Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.9% → 54.6%

Time: 35.5s

Alternatives: 29

Speedup: 5.6×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.9% 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: 54.6% accurate, 0.5× speedup

Math

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

FPCore

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

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * t_2) + Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(i * y1) - Float64(b * y0)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(t_1 * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(-Float64(c * fma(y0, Float64(Float64(z * y3) - Float64(x * y2)), fma(i, t_2, Float64(y4 * t_1)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, (-N[(c * N[(y0 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(i * t$95$2 + N[(y4 * 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 91.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 47.7%

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

4. Final simplification 61.3%

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

Alternative 2: 45.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -c \cdot \mathsf{fma}\left(y0, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(i, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ t_2 := b \cdot y0 - i \cdot y1\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-222}:\\ \;\;\;\;\mathsf{fma}\left(t, i \cdot y5 - b \cdot y4, \mathsf{fma}\left(y3, t\_3, x \cdot t\_2\right)\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-130}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(t\_4, -y, \mathsf{fma}\left(y2, t\_3, z \cdot t\_2\right)\right)\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(t\_4, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (-
          (*
           c
           (fma
            y0
            (- (* z y3) (* x y2))
            (fma i (- (* x y) (* z t)) (* y4 (- (* t y2) (* y y3))))))))
        (t_2 (- (* b y0) (* i y1)))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4 (- (* b y4) (* i y5))))
   (if (<= c -3.5e+37)
     t_1
     (if (<= c -3.4e-222)
       (* (fma t (- (* i y5) (* b y4)) (fma y3 t_3 (* x t_2))) (- j))
       (if (<= c 1.22e-130)
         (* k (fma t_4 (- y) (fma y2 t_3 (* z t_2))))
         (if (<= c 2.35e+150)
           (*
            y
            (fma
             t_4
             (- k)
             (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5))))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -(c * fma(y0, ((z * y3) - (x * y2)), fma(i, ((x * y) - (z * t)), (y4 * ((t * y2) - (y * y3))))));
	double t_2 = (b * y0) - (i * y1);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (b * y4) - (i * y5);
	double tmp;
	if (c <= -3.5e+37) {
		tmp = t_1;
	} else if (c <= -3.4e-222) {
		tmp = fma(t, ((i * y5) - (b * y4)), fma(y3, t_3, (x * t_2))) * -j;
	} else if (c <= 1.22e-130) {
		tmp = k * fma(t_4, -y, fma(y2, t_3, (z * t_2)));
	} else if (c <= 2.35e+150) {
		tmp = y * fma(t_4, -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(-Float64(c * fma(y0, Float64(Float64(z * y3) - Float64(x * y2)), fma(i, Float64(Float64(x * y) - Float64(z * t)), Float64(y4 * Float64(Float64(t * y2) - Float64(y * y3)))))))
	t_2 = Float64(Float64(b * y0) - Float64(i * y1))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (c <= -3.5e+37)
		tmp = t_1;
	elseif (c <= -3.4e-222)
		tmp = Float64(fma(t, Float64(Float64(i * y5) - Float64(b * y4)), fma(y3, t_3, Float64(x * t_2))) * Float64(-j));
	elseif (c <= 1.22e-130)
		tmp = Float64(k * fma(t_4, Float64(-y), fma(y2, t_3, Float64(z * t_2))));
	elseif (c <= 2.35e+150)
		tmp = Float64(y * fma(t_4, Float64(-k), fma(Float64(Float64(a * b) - Float64(c * i)), x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = (-N[(c * N[(y0 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])}, Block[{t$95$2 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.5e+37], t$95$1, If[LessEqual[c, -3.4e-222], N[(N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$3 + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[c, 1.22e-130], N[(k * N[(t$95$4 * (-y) + N[(y2 * t$95$3 + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.35e+150], N[(y * N[(t$95$4 * (-k) + N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.5e37 or 2.35000000000000002e150 < c

   1. Initial program 18.2%

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

   3. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 67.2%

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

   if -3.5e37 < c < -3.4000000000000001e-222

   1. Initial program 34.4%

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

   3. Taylor expanded in 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 56.4%

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

   if -3.4000000000000001e-222 < c < 1.22000000000000003e-130

   1. Initial program 39.2%

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

   3. Taylor expanded in k around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. neg-mul-1 N/A

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

   5. Simplified 61.7%

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

   if 1.22000000000000003e-130 < c < 2.35000000000000002e150

   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 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 55.4%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+37}:\\ \;\;\;\;-c \cdot \mathsf{fma}\left(y0, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(i, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-222}:\\ \;\;\;\;\mathsf{fma}\left(t, i \cdot y5 - b \cdot y4, \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-130}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-c \cdot \mathsf{fma}\left(y0, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(i, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ t_3 := y2 \cdot \mathsf{fma}\left(k, t\_1, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-33}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-173}:\\ \;\;\;\;\mathsf{fma}\left(t, i \cdot y5 - b \cdot y4, \mathsf{fma}\left(y3, t\_1, x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-j\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-24}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2
         (*
          y
          (fma
           (- (* b y4) (* i y5))
           (- k)
           (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5)))))))
        (t_3
         (*
          y2
          (fma
           k
           t_1
           (fma (- (* c y0) (* a y1)) x (* t (- (* a y5) (* c y4))))))))
   (if (<= y -1.6e+98)
     t_2
     (if (<= y -7.6e-33)
       t_3
       (if (<= y -1.7e-173)
         (*
          (fma
           t
           (- (* i y5) (* b y4))
           (fma y3 t_1 (* x (- (* b y0) (* i y1)))))
          (- j))
         (if (<= y 1.7e-24) t_3 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = y * fma(((b * y4) - (i * y5)), -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	double t_3 = y2 * fma(k, t_1, fma(((c * y0) - (a * y1)), x, (t * ((a * y5) - (c * y4)))));
	double tmp;
	if (y <= -1.6e+98) {
		tmp = t_2;
	} else if (y <= -7.6e-33) {
		tmp = t_3;
	} else if (y <= -1.7e-173) {
		tmp = fma(t, ((i * y5) - (b * y4)), fma(y3, t_1, (x * ((b * y0) - (i * y1))))) * -j;
	} else if (y <= 1.7e-24) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(y * fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(-k), fma(Float64(Float64(a * b) - Float64(c * i)), x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))))
	t_3 = Float64(y2 * fma(k, t_1, fma(Float64(Float64(c * y0) - Float64(a * y1)), x, Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))))
	tmp = 0.0
	if (y <= -1.6e+98)
		tmp = t_2;
	elseif (y <= -7.6e-33)
		tmp = t_3;
	elseif (y <= -1.7e-173)
		tmp = Float64(fma(t, Float64(Float64(i * y5) - Float64(b * y4)), fma(y3, t_1, Float64(x * Float64(Float64(b * y0) - Float64(i * y1))))) * Float64(-j));
	elseif (y <= 1.7e-24)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * (-k) + N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(k * t$95$1 + 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[y, -1.6e+98], t$95$2, If[LessEqual[y, -7.6e-33], t$95$3, If[LessEqual[y, -1.7e-173], N[(N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$1 + N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[y, 1.7e-24], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6000000000000001e98 or 1.69999999999999996e-24 < y

