t_1;
	} else if (y1 <= -2.45e-46) {
		tmp = -a * (y * (y3 * y5));
	} else if (y1 <= -2.4e-112) {
		tmp = a * (x * (y * b));
	} else if (y1 <= 6e-120) {
		tmp = y5 * (t * (i * -j));
	} else if (y1 <= 1.45e+55) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (y4 * (k * y1))
	tmp = 0
	if y1 <= -9.2e+44:
		tmp = t_1
	elif y1 <= -2.45e-46:
		tmp = -a * (y * (y3 * y5))
	elif y1 <= -2.4e-112:
		tmp = a * (x * (y * b))
	elif y1 <= 6e-120:
		tmp = y5 * (t * (i * -j))
	elif y1 <= 1.45e+55:
		tmp = b * (j * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(y4 * Float64(k * y1)))
	tmp = 0.0
	if (y1 <= -9.2e+44)
		tmp = t_1;
	elseif (y1 <= -2.45e-46)
		tmp = Float64(Float64(-a) * Float64(y * Float64(y3 * y5)));
	elseif (y1 <= -2.4e-112)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	elseif (y1 <= 6e-120)
		tmp = Float64(y5 * Float64(t * Float64(i * Float64(-j))));
	elseif (y1 <= 1.45e+55)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (y4 * (k * y1));
	tmp = 0.0;
	if (y1 <= -9.2e+44)
		tmp = t_1;
	elseif (y1 <= -2.45e-46)
		tmp = -a * (y * (y3 * y5));
	elseif (y1 <= -2.4e-112)
		tmp = a * (x * (y * b));
	elseif (y1 <= 6e-120)
		tmp = y5 * (t * (i * -j));
	elseif (y1 <= 1.45e+55)
		tmp = b * (j * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -9.2e+44], t$95$1, If[LessEqual[y1, -2.45e-46], N[((-a) * N[(y * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.4e-112], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6e-120], N[(y5 * N[(t * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.45e+55], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -9.20000000000000018e44 or 1.4499999999999999e55 < y1

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 45.9%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 47.7

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 47.7%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 42.8

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 42.8%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   if -9.20000000000000018e44 < y1 < -2.45e-46

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 43.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 40.0

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 40.0%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       6. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(\mathsf{neg}\left(y3 \cdot y5\right)\right)\right)} \]

       7. mul-1-neg N/A

          \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       9. associate-*r* N/A

          \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(\left(-1 \cdot y3\right) \cdot y5\right)}\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(\left(-1 \cdot y3\right) \cdot y5\right)}\right) \]

       11. mul-1-neg N/A

           \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

       12. neg-lowering-neg.f64 36.3

           \[\leadsto a \cdot \left(y \cdot \left(\color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   11. Simplified 36.3%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(\left(-y3\right) \cdot y5\right)\right)} \]

   if -2.45e-46 < y1 < -2.4000000000000001e-112

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 38.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 38.6

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 38.6%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 43.7

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 43.7%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. *-lowering-*.f64 48.4

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied egg-rr 48.4%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

   if -2.4000000000000001e-112 < y1 < 6.00000000000000022e-120

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 52.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right)} \cdot \left(i \cdot y5 - b \cdot y4\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5 - b \cdot y4\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \left(\color{blue}{i \cdot y5} - b \cdot y4\right)\right) \]

      8. *-lowering-*.f64 31.2

         \[\leadsto -\left(j \cdot t\right) \cdot \left(i \cdot y5 - \color{blue}{b \cdot y4}\right) \]

   8. Simplified 31.2%

      \[\leadsto \color{blue}{-\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right)\right) \]

       4. *-lowering-*.f64 22.0

          \[\leadsto -i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 22.0%

       \[\leadsto -\color{blue}{i \cdot \left(j \cdot \left(y5 \cdot t\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(i \cdot j\right) \cdot \left(y5 \cdot t\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(i \cdot j\right) \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right)} \cdot y5\right) \]

       6. *-lowering-*.f64 27.1

          \[\leadsto -\left(\color{blue}{\left(i \cdot j\right)} \cdot t\right) \cdot y5 \]

   13. Applied egg-rr 27.1%

       \[\leadsto -\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5} \]

   if 6.00000000000000022e-120 < y1 < 1.4499999999999999e55

   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 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. *-lowering-*.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. Simplified 39.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 23.2

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 23.2%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 28.4

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 28.4%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -9.2 \cdot 10^{+44}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -2.45 \cdot 10^{-46}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{-120}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 1.45 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 22.8% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{if}\;y1 \leq -1.65 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -2.95 \cdot 10^{-36}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -4.4 \cdot 10^{-113}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq 1.2 \cdot 10^{-119}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7.4 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (* y4 (* k y1)))))
   (if (<= y1 -1.65e+44)
     t_1
     (if (<= y1 -2.95e-36)
       (* k (* y0 (* y2 (- y5))))
       (if (<= y1 -4.4e-113)
         (* b (* (* x y) a))
         (if (<= y1 1.2e-119)
           (* y5 (* t (* i (- j))))
           (if (<= y1 7.4e+55) (* b (* j (* t y4))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -1.65e+44) {
		tmp = t_1;
	} else if (y1 <= -2.95e-36) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y1 <= -4.4e-113) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= 1.2e-119) {
		tmp = y5 * (t * (i * -j));
	} else if (y1 <= 7.4e+55) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * (y4 * (k * y1))
    if (y1 <= (-1.65d+44)) then
        tmp = t_1
    else if (y1 <= (-2.95d-36)) then
        tmp = k * (y0 * (y2 * -y5))
    else if (y1 <= (-4.4d-113)) then
        tmp = b * ((x * y) * a)
    else if (y1 <= 1.2d-119) then
        tmp = y5 * (t * (i * -j))
    else if (y1 <= 7.4d+55) then
        tmp = b * (j * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -1.65e+44) {
		tmp = t_1;
	} else if (y1 <= -2.95e-36) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y1 <= -4.4e-113) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= 1.2e-119) {
		tmp = y5 * (t * (i * -j));
	} else if (y1 <= 7.4e+55) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (y4 * (k * y1))
	tmp = 0
	if y1 <= -1.65e+44:
		tmp = t_1
	elif y1 <= -2.95e-36:
		tmp = k * (y0 * (y2 * -y5))
	elif y1 <= -4.4e-113:
		tmp = b * ((x * y) * a)
	elif y1 <= 1.2e-119:
		tmp = y5 * (t * (i * -j))
	elif y1 <= 7.4e+55:
		tmp = b * (j * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(y4 * Float64(k * y1)))
	tmp = 0.0
	if (y1 <= -1.65e+44)
		tmp = t_1;
	elseif (y1 <= -2.95e-36)
		tmp = Float64(k * Float64(y0 * Float64(y2 * Float64(-y5))));
	elseif (y1 <= -4.4e-113)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (y1 <= 1.2e-119)
		tmp = Float64(y5 * Float64(t * Float64(i * Float64(-j))));
	elseif (y1 <= 7.4e+55)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (y4 * (k * y1));
	tmp = 0.0;
	if (y1 <= -1.65e+44)
		tmp = t_1;
	elseif (y1 <= -2.95e-36)
		tmp = k * (y0 * (y2 * -y5));
	elseif (y1 <= -4.4e-113)
		tmp = b * ((x * y) * a);
	elseif (y1 <= 1.2e-119)
		tmp = y5 * (t * (i * -j));
	elseif (y1 <= 7.4e+55)
		tmp = b * (j * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.65e+44], t$95$1, If[LessEqual[y1, -2.95e-36], N[(k * N[(y0 * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -4.4e-113], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.2e-119], N[(y5 * N[(t * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7.4e+55], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -1.65000000000000007e44 or 7.4000000000000004e55 < y1