   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 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 66.8%

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

   if -1.6000000000000001e98 < y < -7.59999999999999988e-33 or -1.6999999999999999e-173 < y < 1.69999999999999996e-24

   1. Initial program 28.5%

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

   3. Taylor expanded in 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 54.1%

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

   if -7.59999999999999988e-33 < y < -1.6999999999999999e-173

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 59.4%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-33}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-173}:\\ \;\;\;\;\mathsf{fma}\left(t, i \cdot y5 - b \cdot y4, \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-j\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-24}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -4.3 \cdot 10^{+192}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -29000000:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(x, c \cdot y0 - a \cdot y1, y5 \cdot \mathsf{fma}\left(a, t, k \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.25 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -4.3e+192)
   (* j (* y0 (fma x (- b) (* y3 y5))))
   (if (<= y0 -29000000.0)
     (* y2 (fma x (- (* c y0) (* a y1)) (* y5 (fma a t (* k (- y0))))))
     (if (<= y0 1.25e+77)
       (*
        a
        (fma
         y1
         (- (* z y3) (* x y2))
         (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
       (* (* x c) (- (* y0 y2) (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.3e+192) {
		tmp = j * (y0 * fma(x, -b, (y3 * y5)));
	} else if (y0 <= -29000000.0) {
		tmp = y2 * fma(x, ((c * y0) - (a * y1)), (y5 * fma(a, t, (k * -y0))));
	} else if (y0 <= 1.25e+77) {
		tmp = a * fma(y1, ((z * y3) - (x * y2)), fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} else {
		tmp = (x * c) * ((y0 * y2) - (y * i));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -4.3e+192)
		tmp = Float64(j * Float64(y0 * fma(x, Float64(-b), Float64(y3 * y5))));
	elseif (y0 <= -29000000.0)
		tmp = Float64(y2 * fma(x, Float64(Float64(c * y0) - Float64(a * y1)), Float64(y5 * fma(a, t, Float64(k * Float64(-y0))))));
	elseif (y0 <= 1.25e+77)
		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))))));
	else
		tmp = Float64(Float64(x * c) * Float64(Float64(y0 * y2) - Float64(y * i)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -4.3e+192], N[(j * N[(y0 * N[(x * (-b) + N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -29000000.0], N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(a * t + N[(k * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.25e+77], 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], N[(N[(x * c), $MachinePrecision] * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -4.29999999999999976e192

   1. Initial program 20.0%

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

   3. Taylor expanded in 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 56.1%

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

   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. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

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

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(x, -1 \cdot b, y3 \cdot y5\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

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

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      10. *-lowering-*.f64 68.3

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

   8. Simplified 68.3%

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

   if -4.29999999999999976e192 < y0 < -2.9e7

   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 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 57.9%

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

   6. Taylor expanded in y4 around 0

      \[\leadsto \color{blue}{y2 \cdot \left(-1 \cdot \left(k \cdot \left(y0 \cdot y5\right)\right) + \left(a \cdot \left(t \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

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

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

      2. associate-+r+ N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-in N/A

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

      9. +-commutative N/A

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

      10. distribute-rgt-in N/A

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

      11. mul-1-neg N/A

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

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

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

      13. associate-*r* N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r* N/A

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

   8. Simplified 60.5%

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

   if -2.9e7 < y0 < 1.25000000000000001e77

   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%

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

   if 1.25000000000000001e77 < y0

   1. Initial program 21.0%

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

   3. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 59.0%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

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

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

      3. associate-*r* N/A

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

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

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

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

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. unsub-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot x\right) \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(c \cdot x\right) \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

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

          \[\leadsto \mathsf{neg}\left(\left(c \cdot x\right) \cdot \left(\color{blue}{i \cdot y} - y0 \cdot y2\right)\right) \]

      11. *-lowering-*.f64 55.5

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

   8. Simplified 55.5%

      \[\leadsto \color{blue}{-\left(c \cdot x\right) \cdot \left(i \cdot y - y0 \cdot y2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.3 \cdot 10^{+192}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -29000000:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(x, c \cdot y0 - a \cdot y1, y5 \cdot \mathsf{fma}\left(a, t, k \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.25 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2 - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-25}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y
          (fma
           (- (* b y4) (* i y5))
           (- k)
           (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5))))))))
   (if (<= y -2.9e+98)
     t_1
     (if (<= y 2.9e-25)
       (*
        y2
        (fma
         k
         (- (* y1 y4) (* y0 y5))
         (fma (- (* c y0) (* a y1)) x (* t (- (* a y5) (* c 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 = y * fma(((b * y4) - (i * y5)), -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	double tmp;
	if (y <= -2.9e+98) {
		tmp = t_1;
	} else if (y <= 2.9e-25) {
		tmp = y2 * fma(k, ((y1 * y4) - (y0 * y5)), fma(((c * y0) - (a * y1)), x, (t * ((a * y5) - (c * 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(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))))))
	tmp = 0.0
	if (y <= -2.9e+98)
		tmp = t_1;
	elseif (y <= 2.9e-25)
		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 = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * (-k) + N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+98], t$95$1, If[LessEqual[y, 2.9e-25], 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], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000001e98 or 2.9000000000000001e-25 < y

   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 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 66.8%

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

   if -2.9000000000000001e98 < y < 2.9000000000000001e-25

   1. Initial program 29.5%

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

   3. Taylor expanded in 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 48.5%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-25}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+55}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          a
          (fma
           y1
           (- (* z y3) (* x y2))
           (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))))
   (if (<= a -2.55e+20)
     t_1
     (if (<= a 7e+55)
       (*
        k
        (fma
         (- (* b y4) (* i y5))
         (- y)
         (fma y2 (- (* y1 y4) (* y0 y5)) (* z (- (* b y0) (* i y1))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * fma(y1, ((z * y3) - (x * y2)), fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	double tmp;
	if (a <= -2.55e+20) {
		tmp = t_1;
	} else if (a <= 7e+55) {
		tmp = k * fma(((b * y4) - (i * y5)), -y, fma(y2, ((y1 * y4) - (y0 * y5)), (z * ((b * y0) - (i * y1)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(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))))))
	tmp = 0.0
	if (a <= -2.55e+20)
		tmp = t_1;
	elseif (a <= 7e+55)
		tmp = Float64(k * fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(-y), fma(y2, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))));
	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[(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[a, -2.55e+20], t$95$1, If[LessEqual[a, 7e+55], N[(k * N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * (-y) + N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.55e20 or 7.00000000000000021e55 < a