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 45.9%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 47.7

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 47.7%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 42.8

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 42.8%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   if -1.65000000000000007e44 < y1 < -2.94999999999999998e-36

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 44.2%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(\mathsf{neg}\left(y0 \cdot y5\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\mathsf{fma}\left(y1, y4, \mathsf{neg}\left(y0 \cdot y5\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{-1 \cdot \left(y0 \cdot y5\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 40.2

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-y0\right)} \cdot y5\right)\right) \]

   8. Simplified 40.2%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       2. neg-lowering-neg.f64 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot y0\right)\right) \]

       7. *-lowering-*.f64 35.9

          \[\leadsto -k \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot y0\right) \]

   11. Simplified 35.9%

       \[\leadsto \color{blue}{-k \cdot \left(\left(y5 \cdot y2\right) \cdot y0\right)} \]

   if -2.94999999999999998e-36 < y1 < -4.40000000000000008e-113

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 38.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 38.3

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 38.3%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 42.8

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 42.8%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \cdot b \]

       5. *-lowering-*.f64 42.9

          \[\leadsto \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot b \]

   13. Applied egg-rr 42.9%

       \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

   if -4.40000000000000008e-113 < y1 < 1.20000000000000004e-119

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 52.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right)} \cdot \left(i \cdot y5 - b \cdot y4\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5 - b \cdot y4\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \left(\color{blue}{i \cdot y5} - b \cdot y4\right)\right) \]

      8. *-lowering-*.f64 31.2

         \[\leadsto -\left(j \cdot t\right) \cdot \left(i \cdot y5 - \color{blue}{b \cdot y4}\right) \]

   8. Simplified 31.2%

      \[\leadsto \color{blue}{-\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right)\right) \]

       4. *-lowering-*.f64 22.0

          \[\leadsto -i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 22.0%

       \[\leadsto -\color{blue}{i \cdot \left(j \cdot \left(y5 \cdot t\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(i \cdot j\right) \cdot \left(y5 \cdot t\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(i \cdot j\right) \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(i \cdot j\right) \cdot t\right)} \cdot y5\right) \]

       6. *-lowering-*.f64 27.1

          \[\leadsto -\left(\color{blue}{\left(i \cdot j\right)} \cdot t\right) \cdot y5 \]

   13. Applied egg-rr 27.1%

       \[\leadsto -\color{blue}{\left(\left(i \cdot j\right) \cdot t\right) \cdot y5} \]

   if 1.20000000000000004e-119 < y1 < 7.4000000000000004e55

   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 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. *-lowering-*.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. Simplified 39.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 23.2

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 23.2%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 28.4

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 28.4%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.65 \cdot 10^{+44}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -2.95 \cdot 10^{-36}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -4.4 \cdot 10^{-113}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq 1.2 \cdot 10^{-119}:\\ \;\;\;\;y5 \cdot \left(t \cdot \left(i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7.4 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.4% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{if}\;y1 \leq -8 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -4 \cdot 10^{-36}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -2.3 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{-120}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(i \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y1 \leq 8.6 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (* y4 (* k y1)))))
   (if (<= y1 -8e+44)
     t_1
     (if (<= y1 -4e-36)
       (* k (* y0 (* y2 (- y5))))
       (if (<= y1 -2.3e-112)
         (* b (* (* x y) a))
         (if (<= y1 5.2e-120)
           (* (* t j) (* i (- y5)))
           (if (<= y1 8.6e+57) (* b (* j (* t y4))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -8e+44) {
		tmp = t_1;
	} else if (y1 <= -4e-36) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y1 <= -2.3e-112) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= 5.2e-120) {
		tmp = (t * j) * (i * -y5);
	} else if (y1 <= 8.6e+57) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * (y4 * (k * y1))
    if (y1 <= (-8d+44)) then
        tmp = t_1
    else if (y1 <= (-4d-36)) then
        tmp = k * (y0 * (y2 * -y5))
    else if (y1 <= (-2.3d-112)) then
        tmp = b * ((x * y) * a)
    else if (y1 <= 5.2d-120) then
        tmp = (t * j) * (i * -y5)
    else if (y1 <= 8.6d+57) then
        tmp = b * (j * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -8e+44) {
		tmp = t_1;
	} else if (y1 <= -4e-36) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y1 <= -2.3e-112) {
		tmp = b * ((x * y) * a);
	} else if (y1 <= 5.2e-120) {
		tmp = (t * j) * (i * -y5);
	} else if (y1 <= 8.6e+57) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (y4 * (k * y1))
	tmp = 0
	if y1 <= -8e+44:
		tmp = t_1
	elif y1 <= -4e-36:
		tmp = k * (y0 * (y2 * -y5))
	elif y1 <= -2.3e-112:
		tmp = b * ((x * y) * a)
	elif y1 <= 5.2e-120:
		tmp = (t * j) * (i * -y5)
	elif y1 <= 8.6e+57:
		tmp = b * (j * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(y4 * Float64(k * y1)))
	tmp = 0.0
	if (y1 <= -8e+44)
		tmp = t_1;
	elseif (y1 <= -4e-36)
		tmp = Float64(k * Float64(y0 * Float64(y2 * Float64(-y5))));
	elseif (y1 <= -2.3e-112)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (y1 <= 5.2e-120)
		tmp = Float64(Float64(t * j) * Float64(i * Float64(-y5)));
	elseif (y1 <= 8.6e+57)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (y4 * (k * y1));
	tmp = 0.0;
	if (y1 <= -8e+44)
		tmp = t_1;
	elseif (y1 <= -4e-36)
		tmp = k * (y0 * (y2 * -y5));
	elseif (y1 <= -2.3e-112)
		tmp = b * ((x * y) * a);
	elseif (y1 <= 5.2e-120)
		tmp = (t * j) * (i * -y5);
	elseif (y1 <= 8.6e+57)
		tmp = b * (j * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -8e+44], t$95$1, If[LessEqual[y1, -4e-36], N[(k * N[(y0 * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.3e-112], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.2e-120], N[(N[(t * j), $MachinePrecision] * N[(i * (-y5)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 8.6e+57], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -8.0000000000000007e44 or 8.60000000000000066e57 < y1

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 46.4%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 48.2

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 48.2%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 43.2

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 43.2%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   if -8.0000000000000007e44 < y1 < -3.9999999999999998e-36

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 44.2%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(\mathsf{neg}\left(y0 \cdot y5\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\mathsf{fma}\left(y1, y4, \mathsf{neg}\left(y0 \cdot y5\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{-1 \cdot \left(y0 \cdot y5\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 40.2

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-y0\right)} \cdot y5\right)\right) \]

   8. Simplified 40.2%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       2. neg-lowering-neg.f64 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot y0\right)\right) \]

       7. *-lowering-*.f64 35.9

          \[\leadsto -k \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot y0\right) \]

   11. Simplified 35.9%

       \[\leadsto \color{blue}{-k \cdot \left(\left(y5 \cdot y2\right) \cdot y0\right)} \]

   if -3.9999999999999998e-36 < y1 < -2.29999999999999991e-112

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 38.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 38.3

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 38.3%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 42.8

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 42.8%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \cdot b \]

       5. *-lowering-*.f64 42.9

          \[\leadsto \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot b \]

   13. Applied egg-rr 42.9%

       \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

   if -2.29999999999999991e-112 < y1 < 5.2000000000000002e-120

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 52.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right)} \cdot \left(i \cdot y5 - b \cdot y4\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5 - b \cdot y4\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \left(\color{blue}{i \cdot y5} - b \cdot y4\right)\right) \]

      8. *-lowering-*.f64 31.2

         \[\leadsto -\left(j \cdot t\right) \cdot \left(i \cdot y5 - \color{blue}{b \cdot y4}\right) \]

   8. Simplified 31.2%

      \[\leadsto \color{blue}{-\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 23.3

          \[\leadsto -\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5\right)} \]

   11. Simplified 23.3%

       \[\leadsto -\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5\right)} \]

   if 5.2000000000000002e-120 < y1 < 8.60000000000000066e57

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 38.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 25.2

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 25.2%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 27.7

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 27.7%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -8 \cdot 10^{+44}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -4 \cdot 10^{-36}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -2.3 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{-120}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(i \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y1 \leq 8.6 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 32.0% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -3.6 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7.5 \cdot 10^{+67}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, x \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -5e+67)
   (* a (* y1 (fma y3 z (* y2 (- x)))))
   (if (<= y1 -3.6e-74)
     (* a (* y (fma b x (* y3 (- y5)))))
     (if (<= y1 7.5e+67)
       (* j (* y0 (fma y3 y5 (* x (- b)))))
       (* y2 (* y4 (* k 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 <= -5e+67) {
		tmp = a * (y1 * fma(y3, z, (y2 * -x)));
	} else if (y1 <= -3.6e-74) {
		tmp = a * (y * fma(b, x, (y3 * -y5)));
	} else if (y1 <= 7.5e+67) {
		tmp = j * (y0 * fma(y3, y5, (x * -b)));
	} else {
		tmp = y2 * (y4 * (k * 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 <= -5e+67)
		tmp = Float64(a * Float64(y1 * fma(y3, z, Float64(y2 * Float64(-x)))));
	elseif (y1 <= -3.6e-74)
		tmp = Float64(a * Float64(y * fma(b, x, Float64(y3 * Float64(-y5)))));
	elseif (y1 <= 7.5e+67)
		tmp = Float64(j * Float64(y0 * fma(y3, y5, Float64(x * Float64(-b)))));
	else
		tmp = Float64(y2 * Float64(y4 * Float64(k * 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[y1, -5e+67], N[(a * N[(y1 * N[(y3 * z + N[(y2 * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.6e-74], N[(a * N[(y * N[(b * x + N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7.5e+67], N[(j * N[(y0 * N[(y3 * y5 + N[(x * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -4.99999999999999976e67

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 43.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(y3, z, \mathsf{neg}\left(x \cdot y2\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{-1 \cdot \left(x \cdot y2\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-1 \cdot x\right) \cdot y2}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-1 \cdot x\right) \cdot y2}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot y2\right)\right) \]

      8. neg-lowering-neg.f64 48.3

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-x\right)} \cdot y2\right)\right) \]

   8. Simplified 48.3%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if -4.99999999999999976e67 < y1 < -3.6000000000000002e-74

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 44.9%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 43.1

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 43.1%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   if -3.6000000000000002e-74 < y1 < 7.5000000000000005e67

   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 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. *-lowering-*.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. Simplified 46.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y0 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(y3, y5, -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(-1 \cdot b\right) \cdot x}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(-1 \cdot b\right) \cdot x}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot x\right)\right) \]

      8. neg-lowering-neg.f64 34.8

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \color{blue}{\left(-b\right)} \cdot x\right)\right) \]

   8. Simplified 34.8%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)} \]

   if 7.5000000000000005e67 < y1

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 51.9%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 50.9

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 50.9%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 44.9

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 44.9%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -3.6 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7.5 \cdot 10^{+67}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(y3, y5, x \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 32.7% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{if}\;y \leq -750000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+148}:\\ \;\;\;\;a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (fma b x (* y3 (- y5)))))))
   (if (<= y -750000.0)
     t_1
     (if (<= y 2e+22)
       (* c (* z (fma i t (* y0 (- y3)))))
       (if (<= y 5.2e+148) (* a (* y1 (fma y3 z (* y2 (- x))))) 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 * (y * fma(b, x, (y3 * -y5)));
	double tmp;
	if (y <= -750000.0) {
		tmp = t_1;
	} else if (y <= 2e+22) {
		tmp = c * (z * fma(i, t, (y0 * -y3)));
	} else if (y <= 5.2e+148) {
		tmp = a * (y1 * fma(y3, z, (y2 * -x)));
	} 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(y * fma(b, x, Float64(y3 * Float64(-y5)))))
	tmp = 0.0
	if (y <= -750000.0)
		tmp = t_1;
	elseif (y <= 2e+22)
		tmp = Float64(c * Float64(z * fma(i, t, Float64(y0 * Float64(-y3)))));
	elseif (y <= 5.2e+148)
		tmp = Float64(a * Float64(y1 * fma(y3, z, Float64(y2 * Float64(-x)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[(b * x + N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -750000.0], t$95$1, If[LessEqual[y, 2e+22], N[(c * N[(z * N[(i * t + N[(y0 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+148], N[(a * N[(y1 * N[(y3 * z + N[(y2 * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5e5 or 5.2e148 < y

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 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 y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 48.2

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 48.2%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   if -7.5e5 < y < 2e22

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \color{blue}{\left(-1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-1 \cdot z\right)} \]

   5. Simplified 47.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(i, t, -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 33.1

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-y0\right)} \cdot y3\right)\right) \]

   8. Simplified 33.1%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \left(-y0\right) \cdot y3\right)\right)} \]

   if 2e22 < y < 5.2e148

   1. Initial program 33.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 47.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(y3, z, \mathsf{neg}\left(x \cdot y2\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{-1 \cdot \left(x \cdot y2\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-1 \cdot x\right) \cdot y2}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-1 \cdot x\right) \cdot y2}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot y2\right)\right) \]

      8. neg-lowering-neg.f64 44.6

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-x\right)} \cdot y2\right)\right) \]