   1. Initial program 14.3%

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

   3. Taylor expanded in a around inf

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

      1. *-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 60.5%

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

   if -2.55e20 < a < 7.00000000000000021e55

   1. Initial program 39.3%

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

   3. Taylor expanded in k around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. neg-mul-1 N/A

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

   5. Simplified 51.6%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+55}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 32.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.25 \cdot 10^{+150}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot \mathsf{fma}\left(-y1, \frac{z}{y}, y5\right)\right)\right)\\ \mathbf{elif}\;k \leq -4.6 \cdot 10^{-146}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-295}:\\ \;\;\;\;j \cdot \left(\left(-y5\right) \cdot \mathsf{fma}\left(y0, -y3, t \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{+47}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(x, c \cdot y0 - a \cdot y1, y5 \cdot \mathsf{fma}\left(a, t, k \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -1.25e+150)
   (* k (* i (* y (fma (- y1) (/ z y) y5))))
   (if (<= k -4.6e-146)
     (* k (* y2 (fma y5 (- y0) (* y1 y4))))
     (if (<= k 2.9e-295)
       (* j (* (- y5) (fma y0 (- y3) (* t i))))
       (if (<= k 2.6e+47)
         (* y2 (fma x (- (* c y0) (* a y1)) (* y5 (fma a t (* k (- y0))))))
         (if (<= k 4.2e+122)
           (* b (* y4 (fma (- k) y (* t j))))
           (* k (* i (- (* y y5) (* z y1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -1.25e+150) {
		tmp = k * (i * (y * fma(-y1, (z / y), y5)));
	} else if (k <= -4.6e-146) {
		tmp = k * (y2 * fma(y5, -y0, (y1 * y4)));
	} else if (k <= 2.9e-295) {
		tmp = j * (-y5 * fma(y0, -y3, (t * i)));
	} else if (k <= 2.6e+47) {
		tmp = y2 * fma(x, ((c * y0) - (a * y1)), (y5 * fma(a, t, (k * -y0))));
	} else if (k <= 4.2e+122) {
		tmp = b * (y4 * fma(-k, y, (t * j)));
	} else {
		tmp = k * (i * ((y * y5) - (z * y1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (k <= -1.25e+150)
		tmp = Float64(k * Float64(i * Float64(y * fma(Float64(-y1), Float64(z / y), y5))));
	elseif (k <= -4.6e-146)
		tmp = Float64(k * Float64(y2 * fma(y5, Float64(-y0), Float64(y1 * y4))));
	elseif (k <= 2.9e-295)
		tmp = Float64(j * Float64(Float64(-y5) * fma(y0, Float64(-y3), Float64(t * i))));
	elseif (k <= 2.6e+47)
		tmp = Float64(y2 * fma(x, Float64(Float64(c * y0) - Float64(a * y1)), Float64(y5 * fma(a, t, Float64(k * Float64(-y0))))));
	elseif (k <= 4.2e+122)
		tmp = Float64(b * Float64(y4 * fma(Float64(-k), y, Float64(t * j))));
	else
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * 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[k, -1.25e+150], N[(k * N[(i * N[(y * N[((-y1) * N[(z / y), $MachinePrecision] + y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.6e-146], N[(k * N[(y2 * N[(y5 * (-y0) + N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.9e-295], N[(j * N[((-y5) * N[(y0 * (-y3) + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.6e+47], N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(a * t + N[(k * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.2e+122], N[(b * N[(y4 * N[((-k) * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -1.25000000000000002e150

   1. Initial program 24.7%

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

   3. Taylor expanded in k around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. neg-mul-1 N/A

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

   5. Simplified 63.6%

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

   6. Taylor expanded in i around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

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

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

      7. *-lowering-*.f64 58.7

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

   8. Simplified 58.7%

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

   9. Taylor expanded in y around inf

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

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

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

       2. +-commutative N/A

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

       3. mul-1-neg N/A

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

       4. associate-/l* N/A

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

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

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

       6. mul-1-neg N/A

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

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

          \[\leadsto k \cdot \left(i \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y1, \frac{z}{y}, y5\right)}\right)\right) \]

       8. mul-1-neg N/A

          \[\leadsto k \cdot \left(i \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y1\right)}, \frac{z}{y}, y5\right)\right)\right) \]

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

          \[\leadsto k \cdot \left(i \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y1\right)}, \frac{z}{y}, y5\right)\right)\right) \]

       10. /-lowering-/.f64 61.1

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

   11. Simplified 61.1%

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

   if -1.25000000000000002e150 < k < -4.6000000000000001e-146

   1. Initial program 29.2%

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

   3. Taylor expanded in 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 40.4%

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

   6. Taylor expanded in k around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 48.0

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

   8. Simplified 48.0%

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

   if -4.6000000000000001e-146 < k < 2.90000000000000015e-295

   1. Initial program 40.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 34.8%

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

   6. Taylor expanded in y5 around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. mul-1-neg N/A

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

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

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

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

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

      14. mul-1-neg N/A

          \[\leadsto \left(y5 \cdot \mathsf{fma}\left(y0, \mathsf{neg}\left(y3\right), i \cdot t\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \]

      15. neg-lowering-neg.f64 44.5

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

   8. Simplified 44.5%

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

   if 2.90000000000000015e-295 < k < 2.60000000000000003e47

   1. Initial program 30.6%

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

   3. Taylor expanded in 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 48.5%

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

   6. Taylor expanded in y4 around 0

      \[\leadsto \color{blue}{y2 \cdot \left(-1 \cdot \left(k \cdot \left(y0 \cdot y5\right)\right) + \left(a \cdot \left(t \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

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

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

      2. associate-+r+ N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-in N/A

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

      9. +-commutative N/A

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

      10. distribute-rgt-in N/A

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

      11. mul-1-neg N/A

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

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

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

      13. associate-*r* N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r* N/A

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

   8. Simplified 53.7%

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

   if 2.60000000000000003e47 < k < 4.20000000000000032e122

   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 y4 around inf

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

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

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

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

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

   5. Simplified 38.3%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. associate-*r* N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. *-lowering-*.f64 63.2

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

   8. Simplified 63.2%

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

   if 4.20000000000000032e122 < k

   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 k around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. neg-mul-1 N/A