   8. Simplified 44.6%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -750000:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+148}:\\ \;\;\;\;a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 31.4% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -3.4 \cdot 10^{+220}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y5 \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -3.35 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -3.4e+220)
   (* y2 (* k (* y5 (- y0))))
   (if (<= y5 -3.35e+69)
     (* a (* y5 (- (* t y2) (* y y3))))
     (if (<= y5 1.3e-58)
       (* a (* y1 (fma y3 z (* y2 (- x)))))
       (* a (* y (fma b x (* y3 (- 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 (y5 <= -3.4e+220) {
		tmp = y2 * (k * (y5 * -y0));
	} else if (y5 <= -3.35e+69) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y5 <= 1.3e-58) {
		tmp = a * (y1 * fma(y3, z, (y2 * -x)));
	} else {
		tmp = a * (y * fma(b, x, (y3 * -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 (y5 <= -3.4e+220)
		tmp = Float64(y2 * Float64(k * Float64(y5 * Float64(-y0))));
	elseif (y5 <= -3.35e+69)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y5 <= 1.3e-58)
		tmp = Float64(a * Float64(y1 * fma(y3, z, Float64(y2 * Float64(-x)))));
	else
		tmp = Float64(a * Float64(y * fma(b, x, Float64(y3 * Float64(-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[y5, -3.4e+220], N[(y2 * N[(k * N[(y5 * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3.35e+69], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.3e-58], N[(a * N[(y1 * N[(y3 * z + N[(y2 * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(b * x + N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -3.4e220

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 58.4%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(\mathsf{neg}\left(y0 \cdot y5\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\mathsf{fma}\left(y1, y4, \mathsf{neg}\left(y0 \cdot y5\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{-1 \cdot \left(y0 \cdot y5\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 59.3

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-y0\right)} \cdot y5\right)\right) \]

   8. Simplified 59.3%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(\mathsf{neg}\left(y0 \cdot y5\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto y2 \cdot \left(k \cdot \left(\mathsf{neg}\left(\color{blue}{y5 \cdot y0}\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y0\right)\right)\right)}\right) \]

       4. mul-1-neg N/A

          \[\leadsto y2 \cdot \left(k \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot y0\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot y0\right)\right)}\right) \]

       6. mul-1-neg N/A

          \[\leadsto y2 \cdot \left(k \cdot \left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)}\right)\right) \]

       7. neg-lowering-neg.f64 55.1

          \[\leadsto y2 \cdot \left(k \cdot \left(y5 \cdot \color{blue}{\left(-y0\right)}\right)\right) \]

   11. Simplified 55.1%

       \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y5 \cdot \left(-y0\right)\right)}\right) \]

   if -3.4e220 < y5 < -3.35000000000000005e69

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 43.2%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-lowering-*.f64 51.6

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   8. Simplified 51.6%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -3.35000000000000005e69 < y5 < 1.30000000000000003e-58

   1. Initial program 37.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 41.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(y3, z, \mathsf{neg}\left(x \cdot y2\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{-1 \cdot \left(x \cdot y2\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-1 \cdot x\right) \cdot y2}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-1 \cdot x\right) \cdot y2}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot y2\right)\right) \]

      8. neg-lowering-neg.f64 33.5

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-x\right)} \cdot y2\right)\right) \]

   8. Simplified 33.5%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if 1.30000000000000003e-58 < y5

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 30.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 37.7

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 37.7%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.4 \cdot 10^{+220}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y5 \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -3.35 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{if}\;y1 \leq -1.45 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -3.7 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-120}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7.5 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (* y4 (* k y1)))))
   (if (<= y1 -1.45e+30)
     t_1
     (if (<= y1 -3.7e-249)
       (* a (* y5 (* t y2)))
       (if (<= y1 3.1e-120)
         (* i (* j (* t (- y5))))
         (if (<= y1 7.5e+57) (* b (* j (* t y4))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -1.45e+30) {
		tmp = t_1;
	} else if (y1 <= -3.7e-249) {
		tmp = a * (y5 * (t * y2));
	} else if (y1 <= 3.1e-120) {
		tmp = i * (j * (t * -y5));
	} else if (y1 <= 7.5e+57) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * (y4 * (k * y1))
    if (y1 <= (-1.45d+30)) then
        tmp = t_1
    else if (y1 <= (-3.7d-249)) then
        tmp = a * (y5 * (t * y2))
    else if (y1 <= 3.1d-120) then
        tmp = i * (j * (t * -y5))
    else if (y1 <= 7.5d+57) then
        tmp = b * (j * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y4 * (k * y1));
	double tmp;
	if (y1 <= -1.45e+30) {
		tmp = t_1;
	} else if (y1 <= -3.7e-249) {
		tmp = a * (y5 * (t * y2));
	} else if (y1 <= 3.1e-120) {
		tmp = i * (j * (t * -y5));
	} else if (y1 <= 7.5e+57) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (y4 * (k * y1))
	tmp = 0
	if y1 <= -1.45e+30:
		tmp = t_1
	elif y1 <= -3.7e-249:
		tmp = a * (y5 * (t * y2))
	elif y1 <= 3.1e-120:
		tmp = i * (j * (t * -y5))
	elif y1 <= 7.5e+57:
		tmp = b * (j * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(y4 * Float64(k * y1)))
	tmp = 0.0
	if (y1 <= -1.45e+30)
		tmp = t_1;
	elseif (y1 <= -3.7e-249)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y1 <= 3.1e-120)
		tmp = Float64(i * Float64(j * Float64(t * Float64(-y5))));
	elseif (y1 <= 7.5e+57)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (y4 * (k * y1));
	tmp = 0.0;
	if (y1 <= -1.45e+30)
		tmp = t_1;
	elseif (y1 <= -3.7e-249)
		tmp = a * (y5 * (t * y2));
	elseif (y1 <= 3.1e-120)
		tmp = i * (j * (t * -y5));
	elseif (y1 <= 7.5e+57)
		tmp = b * (j * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.45e+30], t$95$1, If[LessEqual[y1, -3.7e-249], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.1e-120], N[(i * N[(j * N[(t * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7.5e+57], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -1.4499999999999999e30 or 7.5000000000000006e57 < y1

   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 y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 46.6%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 49.3

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 49.3%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 42.5

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 42.5%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   if -1.4499999999999999e30 < y1 < -3.69999999999999977e-249

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 46.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-lowering-*.f64 37.4

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   8. Simplified 37.4%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 25.5

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   11. Simplified 25.5%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   if -3.69999999999999977e-249 < y1 < 3.10000000000000019e-120

   1. Initial program 39.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 51.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(j \cdot t\right)} \cdot \left(i \cdot y5 - b \cdot y4\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \color{blue}{\left(i \cdot y5 - b \cdot y4\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(j \cdot t\right) \cdot \left(\color{blue}{i \cdot y5} - b \cdot y4\right)\right) \]

      8. *-lowering-*.f64 25.2

         \[\leadsto -\left(j \cdot t\right) \cdot \left(i \cdot y5 - \color{blue}{b \cdot y4}\right) \]

   8. Simplified 25.2%

      \[\leadsto \color{blue}{-\left(j \cdot t\right) \cdot \left(i \cdot y5 - b \cdot y4\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right)}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right)\right) \]

       4. *-lowering-*.f64 25.2

          \[\leadsto -i \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 25.2%

       \[\leadsto -\color{blue}{i \cdot \left(j \cdot \left(y5 \cdot t\right)\right)} \]

   if 3.10000000000000019e-120 < y1 < 7.5000000000000006e57

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 38.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 25.2

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 25.2%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 27.7

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 27.7%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.45 \cdot 10^{+30}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -3.7 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 3.1 \cdot 10^{-120}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7.5 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 32.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -2.1 \cdot 10^{+138}:\\ \;\;\;\;y1 \cdot \left(k \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 12500000000000:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, y5 \cdot \left(-y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -2.1e+138)
   (* y1 (* k (fma z (- i) (* y2 y4))))
   (if (<= k 12500000000000.0)
     (* c (* z (fma i t (* y0 (- y3)))))
     (* y2 (* k (fma y1 y4 (* 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) {
	double tmp;
	if (k <= -2.1e+138) {
		tmp = y1 * (k * fma(z, -i, (y2 * y4)));
	} else if (k <= 12500000000000.0) {
		tmp = c * (z * fma(i, t, (y0 * -y3)));
	} else {
		tmp = y2 * (k * fma(y1, y4, (y5 * -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 (k <= -2.1e+138)
		tmp = Float64(y1 * Float64(k * fma(z, Float64(-i), Float64(y2 * y4))));
	elseif (k <= 12500000000000.0)
		tmp = Float64(c * Float64(z * fma(i, t, Float64(y0 * Float64(-y3)))));
	else
		tmp = Float64(y2 * Float64(k * fma(y1, y4, Float64(y5 * Float64(-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[k, -2.1e+138], N[(y1 * N[(k * N[(z * (-i) + N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 12500000000000.0], N[(c * N[(z * N[(i * t + N[(y0 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(k * N[(y1 * y4 + N[(y5 * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -2.10000000000000007e138

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y1 \cdot \left(\color{blue}{a \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\mathsf{fma}\left(a, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]

   5. Simplified 48.2%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(i \cdot z\right)\right)} + y2 \cdot y4\right)\right) \]

      3. *-commutative N/A

         \[\leadsto y1 \cdot \left(k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot i}\right)\right) + y2 \cdot y4\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto y1 \cdot \left(k \cdot \left(\color{blue}{z \cdot \left(\mathsf{neg}\left(i\right)\right)} + y2 \cdot y4\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot i\right)} + y2 \cdot y4\right)\right) \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\mathsf{fma}\left(z, -1 \cdot i, y2 \cdot y4\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(k \cdot \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(i\right)}, y2 \cdot y4\right)\right) \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto y1 \cdot \left(k \cdot \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(i\right)}, y2 \cdot y4\right)\right) \]

      9. *-lowering-*.f64 50.6

         \[\leadsto y1 \cdot \left(k \cdot \mathsf{fma}\left(z, -i, \color{blue}{y2 \cdot y4}\right)\right) \]

   8. Simplified 50.6%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)} \]

   if -2.10000000000000007e138 < k < 1.25e13

   1. Initial program 39.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \color{blue}{\left(-1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-1 \cdot z\right)} \]

   5. Simplified 46.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(i, t, -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 37.2

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-y0\right)} \cdot y3\right)\right) \]

   8. Simplified 37.2%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \left(-y0\right) \cdot y3\right)\right)} \]

   if 1.25e13 < k

   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 y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 43.5%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(\mathsf{neg}\left(y0 \cdot y5\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\mathsf{fma}\left(y1, y4, \mathsf{neg}\left(y0 \cdot y5\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{-1 \cdot \left(y0 \cdot y5\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 53.6

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-y0\right)} \cdot y5\right)\right) \]

   8. Simplified 53.6%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.1 \cdot 10^{+138}:\\ \;\;\;\;y1 \cdot \left(k \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 12500000000000:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, y5 \cdot \left(-y0\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 32.4% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(k \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)\\ \mathbf{if}\;k \leq -1.2 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* k (fma z (- i) (* y2 y4))))))
   (if (<= k -1.2e+139)
     t_1
     (if (<= k 1.22e+14) (* c (* z (fma i t (* y0 (- 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 = y1 * (k * fma(z, -i, (y2 * y4)));
	double tmp;
	if (k <= -1.2e+139) {
		tmp = t_1;
	} else if (k <= 1.22e+14) {
		tmp = c * (z * fma(i, t, (y0 * -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(y1 * Float64(k * fma(z, Float64(-i), Float64(y2 * y4))))
	tmp = 0.0
	if (k <= -1.2e+139)
		tmp = t_1;
	elseif (k <= 1.22e+14)
		tmp = Float64(c * Float64(z * fma(i, t, Float64(y0 * Float64(-y3)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(k * N[(z * (-i) + N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.2e+139], t$95$1, If[LessEqual[k, 1.22e+14], N[(c * N[(z * N[(i * t + N[(y0 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if k < -1.20000000000000004e139 or 1.22e14 < k

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y1 \cdot \left(\color{blue}{a \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\mathsf{fma}\left(a, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]

   5. Simplified 45.9%

      \[\leadsto \color{blue}{y1 \cdot \mathsf{fma}\left(a, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y4, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(i \cdot z\right)\right)} + y2 \cdot y4\right)\right) \]

      3. *-commutative N/A

         \[\leadsto y1 \cdot \left(k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot i}\right)\right) + y2 \cdot y4\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto y1 \cdot \left(k \cdot \left(\color{blue}{z \cdot \left(\mathsf{neg}\left(i\right)\right)} + y2 \cdot y4\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(-1 \cdot i\right)} + y2 \cdot y4\right)\right) \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \left(k \cdot \color{blue}{\mathsf{fma}\left(z, -1 \cdot i, y2 \cdot y4\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(k \cdot \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(i\right)}, y2 \cdot y4\right)\right) \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto y1 \cdot \left(k \cdot \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(i\right)}, y2 \cdot y4\right)\right) \]

      9. *-lowering-*.f64 50.6

         \[\leadsto y1 \cdot \left(k \cdot \mathsf{fma}\left(z, -i, \color{blue}{y2 \cdot y4}\right)\right) \]

   8. Simplified 50.6%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)} \]

   if -1.20000000000000004e139 < k < 1.22e14

   1. Initial program 39.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \color{blue}{\left(-1 \cdot z\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-1 \cdot z\right)} \]

   5. Simplified 46.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(y3, c \cdot y0 - a \cdot y1, t \cdot \left(a \cdot b - c \cdot i\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(i, t, -1 \cdot \left(y0 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-1 \cdot y0\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 37.2

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \color{blue}{\left(-y0\right)} \cdot y3\right)\right) \]

   8. Simplified 37.2%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \mathsf{fma}\left(i, t, \left(-y0\right) \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.2 \cdot 10^{+139}:\\ \;\;\;\;y1 \cdot \left(k \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(i, t, y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(k \cdot \mathsf{fma}\left(z, -i, y2 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 30.3% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -9 \cdot 10^{+69}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{-62}:\\ \;\;\;\;a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -9e+69)
   (* k (* y0 (* y2 (- y5))))
   (if (<= y5 1e-62)
     (* a (* y1 (fma y3 z (* y2 (- x)))))
     (* a (* y (fma b x (* y3 (- 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 (y5 <= -9e+69) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y5 <= 1e-62) {
		tmp = a * (y1 * fma(y3, z, (y2 * -x)));
	} else {
		tmp = a * (y * fma(b, x, (y3 * -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 (y5 <= -9e+69)
		tmp = Float64(k * Float64(y0 * Float64(y2 * Float64(-y5))));
	elseif (y5 <= 1e-62)
		tmp = Float64(a * Float64(y1 * fma(y3, z, Float64(y2 * Float64(-x)))));
	else
		tmp = Float64(a * Float64(y * fma(b, x, Float64(y3 * Float64(-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[y5, -9e+69], N[(k * N[(y0 * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1e-62], N[(a * N[(y1 * N[(y3 * z + N[(y2 * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(b * x + N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -8.9999999999999999e69