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

   5. Simplified 60.8%

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

   6. Taylor expanded in i around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

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

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

      7. *-lowering-*.f64 55.9

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

   8. Simplified 55.9%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.25 \cdot 10^{+150}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot \mathsf{fma}\left(-y1, \frac{z}{y}, y5\right)\right)\right)\\ \mathbf{elif}\;k \leq -4.6 \cdot 10^{-146}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-295}:\\ \;\;\;\;j \cdot \left(\left(-y5\right) \cdot \mathsf{fma}\left(y0, -y3, t \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{+47}:\\ \;\;\;\;y2 \cdot \mathsf{fma}\left(x, c \cdot y0 - a \cdot y1, y5 \cdot \mathsf{fma}\left(a, t, k \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;k \leq -6 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -5.2 \cdot 10^{-76}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{-251}:\\ \;\;\;\;\left(x \cdot y1 - t \cdot y5\right) \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;k \leq 6.8 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= k -6e+151)
     t_1
     (if (<= k -5.2e-76)
       (* k (* y2 (fma y5 (- y0) (* y1 y4))))
       (if (<= k 1.22e-251)
         (* (- (* x y1) (* t y5)) (* i j))
         (if (<= k 6.8e-40)
           (* c (* y2 (fma (- t) y4 (* x y0))))
           (if (<= k 1.15e+58)
             (* c (* y (fma (- i) x (* y3 y4))))
             (if (<= k 5.5e+122) (* b (* y4 (fma (- k) y (* t j)))) 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (k <= -6e+151) {
		tmp = t_1;
	} else if (k <= -5.2e-76) {
		tmp = k * (y2 * fma(y5, -y0, (y1 * y4)));
	} else if (k <= 1.22e-251) {
		tmp = ((x * y1) - (t * y5)) * (i * j);
	} else if (k <= 6.8e-40) {
		tmp = c * (y2 * fma(-t, y4, (x * y0)));
	} else if (k <= 1.15e+58) {
		tmp = c * (y * fma(-i, x, (y3 * y4)));
	} else if (k <= 5.5e+122) {
		tmp = b * (y4 * fma(-k, y, (t * j)));
	} 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(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (k <= -6e+151)
		tmp = t_1;
	elseif (k <= -5.2e-76)
		tmp = Float64(k * Float64(y2 * fma(y5, Float64(-y0), Float64(y1 * y4))));
	elseif (k <= 1.22e-251)
		tmp = Float64(Float64(Float64(x * y1) - Float64(t * y5)) * Float64(i * j));
	elseif (k <= 6.8e-40)
		tmp = Float64(c * Float64(y2 * fma(Float64(-t), y4, Float64(x * y0))));
	elseif (k <= 1.15e+58)
		tmp = Float64(c * Float64(y * fma(Float64(-i), x, Float64(y3 * y4))));
	elseif (k <= 5.5e+122)
		tmp = Float64(b * Float64(y4 * fma(Float64(-k), y, Float64(t * j))));
	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[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -6e+151], t$95$1, If[LessEqual[k, -5.2e-76], N[(k * N[(y2 * N[(y5 * (-y0) + N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.22e-251], N[(N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.8e-40], N[(c * N[(y2 * N[((-t) * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.15e+58], N[(c * N[(y * N[((-i) * x + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.5e+122], N[(b * N[(y4 * N[((-k) * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -5.9999999999999998e151 or 5.4999999999999998e122 < k

   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 k around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. neg-mul-1 N/A

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

   5. Simplified 62.4%

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

   6. Taylor expanded in i around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

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

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

      7. *-lowering-*.f64 57.5

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

   8. Simplified 57.5%

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

   if -5.9999999999999998e151 < k < -5.1999999999999999e-76

   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 43.9%

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

   6. Taylor expanded in k around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 48.6

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

   8. Simplified 48.6%

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

   if -5.1999999999999999e-76 < k < 1.2200000000000001e-251

   1. Initial program 40.5%

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

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

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

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

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

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

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

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

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

      10. *-commutative N/A

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

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

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

      12. *-lowering-*.f64 43.3

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

   8. Simplified 43.3%

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

   if 1.2200000000000001e-251 < k < 6.79999999999999968e-40

   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 c around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 50.3%

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

   6. Taylor expanded in y2 around -inf

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

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

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

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

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

      7. *-lowering-*.f64 48.9

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

   8. Simplified 48.9%

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

   if 6.79999999999999968e-40 < k < 1.15000000000000001e58

   1. Initial program 24.9%

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

   3. Taylor expanded in 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 33.5%

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

   6. Taylor expanded in c around inf

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

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

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

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

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

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

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      7. *-lowering-*.f64 53.1

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

   8. Simplified 53.1%

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

   if 1.15000000000000001e58 < k < 5.4999999999999998e122

   1. Initial program 7.7%

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

   3. Taylor expanded in y4 around inf

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

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

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

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

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

   5. Simplified 39.2%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. associate-*r* N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. *-lowering-*.f64 69.8

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

   8. Simplified 69.8%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6 \cdot 10^{+151}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -5.2 \cdot 10^{-76}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{-251}:\\ \;\;\;\;\left(x \cdot y1 - t \cdot y5\right) \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;k \leq 6.8 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 30.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;k \leq -2.4 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -4 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 3.3 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-40}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= k -2.4e+149)
     t_1
     (if (<= k -4e-46)
       (* k (* y2 (fma y5 (- y0) (* y1 y4))))
       (if (<= k 3.3e-80)
         (* j (* y0 (fma x (- b) (* y3 y5))))
         (if (<= k 2e-40)
           (* k (* y5 (- (* y i) (* y0 y2))))
           (if (<= k 3.4e+59)
             (* c (* y (fma (- i) x (* y3 y4))))
             (if (<= k 6e+122) (* b (* y4 (fma (- k) y (* t j)))) 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (k <= -2.4e+149) {
		tmp = t_1;
	} else if (k <= -4e-46) {
		tmp = k * (y2 * fma(y5, -y0, (y1 * y4)));
	} else if (k <= 3.3e-80) {
		tmp = j * (y0 * fma(x, -b, (y3 * y5)));
	} else if (k <= 2e-40) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (k <= 3.4e+59) {
		tmp = c * (y * fma(-i, x, (y3 * y4)));
	} else if (k <= 6e+122) {
		tmp = b * (y4 * fma(-k, y, (t * j)));
	} 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(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (k <= -2.4e+149)
		tmp = t_1;
	elseif (k <= -4e-46)
		tmp = Float64(k * Float64(y2 * fma(y5, Float64(-y0), Float64(y1 * y4))));
	elseif (k <= 3.3e-80)
		tmp = Float64(j * Float64(y0 * fma(x, Float64(-b), Float64(y3 * y5))));
	elseif (k <= 2e-40)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (k <= 3.4e+59)
		tmp = Float64(c * Float64(y * fma(Float64(-i), x, Float64(y3 * y4))));
	elseif (k <= 6e+122)
		tmp = Float64(b * Float64(y4 * fma(Float64(-k), y, Float64(t * j))));
	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[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.4e+149], t$95$1, If[LessEqual[k, -4e-46], N[(k * N[(y2 * N[(y5 * (-y0) + N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.3e-80], N[(j * N[(y0 * N[(x * (-b) + N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2e-40], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.4e+59], N[(c * N[(y * N[((-i) * x + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6e+122], N[(b * N[(y4 * N[((-k) * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -2.40000000000000012e149 or 5.99999999999999972e122 < k

   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 k around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. neg-mul-1 N/A