   1. Initial program 17.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 58.4%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(\mathsf{neg}\left(y0 \cdot y5\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\mathsf{fma}\left(y1, y4, \mathsf{neg}\left(y0 \cdot y5\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{-1 \cdot \left(y0 \cdot y5\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-1 \cdot y0\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(\mathsf{neg}\left(y0\right)\right)} \cdot y5\right)\right) \]

      8. neg-lowering-neg.f64 45.0

         \[\leadsto y2 \cdot \left(k \cdot \mathsf{fma}\left(y1, y4, \color{blue}{\left(-y0\right)} \cdot y5\right)\right) \]

   8. Simplified 45.0%

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \mathsf{fma}\left(y1, y4, \left(-y0\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       2. neg-lowering-neg.f64 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot y0\right)\right) \]

       7. *-lowering-*.f64 42.8

          \[\leadsto -k \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot y0\right) \]

   11. Simplified 42.8%

       \[\leadsto \color{blue}{-k \cdot \left(\left(y5 \cdot y2\right) \cdot y0\right)} \]

   if -8.9999999999999999e69 < y5 < 1e-62

   1. Initial program 37.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 41.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z + \left(\mathsf{neg}\left(x \cdot y2\right)\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(y3, z, \mathsf{neg}\left(x \cdot y2\right)\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{-1 \cdot \left(x \cdot y2\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-1 \cdot x\right) \cdot y2}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-1 \cdot x\right) \cdot y2}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot y2\right)\right) \]

      8. neg-lowering-neg.f64 33.5

         \[\leadsto a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, \color{blue}{\left(-x\right)} \cdot y2\right)\right) \]

   8. Simplified 33.5%

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(y3, z, \left(-x\right) \cdot y2\right)\right)} \]

   if 1e-62 < y5

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 30.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 37.7

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 37.7%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -9 \cdot 10^{+69}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{-62}:\\ \;\;\;\;a \cdot \left(y1 \cdot \mathsf{fma}\left(y3, z, y2 \cdot \left(-x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 28.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -5 \cdot 10^{+69}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -5e+69)
   (* j (* y4 (* y1 (- y3))))
   (if (<= y1 7e+77)
     (* a (* y (fma b x (* y3 (- y5)))))
     (* y2 (* y4 (* k 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 <= -5e+69) {
		tmp = j * (y4 * (y1 * -y3));
	} else if (y1 <= 7e+77) {
		tmp = a * (y * fma(b, x, (y3 * -y5)));
	} else {
		tmp = y2 * (y4 * (k * 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 <= -5e+69)
		tmp = Float64(j * Float64(y4 * Float64(y1 * Float64(-y3))));
	elseif (y1 <= 7e+77)
		tmp = Float64(a * Float64(y * fma(b, x, Float64(y3 * Float64(-y5)))));
	else
		tmp = Float64(y2 * Float64(y4 * Float64(k * 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[y1, -5e+69], N[(j * N[(y4 * N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7e+77], N[(a * N[(y * N[(b * x + N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -5.00000000000000036e69

   1. Initial program 23.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. *-lowering-*.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. Simplified 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 y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 49.3

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 49.3%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(\mathsf{neg}\left(y1 \cdot y3\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto j \cdot \left(y4 \cdot \left(\mathsf{neg}\left(\color{blue}{y3 \cdot y1}\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot \left(\mathsf{neg}\left(y1\right)\right)\right)}\right) \]

       4. mul-1-neg N/A

          \[\leadsto j \cdot \left(y4 \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot y1\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot y1\right)\right)}\right) \]

       6. mul-1-neg N/A

          \[\leadsto j \cdot \left(y4 \cdot \left(y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)}\right)\right) \]

       7. neg-lowering-neg.f64 44.6

          \[\leadsto j \cdot \left(y4 \cdot \left(y3 \cdot \color{blue}{\left(-y1\right)}\right)\right) \]

   11. Simplified 44.6%

       \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot \left(-y1\right)\right)}\right) \]

   if -5.00000000000000036e69 < y1 < 7.0000000000000003e77

   1. Initial program 35.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 37.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 31.9

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 31.9%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   if 7.0000000000000003e77 < y1

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 47.5%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 46.4

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 46.4%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 42.1

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 42.1%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -5 \cdot 10^{+69}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \left(y \cdot \mathsf{fma}\left(b, x, y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 22.0% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{if}\;y \leq -2400:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-110}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* x (* y b)))))
   (if (<= y -2400.0)
     t_1
     (if (<= y 4.2e-110)
       (* y2 (* y4 (* k y1)))
       (if (<= y 9e+50) (* b (* j (* t y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (x * (y * b));
	double tmp;
	if (y <= -2400.0) {
		tmp = t_1;
	} else if (y <= 4.2e-110) {
		tmp = y2 * (y4 * (k * y1));
	} else if (y <= 9e+50) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (x * (y * b))
    if (y <= (-2400.0d0)) then
        tmp = t_1
    else if (y <= 4.2d-110) then
        tmp = y2 * (y4 * (k * y1))
    else if (y <= 9d+50) then
        tmp = b * (j * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (x * (y * b));
	double tmp;
	if (y <= -2400.0) {
		tmp = t_1;
	} else if (y <= 4.2e-110) {
		tmp = y2 * (y4 * (k * y1));
	} else if (y <= 9e+50) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (x * (y * b))
	tmp = 0
	if y <= -2400.0:
		tmp = t_1
	elif y <= 4.2e-110:
		tmp = y2 * (y4 * (k * y1))
	elif y <= 9e+50:
		tmp = b * (j * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(x * Float64(y * b)))
	tmp = 0.0
	if (y <= -2400.0)
		tmp = t_1;
	elseif (y <= 4.2e-110)
		tmp = Float64(y2 * Float64(y4 * Float64(k * y1)));
	elseif (y <= 9e+50)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (x * (y * b));
	tmp = 0.0;
	if (y <= -2400.0)
		tmp = t_1;
	elseif (y <= 4.2e-110)
		tmp = y2 * (y4 * (k * y1));
	elseif (y <= 9e+50)
		tmp = b * (j * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2400.0], t$95$1, If[LessEqual[y, 4.2e-110], N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+50], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2400 or 9.00000000000000027e50 < y

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 42.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 43.5

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 43.5%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 30.6

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 30.6%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. *-lowering-*.f64 32.3

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied egg-rr 32.3%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

   if -2400 < y < 4.20000000000000004e-110

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 42.3%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 34.1

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 34.1%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 28.1

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 28.1%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   if 4.20000000000000004e-110 < y < 9.00000000000000027e50

   1. Initial program 42.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 48.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 33.4

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 33.4%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 31.0