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

   5. Simplified 62.4%

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

   6. Taylor expanded in i around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

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

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

      7. *-lowering-*.f64 57.5

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

   8. Simplified 57.5%

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

   if -2.40000000000000012e149 < k < -4.00000000000000009e-46

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 46.9%

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

   6. Taylor expanded in k around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 49.6

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

   8. Simplified 49.6%

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

   if -4.00000000000000009e-46 < k < 3.3e-80

   1. Initial program 36.1%

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

   3. Taylor expanded in 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 43.6%

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

   6. Taylor expanded in 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. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

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

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(x, -1 \cdot b, y3 \cdot y5\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

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

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      10. *-lowering-*.f64 40.6

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

   8. Simplified 40.6%

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

   if 3.3e-80 < k < 1.9999999999999999e-40

   1. Initial program 26.7%

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

   3. Taylor expanded in k around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. neg-mul-1 N/A

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

   5. Simplified 46.9%

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

   6. Taylor expanded in y5 around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

         \[\leadsto k \cdot \left(y5 \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

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

         \[\leadsto k \cdot \left(y5 \cdot \color{blue}{\left(i \cdot y - y0 \cdot y2\right)}\right) \]

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

         \[\leadsto k \cdot \left(y5 \cdot \left(\color{blue}{i \cdot y} - y0 \cdot y2\right)\right) \]

      7. *-lowering-*.f64 60.7

         \[\leadsto k \cdot \left(y5 \cdot \left(i \cdot y - \color{blue}{y0 \cdot y2}\right)\right) \]

   8. Simplified 60.7%

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(i \cdot y - y0 \cdot y2\right)\right)} \]

   if 1.9999999999999999e-40 < k < 3.40000000000000006e59

   1. Initial program 24.9%

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

   3. Taylor expanded in 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 33.5%

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

   6. Taylor expanded in c around inf

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

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

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

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

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

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

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      7. *-lowering-*.f64 53.1

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

   8. Simplified 53.1%

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

   if 3.40000000000000006e59 < k < 5.99999999999999972e122

   1. Initial program 7.7%

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

   3. Taylor expanded in y4 around inf

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

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

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

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

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

   5. Simplified 39.2%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. associate-*r* N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. *-lowering-*.f64 69.8

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

   8. Simplified 69.8%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.4 \cdot 10^{+149}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -4 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 3.3 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 2 \cdot 10^{-40}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{if}\;k \leq -1.9 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -2.35 \cdot 10^{-48}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{-237}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 7.6 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (- (* y y5) (* z y1))))))
   (if (<= k -1.9e+150)
     t_1
     (if (<= k -2.35e-48)
       (* k (* y2 (fma y5 (- y0) (* y1 y4))))
       (if (<= k 1.3e-237)
         (* j (* y0 (fma x (- b) (* y3 y5))))
         (if (<= k 7.6e-40)
           (* c (* y2 (fma (- t) y4 (* x y0))))
           (if (<= k 2.3e+58)
             (* c (* y (fma (- i) x (* y3 y4))))
             (if (<= k 6.2e+122) (* b (* y4 (fma (- k) y (* t j)))) 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 = k * (i * ((y * y5) - (z * y1)));
	double tmp;
	if (k <= -1.9e+150) {
		tmp = t_1;
	} else if (k <= -2.35e-48) {
		tmp = k * (y2 * fma(y5, -y0, (y1 * y4)));
	} else if (k <= 1.3e-237) {
		tmp = j * (y0 * fma(x, -b, (y3 * y5)));
	} else if (k <= 7.6e-40) {
		tmp = c * (y2 * fma(-t, y4, (x * y0)));
	} else if (k <= 2.3e+58) {
		tmp = c * (y * fma(-i, x, (y3 * y4)));
	} else if (k <= 6.2e+122) {
		tmp = b * (y4 * fma(-k, y, (t * j)));
	} 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(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))))
	tmp = 0.0
	if (k <= -1.9e+150)
		tmp = t_1;
	elseif (k <= -2.35e-48)
		tmp = Float64(k * Float64(y2 * fma(y5, Float64(-y0), Float64(y1 * y4))));
	elseif (k <= 1.3e-237)
		tmp = Float64(j * Float64(y0 * fma(x, Float64(-b), Float64(y3 * y5))));
	elseif (k <= 7.6e-40)
		tmp = Float64(c * Float64(y2 * fma(Float64(-t), y4, Float64(x * y0))));
	elseif (k <= 2.3e+58)
		tmp = Float64(c * Float64(y * fma(Float64(-i), x, Float64(y3 * y4))));
	elseif (k <= 6.2e+122)
		tmp = Float64(b * Float64(y4 * fma(Float64(-k), y, Float64(t * j))));
	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[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.9e+150], t$95$1, If[LessEqual[k, -2.35e-48], N[(k * N[(y2 * N[(y5 * (-y0) + N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.3e-237], N[(j * N[(y0 * N[(x * (-b) + N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.6e-40], N[(c * N[(y2 * N[((-t) * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.3e+58], N[(c * N[(y * N[((-i) * x + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.2e+122], N[(b * N[(y4 * N[((-k) * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -1.89999999999999995e150 or 6.19999999999999998e122 < k

   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 k around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. neg-mul-1 N/A

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

   5. Simplified 62.4%

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

   6. Taylor expanded in i around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

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

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

      7. *-lowering-*.f64 57.5

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

   8. Simplified 57.5%

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

   if -1.89999999999999995e150 < k < -2.3499999999999999e-48

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 46.9%

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

   6. Taylor expanded in k around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 49.6

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

   8. Simplified 49.6%

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

   if -2.3499999999999999e-48 < k < 1.3000000000000001e-237

   1. Initial program 39.1%

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

   3. Taylor expanded in 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 46.0%

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

   6. Taylor expanded in 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. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

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

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(x, -1 \cdot b, y3 \cdot y5\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

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

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      10. *-lowering-*.f64 39.9

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

   8. Simplified 39.9%

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

   if 1.3000000000000001e-237 < k < 7.5999999999999998e-40

   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 c around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 47.9%

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

   6. Taylor expanded in y2 around -inf

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

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

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

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

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

      7. *-lowering-*.f64 48.7

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

   8. Simplified 48.7%

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

   if 7.5999999999999998e-40 < k < 2.30000000000000002e58

   1. Initial program 24.9%

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

   3. Taylor expanded in 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 33.5%

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

   6. Taylor expanded in c around inf

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

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

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

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

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

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

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      7. *-lowering-*.f64 53.1

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

   8. Simplified 53.1%

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

   if 2.30000000000000002e58 < k < 6.19999999999999998e122

   1. Initial program 7.7%

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

   3. Taylor expanded in y4 around inf

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

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

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

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

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

   5. Simplified 39.2%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. associate-*r* N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. *-lowering-*.f64 69.8

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

   8. Simplified 69.8%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.9 \cdot 10^{+150}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -2.35 \cdot 10^{-48}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{-237}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 7.6 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 31.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(i \cdot \left(y \cdot \mathsf{fma}\left(-y1, \frac{z}{y}, y5\right)\right)\right)\\ \mathbf{if}\;k \leq -8.5 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -9.2 \cdot 10^{-76}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-250}:\\ \;\;\;\;\left(x \cdot y1 - t \cdot y5\right) \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;k \leq 2.35 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* i (* y (fma (- y1) (/ z y) y5))))))
   (if (<= k -8.5e+148)
     t_1
     (if (<= k -9.2e-76)
       (* k (* y2 (fma y5 (- y0) (* y1 y4))))
       (if (<= k 4.8e-250)
         (* (- (* x y1) (* t y5)) (* i j))
         (if (<= k 2.35e-58) (* c (* y2 (fma (- t) y4 (* x 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 = k * (i * (y * fma(-y1, (z / y), y5)));
	double tmp;
	if (k <= -8.5e+148) {
		tmp = t_1;
	} else if (k <= -9.2e-76) {
		tmp = k * (y2 * fma(y5, -y0, (y1 * y4)));
	} else if (k <= 4.8e-250) {
		tmp = ((x * y1) - (t * y5)) * (i * j);
	} else if (k <= 2.35e-58) {
		tmp = c * (y2 * fma(-t, y4, (x * 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(k * Float64(i * Float64(y * fma(Float64(-y1), Float64(z / y), y5))))
	tmp = 0.0
	if (k <= -8.5e+148)
		tmp = t_1;
	elseif (k <= -9.2e-76)
		tmp = Float64(k * Float64(y2 * fma(y5, Float64(-y0), Float64(y1 * y4))));
	elseif (k <= 4.8e-250)
		tmp = Float64(Float64(Float64(x * y1) - Float64(t * y5)) * Float64(i * j));
	elseif (k <= 2.35e-58)
		tmp = Float64(c * Float64(y2 * fma(Float64(-t), y4, Float64(x * 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[(k * N[(i * N[(y * N[((-y1) * N[(z / y), $MachinePrecision] + y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -8.5e+148], t$95$1, If[LessEqual[k, -9.2e-76], N[(k * N[(y2 * N[(y5 * (-y0) + N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.8e-250], N[(N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.35e-58], N[(c * N[(y2 * N[((-t) * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -8.4999999999999996e148 or 2.34999999999999997e-58 < k

   1. Initial program 22.3%

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

   3. Taylor expanded in k around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. neg-mul-1 N/A

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

   5. Simplified 54.5%

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

   6. Taylor expanded in i around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

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

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

      7. *-lowering-*.f64 46.8

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

   8. Simplified 46.8%

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

   9. Taylor expanded in y around inf

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

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

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

       2. +-commutative N/A

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

       3. mul-1-neg N/A

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

       4. associate-/l* N/A

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

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

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

       6. mul-1-neg N/A

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

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

          \[\leadsto k \cdot \left(i \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y1, \frac{z}{y}, y5\right)}\right)\right) \]

       8. mul-1-neg N/A

          \[\leadsto k \cdot \left(i \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y1\right)}, \frac{z}{y}, y5\right)\right)\right) \]

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

          \[\leadsto k \cdot \left(i \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y1\right)}, \frac{z}{y}, y5\right)\right)\right) \]

       10. /-lowering-/.f64 50.8

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

   11. Simplified 50.8%

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

   if -8.4999999999999996e148 < k < -9.20000000000000025e-76

   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 43.9%

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

   6. Taylor expanded in k around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 48.6

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

   8. Simplified 48.6%

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

   if -9.20000000000000025e-76 < k < 4.7999999999999998e-250

   1. Initial program 40.5%

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

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

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

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

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

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

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

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

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

      10. *-commutative N/A

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

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

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

      12. *-lowering-*.f64 43.3

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

   8. Simplified 43.3%

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

   if 4.7999999999999998e-250 < k < 2.34999999999999997e-58

   1. Initial program 27.5%

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

   3. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

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

   5. Simplified 52.9%

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

   6. Taylor expanded in y2 around -inf

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

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

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

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

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

      7. *-lowering-*.f64 53.5

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

   8. Simplified 53.5%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -8.5 \cdot 10^{+148}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot \mathsf{fma}\left(-y1, \frac{z}{y}, y5\right)\right)\right)\\ \mathbf{elif}\;k \leq -9.2 \cdot 10^{-76}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-250}:\\ \;\;\;\;\left(x \cdot y1 - t \cdot y5\right) \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;k \leq 2.35 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot \mathsf{fma}\left(-y1, \frac{z}{y}, y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -8.2 \cdot 10^{+226}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -1.02 \cdot 10^{+80}:\\ \;\;\;\;k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, y4 \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -1.05 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(\left(-y5\right) \cdot \mathsf{fma}\left(y0, -y3, t \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(a \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 4.2 \cdot 10^{+165}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -8.2e+226)
   (* j (* y0 (fma x (- b) (* y3 y5))))
   (if (<= y0 -1.02e+80)
     (* k (* b (fma y0 z (* y4 (- y)))))
     (if (<= y0 -1.05e-35)
       (* j (* (- y5) (fma y0 (- y3) (* t i))))
       (if (<= y0 3.5e-284)
         (* y (* a (fma (- y3) y5 (* x b))))
         (if (<= y0 4.2e+165)
           (* y (* i (- (* k y5) (* x c))))
           (* c (* y2 (fma (- t) y4 (* x y0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -8.2e+226) {
		tmp = j * (y0 * fma(x, -b, (y3 * y5)));
	} else if (y0 <= -1.02e+80) {
		tmp = k * (b * fma(y0, z, (y4 * -y)));
	} else if (y0 <= -1.05e-35) {
		tmp = j * (-y5 * fma(y0, -y3, (t * i)));
	} else if (y0 <= 3.5e-284) {
		tmp = y * (a * fma(-y3, y5, (x * b)));
	} else if (y0 <= 4.2e+165) {
		tmp = y * (i * ((k * y5) - (x * c)));
	} else {
		tmp = c * (y2 * fma(-t, y4, (x * y0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -8.2e+226)
		tmp = Float64(j * Float64(y0 * fma(x, Float64(-b), Float64(y3 * y5))));
	elseif (y0 <= -1.02e+80)
		tmp = Float64(k * Float64(b * fma(y0, z, Float64(y4 * Float64(-y)))));
	elseif (y0 <= -1.05e-35)
		tmp = Float64(j * Float64(Float64(-y5) * fma(y0, Float64(-y3), Float64(t * i))));
	elseif (y0 <= 3.5e-284)
		tmp = Float64(y * Float64(a * fma(Float64(-y3), y5, Float64(x * b))));
	elseif (y0 <= 4.2e+165)
		tmp = Float64(y * Float64(i * Float64(Float64(k * y5) - Float64(x * c))));
	else
		tmp = Float64(c * Float64(y2 * fma(Float64(-t), y4, Float64(x * y0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -8.2e+226], N[(j * N[(y0 * N[(x * (-b) + N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.02e+80], N[(k * N[(b * N[(y0 * z + N[(y4 * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.05e-35], N[(j * N[((-y5) * N[(y0 * (-y3) + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.5e-284], N[(y * N[(a * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.2e+165], N[(y * N[(i * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y2 * N[((-t) * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -8.19999999999999971e226