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 31.0%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2400:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-110}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 22.0% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{if}\;y \leq -3300:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-110}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* x (* y b)))))
   (if (<= y -3300.0)
     t_1
     (if (<= y 2.55e-110)
       (* y2 (* k (* y1 y4)))
       (if (<= y 1.05e+51) (* b (* j (* t y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (x * (y * b));
	double tmp;
	if (y <= -3300.0) {
		tmp = t_1;
	} else if (y <= 2.55e-110) {
		tmp = y2 * (k * (y1 * y4));
	} else if (y <= 1.05e+51) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (x * (y * b))
    if (y <= (-3300.0d0)) then
        tmp = t_1
    else if (y <= 2.55d-110) then
        tmp = y2 * (k * (y1 * y4))
    else if (y <= 1.05d+51) then
        tmp = b * (j * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (x * (y * b));
	double tmp;
	if (y <= -3300.0) {
		tmp = t_1;
	} else if (y <= 2.55e-110) {
		tmp = y2 * (k * (y1 * y4));
	} else if (y <= 1.05e+51) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (x * (y * b))
	tmp = 0
	if y <= -3300.0:
		tmp = t_1
	elif y <= 2.55e-110:
		tmp = y2 * (k * (y1 * y4))
	elif y <= 1.05e+51:
		tmp = b * (j * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(x * Float64(y * b)))
	tmp = 0.0
	if (y <= -3300.0)
		tmp = t_1;
	elseif (y <= 2.55e-110)
		tmp = Float64(y2 * Float64(k * Float64(y1 * y4)));
	elseif (y <= 1.05e+51)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (x * (y * b));
	tmp = 0.0;
	if (y <= -3300.0)
		tmp = t_1;
	elseif (y <= 2.55e-110)
		tmp = y2 * (k * (y1 * y4));
	elseif (y <= 1.05e+51)
		tmp = b * (j * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3300.0], t$95$1, If[LessEqual[y, 2.55e-110], N[(y2 * N[(k * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+51], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3300 or 1.0500000000000001e51 < y

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 42.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 43.5

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 43.5%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 30.6

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 30.6%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. *-lowering-*.f64 32.3

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied egg-rr 32.3%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

   if -3300 < y < 2.5500000000000001e-110

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 42.3%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 34.1

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 34.1%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 26.2

          \[\leadsto y2 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y4\right)}\right) \]

   11. Simplified 26.2%

       \[\leadsto y2 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y4\right)\right)} \]

   if 2.5500000000000001e-110 < y < 1.0500000000000001e51

   1. Initial program 42.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 48.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 33.4

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 33.4%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 31.0

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 31.0%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3300:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-110}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 21.9% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{if}\;y \leq -470:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-110}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* x (* y b)))))
   (if (<= y -470.0)
     t_1
     (if (<= y 2.45e-110)
       (* k (* y1 (* y2 y4)))
       (if (<= y 1.2e+51) (* b (* j (* t y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (x * (y * b));
	double tmp;
	if (y <= -470.0) {
		tmp = t_1;
	} else if (y <= 2.45e-110) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y <= 1.2e+51) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (x * (y * b))
    if (y <= (-470.0d0)) then
        tmp = t_1
    else if (y <= 2.45d-110) then
        tmp = k * (y1 * (y2 * y4))
    else if (y <= 1.2d+51) then
        tmp = b * (j * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (x * (y * b));
	double tmp;
	if (y <= -470.0) {
		tmp = t_1;
	} else if (y <= 2.45e-110) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y <= 1.2e+51) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (x * (y * b))
	tmp = 0
	if y <= -470.0:
		tmp = t_1
	elif y <= 2.45e-110:
		tmp = k * (y1 * (y2 * y4))
	elif y <= 1.2e+51:
		tmp = b * (j * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(x * Float64(y * b)))
	tmp = 0.0
	if (y <= -470.0)
		tmp = t_1;
	elseif (y <= 2.45e-110)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y <= 1.2e+51)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (x * (y * b));
	tmp = 0.0;
	if (y <= -470.0)
		tmp = t_1;
	elseif (y <= 2.45e-110)
		tmp = k * (y1 * (y2 * y4));
	elseif (y <= 1.2e+51)
		tmp = b * (j * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -470.0], t$95$1, If[LessEqual[y, 2.45e-110], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+51], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -470 or 1.1999999999999999e51 < y

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 42.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 43.5

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 43.5%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 30.6

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 30.6%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. *-lowering-*.f64 32.3

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied egg-rr 32.3%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

   if -470 < y < 2.4499999999999999e-110

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 42.3%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 34.1

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 34.1%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto k \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

       3. *-lowering-*.f64 25.6

          \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y2 \cdot y4\right)}\right) \]

   11. Simplified 25.6%

       \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 2.4499999999999999e-110 < y < 1.1999999999999999e51

   1. Initial program 42.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-lowering-*.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. Simplified 48.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 33.4

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 33.4%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 31.0

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 31.0%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -470:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-110}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 20.9% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+140}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -5.5e-9)
   (* x (* y (* a b)))
   (if (<= a 1.9e+140) (* y2 (* y4 (* k y1))) (* b (* (* x y) a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -5.5e-9) {
		tmp = x * (y * (a * b));
	} else if (a <= 1.9e+140) {
		tmp = y2 * (y4 * (k * y1));
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-5.5d-9)) then
        tmp = x * (y * (a * b))
    else if (a <= 1.9d+140) then
        tmp = y2 * (y4 * (k * y1))
    else
        tmp = b * ((x * y) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -5.5e-9) {
		tmp = x * (y * (a * b));
	} else if (a <= 1.9e+140) {
		tmp = y2 * (y4 * (k * y1));
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -5.5e-9:
		tmp = x * (y * (a * b))
	elif a <= 1.9e+140:
		tmp = y2 * (y4 * (k * y1))
	else:
		tmp = b * ((x * y) * a)
	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 <= -5.5e-9)
		tmp = Float64(x * Float64(y * Float64(a * b)));
	elseif (a <= 1.9e+140)
		tmp = Float64(y2 * Float64(y4 * Float64(k * y1)));
	else
		tmp = Float64(b * Float64(Float64(x * y) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -5.5e-9)
		tmp = x * (y * (a * b));
	elseif (a <= 1.9e+140)
		tmp = y2 * (y4 * (k * y1));
	else
		tmp = b * ((x * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[a, -5.5e-9], N[(x * N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+140], N[(y2 * N[(y4 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.4999999999999996e-9

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 45.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 39.1

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 39.1%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 25.7

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 25.7%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot \left(x \cdot y\right)} \]

       2. *-commutative N/A

          \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{\left(y \cdot x\right)} \]

       3. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\left(a \cdot b\right) \cdot y\right) \cdot x} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(a \cdot b\right) \cdot y\right) \cdot x} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(a \cdot b\right) \cdot y\right)} \cdot x \]

       6. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(b \cdot a\right)} \cdot y\right) \cdot x \]

       7. *-lowering-*.f64 32.9

          \[\leadsto \left(\color{blue}{\left(b \cdot a\right)} \cdot y\right) \cdot x \]

   13. Applied egg-rr 32.9%

       \[\leadsto \color{blue}{\left(\left(b \cdot a\right) \cdot y\right) \cdot x} \]

   if -5.4999999999999996e-9 < a < 1.9e140

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. 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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. accelerator-lowering-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. --lowering--.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. *-lowering-*.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. *-lowering-*.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. Simplified 41.4%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1 + -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(k, y1, -1 \cdot \left(c \cdot t\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-1 \cdot c\right) \cdot t}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot t\right)\right) \]

      8. neg-lowering-neg.f64 35.1

         \[\leadsto y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \color{blue}{\left(-c\right)} \cdot t\right)\right) \]

   8. Simplified 35.1%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \mathsf{fma}\left(k, y1, \left(-c\right) \cdot t\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 26.1

          \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   11. Simplified 26.1%

       \[\leadsto y2 \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \]

   if 1.9e140 < a

   1. Initial program 24.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 65.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 44.5

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 44.5%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 31.1

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 31.1%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \cdot b \]

       5. *-lowering-*.f64 36.1

          \[\leadsto \left(a \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot b \]

   13. Applied egg-rr 36.1%

       \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+140}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 21.8% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -4.5e+85)
   (* b (* j (* t y4)))
   (if (<= t 1.55e+57) (* a (* x (* y b))) (* a (* y5 (* t 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 (t <= -4.5e+85) {
		tmp = b * (j * (t * y4));
	} else if (t <= 1.55e+57) {
		tmp = a * (x * (y * b));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (t <= (-4.5d+85)) then
        tmp = b * (j * (t * y4))
    else if (t <= 1.55d+57) then
        tmp = a * (x * (y * b))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -4.5e+85) {
		tmp = b * (j * (t * y4));
	} else if (t <= 1.55e+57) {
		tmp = a * (x * (y * b));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -4.5e+85:
		tmp = b * (j * (t * y4))
	elif t <= 1.55e+57:
		tmp = a * (x * (y * b))
	else:
		tmp = a * (y5 * (t * 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 (t <= -4.5e+85)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (t <= 1.55e+57)
		tmp = Float64(a * Float64(x * Float64(y * b)));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -4.5e+85)
		tmp = b * (j * (t * y4));
	elseif (t <= 1.55e+57)
		tmp = a * (x * (y * b));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -4.5e+85], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+57], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.50000000000000007e85

   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 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. *-lowering-*.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. Simplified 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 y4 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(y1 \cdot y3\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-1 \cdot y1\right) \cdot y3}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \cdot y3\right)\right) \]

      8. neg-lowering-neg.f64 51.2

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \color{blue}{\left(-y1\right)} \cdot y3\right)\right) \]

   8. Simplified 51.2%

      \[\leadsto \color{blue}{j \cdot \left(y4 \cdot \mathsf{fma}\left(b, t, \left(-y1\right) \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       4. *-lowering-*.f64 46.2

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 46.2%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -4.50000000000000007e85 < t < 1.55000000000000007e57

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 37.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 29.1

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 29.1%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 20.3

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 20.3%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. *-lowering-*.f64 21.5

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied egg-rr 21.5%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

   if 1.55000000000000007e57 < t

   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 34.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-lowering-*.f64 34.5

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   8. Simplified 34.5%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 30.0

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   11. Simplified 30.0%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 21.3% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{if}\;y5 \leq -3.05 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 2.4 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (* t y2)))))
   (if (<= y5 -3.05e-61) t_1 (if (<= y5 2.4e+55) (* a (* (* x y) b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * (t * y2));
	double tmp;
	if (y5 <= -3.05e-61) {
		tmp = t_1;
	} else if (y5 <= 2.4e+55) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y5 * (t * y2))
    if (y5 <= (-3.05d-61)) then
        tmp = t_1
    else if (y5 <= 2.4d+55) then
        tmp = a * ((x * y) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * (t * y2));
	double tmp;
	if (y5 <= -3.05e-61) {
		tmp = t_1;
	} else if (y5 <= 2.4e+55) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * (t * y2))
	tmp = 0
	if y5 <= -3.05e-61:
		tmp = t_1
	elif y5 <= 2.4e+55:
		tmp = a * ((x * y) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(t * y2)))
	tmp = 0.0
	if (y5 <= -3.05e-61)
		tmp = t_1;
	elseif (y5 <= 2.4e+55)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * (t * y2));
	tmp = 0.0;
	if (y5 <= -3.05e-61)
		tmp = t_1;
	elseif (y5 <= 2.4e+55)
		tmp = a * ((x * y) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3.05e-61], t$95$1, If[LessEqual[y5, 2.4e+55], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y5 < -3.05e-61 or 2.3999999999999999e55 < y5

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 34.9%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-lowering-*.f64 36.2

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   8. Simplified 36.2%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 24.8

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   11. Simplified 24.8%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   if -3.05e-61 < y5 < 2.3999999999999999e55

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 39.2%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 24.2

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 24.2%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 22.4

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 22.4%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.05 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.4 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 18.7% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -3.7 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -3.7e-6) (* a (* y5 (* t y2))) (* a (* x (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -3.7e-6) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-3.7d-6)) then
        tmp = a * (y5 * (t * y2))
    else
        tmp = a * (x * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -3.7e-6) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -3.7e-6:
		tmp = a * (y5 * (t * y2))
	else:
		tmp = a * (x * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -3.7e-6)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	else
		tmp = Float64(a * Float64(x * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -3.7e-6)
		tmp = a * (y5 * (t * y2));
	else
		tmp = a * (x * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -3.7e-6], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y5 < -3.7000000000000002e-6

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 38.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

      4. *-lowering-*.f64 35.9

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   8. Simplified 35.9%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 31.4

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   11. Simplified 31.4%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   if -3.7000000000000002e-6 < y5

   1. Initial program 35.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 36.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

      7. neg-lowering-neg.f64 29.3

         \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

   8. Simplified 29.3%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

       2. *-lowering-*.f64 18.7

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

   11. Simplified 18.7%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]

       4. *-lowering-*.f64 19.3

          \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot y\right)} \cdot x\right) \]

   13. Applied egg-rr 19.3%

       \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.7 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 16.4% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 31.8%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   2. associate--l+ N/A

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

   3. mul-1-neg N/A

      \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   4. distribute-rgt-neg-in N/A

      \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   5. accelerator-lowering-fma.f64 N/A

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. neg-lowering-neg.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   7. --lowering--.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. *-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. *-lowering-*.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. *-lowering-*.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. Simplified 37.0%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in y around inf

   \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

   2. +-commutative N/A

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

   3. accelerator-lowering-fma.f64 N/A

      \[\leadsto a \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(b, x, -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

   4. associate-*r* N/A

      \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-1 \cdot y3\right) \cdot y5}\right)\right) \]

   6. mul-1-neg N/A

      \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)} \cdot y5\right)\right) \]

   7. neg-lowering-neg.f64 27.1

      \[\leadsto a \cdot \left(y \cdot \mathsf{fma}\left(b, x, \color{blue}{\left(-y3\right)} \cdot y5\right)\right) \]

8. Simplified 27.1%

   \[\leadsto a \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(b, x, \left(-y3\right) \cdot y5\right)\right)} \]

9. Taylor expanded in b around inf

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
10. Step-by-step derivation

    1. *-lowering-*.f64 N/A

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

    2. *-lowering-*.f64 16.3

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

11. Simplified 16.3%

    \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

12. Final simplification 16.3%

    \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
13. Add Preprocessing

Developer Target 1: 26.4% 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 2024205 
(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)))))