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 61.2%

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

   6. Taylor expanded in 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. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

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

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(x, -1 \cdot b, y3 \cdot y5\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

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

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      10. *-lowering-*.f64 77.9

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

   8. Simplified 77.9%

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

   if -8.19999999999999971e226 < y0 < -1.02e80

   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 k around inf

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

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. neg-mul-1 N/A

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

   5. Simplified 62.2%

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

   6. Taylor expanded in b around inf

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

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

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

      2. +-commutative N/A

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

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

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

      4. associate-*r* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. neg-lowering-neg.f64 52.5

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

   8. Simplified 52.5%

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

   if -1.02e80 < y0 < -1.05e-35

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 57.8%

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

   6. Taylor expanded in y5 around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. mul-1-neg N/A

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

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

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

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

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

      14. mul-1-neg N/A

          \[\leadsto \left(y5 \cdot \mathsf{fma}\left(y0, \mathsf{neg}\left(y3\right), i \cdot t\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(j\right)\right)} \]

      15. neg-lowering-neg.f64 50.9

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

   8. Simplified 50.9%

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

   if -1.05e-35 < y0 < 3.49999999999999975e-284

   1. Initial program 30.6%

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

   3. Taylor expanded in 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 50.0%

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

   6. Taylor expanded in a around inf

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

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

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

      2. associate-*r* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. *-lowering-*.f64 44.2

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

   8. Simplified 44.2%

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

   if 3.49999999999999975e-284 < y0 < 4.2000000000000001e165

   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 46.2%

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

   6. Taylor expanded in i around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

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

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

      7. *-lowering-*.f64 42.2

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

   8. Simplified 42.2%

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

   if 4.2000000000000001e165 < y0

   1. Initial program 20.4%

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

   3. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

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

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 54.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around -inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot t\right) \cdot y4} + x \cdot y0\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot t, y4, x \cdot y0\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      7. *-lowering-*.f64 63.5

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, \color{blue}{x \cdot y0}\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -8.2 \cdot 10^{+226}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -1.02 \cdot 10^{+80}:\\ \;\;\;\;k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, y4 \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -1.05 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(\left(-y5\right) \cdot \mathsf{fma}\left(y0, -y3, t \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(a \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 4.2 \cdot 10^{+165}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -1.6 \cdot 10^{+193}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -8.4 \cdot 10^{+130}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -3.4 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \left(a \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -1.6e+193)
   (* j (* y0 (fma x (- b) (* y3 y5))))
   (if (<= y0 -8.4e+130)
     (* k (* y2 (fma y5 (- y0) (* y1 y4))))
     (if (<= y0 -3.4e-101)
       (* b (* y4 (fma (- k) y (* t j))))
       (if (<= y0 7.5e-282)
         (* y (* a (fma (- y3) y5 (* x b))))
         (if (<= y0 6e+168)
           (* y (* i (- (* k y5) (* x c))))
           (* c (* y2 (fma (- t) y4 (* x y0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1.6e+193) {
		tmp = j * (y0 * fma(x, -b, (y3 * y5)));
	} else if (y0 <= -8.4e+130) {
		tmp = k * (y2 * fma(y5, -y0, (y1 * y4)));
	} else if (y0 <= -3.4e-101) {
		tmp = b * (y4 * fma(-k, y, (t * j)));
	} else if (y0 <= 7.5e-282) {
		tmp = y * (a * fma(-y3, y5, (x * b)));
	} else if (y0 <= 6e+168) {
		tmp = y * (i * ((k * y5) - (x * c)));
	} else {
		tmp = c * (y2 * fma(-t, y4, (x * y0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -1.6e+193)
		tmp = Float64(j * Float64(y0 * fma(x, Float64(-b), Float64(y3 * y5))));
	elseif (y0 <= -8.4e+130)
		tmp = Float64(k * Float64(y2 * fma(y5, Float64(-y0), Float64(y1 * y4))));
	elseif (y0 <= -3.4e-101)
		tmp = Float64(b * Float64(y4 * fma(Float64(-k), y, Float64(t * j))));
	elseif (y0 <= 7.5e-282)
		tmp = Float64(y * Float64(a * fma(Float64(-y3), y5, Float64(x * b))));
	elseif (y0 <= 6e+168)
		tmp = Float64(y * Float64(i * Float64(Float64(k * y5) - Float64(x * c))));
	else
		tmp = Float64(c * Float64(y2 * fma(Float64(-t), y4, Float64(x * y0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -1.6e+193], N[(j * N[(y0 * N[(x * (-b) + N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -8.4e+130], N[(k * N[(y2 * N[(y5 * (-y0) + N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.4e-101], N[(b * N[(y4 * N[((-k) * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7.5e-282], N[(y * N[(a * N[((-y3) * y5 + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6e+168], N[(y * N[(i * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y2 * N[((-t) * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -1.60000000000000007e193

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 56.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   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. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot x\right)\right)} + y3 \cdot y5\right)\right) \]

      4. *-commutative N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\left(\mathsf{neg}\left(\color{blue}{x \cdot b}\right)\right) + y3 \cdot y5\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{x \cdot \left(\mathsf{neg}\left(b\right)\right)} + y3 \cdot y5\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(x \cdot \color{blue}{\left(-1 \cdot b\right)} + y3 \cdot y5\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(x, -1 \cdot b, y3 \cdot y5\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      10. *-lowering-*.f64 68.3

          \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, \color{blue}{y3 \cdot y5}\right)\right) \]

   8. Simplified 68.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)} \]

   if -1.60000000000000007e193 < y0 < -8.39999999999999962e130

   1. Initial program 18.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 50.3%

      \[\leadsto \color{blue}{y2 \cdot \mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, \left(c \cdot y4 - a \cdot y5\right) \cdot \left(-t\right)\right)\right)} \]

   6. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot y4 + \left(\mathsf{neg}\left(y0 \cdot y5\right)\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y0 \cdot y5\right)\right) + y1 \cdot y4\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(\left(\mathsf{neg}\left(\color{blue}{y5 \cdot y0}\right)\right) + y1 \cdot y4\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(\color{blue}{y5 \cdot \left(\mathsf{neg}\left(y0\right)\right)} + y1 \cdot y4\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto k \cdot \left(y2 \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot y0\right)} + y1 \cdot y4\right)\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto k \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(y5, -1 \cdot y0, y1 \cdot y4\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, \color{blue}{\mathsf{neg}\left(y0\right)}, y1 \cdot y4\right)\right) \]

      10. neg-lowering-neg.f64 N/A

          \[\leadsto k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, \color{blue}{\mathsf{neg}\left(y0\right)}, y1 \cdot y4\right)\right) \]

      11. *-commutative N/A

          \[\leadsto k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, \mathsf{neg}\left(y0\right), \color{blue}{y4 \cdot y1}\right)\right) \]

      12. *-lowering-*.f64 63.5

          \[\leadsto k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, \color{blue}{y4 \cdot y1}\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y4 \cdot y1\right)\right)} \]

   if -8.39999999999999962e130 < y0 < -3.39999999999999989e-101

   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 y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 43.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(k \cdot y\right)\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(k \cdot y\right)\right) + j \cdot t\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{-1 \cdot \left(k \cdot y\right)} + j \cdot t\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot y} + j \cdot t\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot k, y, j \cdot t\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      10. *-lowering-*.f64 45.9

          \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, \color{blue}{j \cdot t}\right)\right) \]

   8. Simplified 45.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]

   if -3.39999999999999989e-101 < y0 < 7.49999999999999937e-282

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 55.6%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto y \cdot \left(a \cdot \left(\color{blue}{\left(-1 \cdot y3\right) \cdot y5} + b \cdot x\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y3, y5, b \cdot x\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto y \cdot \left(a \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y3\right)}, y5, b \cdot x\right)\right) \]

      6. *-lowering-*.f64 43.3

         \[\leadsto y \cdot \left(a \cdot \mathsf{fma}\left(-y3, y5, \color{blue}{b \cdot x}\right)\right) \]

   8. Simplified 43.3%

      \[\leadsto y \cdot \color{blue}{\left(a \cdot \mathsf{fma}\left(-y3, y5, b \cdot x\right)\right)} \]

   if 7.49999999999999937e-282 < y0 < 5.9999999999999996e168

   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 46.2%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y \cdot \left(i \cdot \color{blue}{\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(i \cdot \left(k \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(c \cdot x\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto y \cdot \left(i \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto y \cdot \left(i \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto y \cdot \left(i \cdot \left(\color{blue}{k \cdot y5} - c \cdot x\right)\right) \]

      7. *-lowering-*.f64 42.2

         \[\leadsto y \cdot \left(i \cdot \left(k \cdot y5 - \color{blue}{c \cdot x}\right)\right) \]

   8. Simplified 42.2%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(k \cdot y5 - c \cdot x\right)\right)} \]

   if 5.9999999999999996e168 < y0

   1. Initial program 20.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 54.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around -inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot t\right) \cdot y4} + x \cdot y0\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot t, y4, x \cdot y0\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      7. *-lowering-*.f64 63.5

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, \color{blue}{x \cdot y0}\right)\right) \]

   8. Simplified 63.5%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.6 \cdot 10^{+193}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -8.4 \cdot 10^{+130}:\\ \;\;\;\;k \cdot \left(y2 \cdot \mathsf{fma}\left(y5, -y0, y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -3.4 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 7.5 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \left(a \cdot \mathsf{fma}\left(-y3, y5, x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 6 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -4.6 \cdot 10^{+226}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -2.9 \cdot 10^{+131}:\\ \;\;\;\;k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, y4 \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -8.2 \cdot 10^{-188}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 2.65 \cdot 10^{-89}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 2.3 \cdot 10^{+128}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -4.6e+226)
   (* j (* y0 (fma x (- b) (* y3 y5))))
   (if (<= y0 -2.9e+131)
     (* k (* b (fma y0 z (* y4 (- y)))))
     (if (<= y0 -8.2e-188)
       (* b (* y4 (fma (- k) y (* t j))))
       (if (<= y0 2.65e-89)
         (* k (* i (- (* y y5) (* z y1))))
         (if (<= y0 2.3e+128)
           (* c (* y (fma (- i) x (* y3 y4))))
           (* c (* y2 (fma (- t) y4 (* x y0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.6e+226) {
		tmp = j * (y0 * fma(x, -b, (y3 * y5)));
	} else if (y0 <= -2.9e+131) {
		tmp = k * (b * fma(y0, z, (y4 * -y)));
	} else if (y0 <= -8.2e-188) {
		tmp = b * (y4 * fma(-k, y, (t * j)));
	} else if (y0 <= 2.65e-89) {
		tmp = k * (i * ((y * y5) - (z * y1)));
	} else if (y0 <= 2.3e+128) {
		tmp = c * (y * fma(-i, x, (y3 * y4)));
	} else {
		tmp = c * (y2 * fma(-t, y4, (x * y0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -4.6e+226)
		tmp = Float64(j * Float64(y0 * fma(x, Float64(-b), Float64(y3 * y5))));
	elseif (y0 <= -2.9e+131)
		tmp = Float64(k * Float64(b * fma(y0, z, Float64(y4 * Float64(-y)))));
	elseif (y0 <= -8.2e-188)
		tmp = Float64(b * Float64(y4 * fma(Float64(-k), y, Float64(t * j))));
	elseif (y0 <= 2.65e-89)
		tmp = Float64(k * Float64(i * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (y0 <= 2.3e+128)
		tmp = Float64(c * Float64(y * fma(Float64(-i), x, Float64(y3 * y4))));
	else
		tmp = Float64(c * Float64(y2 * fma(Float64(-t), y4, Float64(x * y0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -4.6e+226], N[(j * N[(y0 * N[(x * (-b) + N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.9e+131], N[(k * N[(b * N[(y0 * z + N[(y4 * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -8.2e-188], N[(b * N[(y4 * N[((-k) * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.65e-89], N[(k * N[(i * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.3e+128], N[(c * N[(y * N[((-i) * x + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y2 * N[((-t) * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -4.5999999999999999e226

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 61.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in 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. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot x\right)\right)} + y3 \cdot y5\right)\right) \]

      4. *-commutative N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\left(\mathsf{neg}\left(\color{blue}{x \cdot b}\right)\right) + y3 \cdot y5\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{x \cdot \left(\mathsf{neg}\left(b\right)\right)} + y3 \cdot y5\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(x \cdot \color{blue}{\left(-1 \cdot b\right)} + y3 \cdot y5\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(x, -1 \cdot b, y3 \cdot y5\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      10. *-lowering-*.f64 77.9

          \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, \color{blue}{y3 \cdot y5}\right)\right) \]

   8. Simplified 77.9%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)} \]

   if -4.5999999999999999e226 < y0 < -2.9000000000000001e131

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 63.6%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto k \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \left(y \cdot y4\right) + y0 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \left(y \cdot y4\right) + y0 \cdot z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(b \cdot \color{blue}{\left(y0 \cdot z + -1 \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto k \cdot \left(b \cdot \color{blue}{\mathsf{fma}\left(y0, z, -1 \cdot \left(y \cdot y4\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, \color{blue}{\left(-1 \cdot y\right) \cdot y4}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, \color{blue}{\left(-1 \cdot y\right) \cdot y4}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y4\right)\right) \]

      7. neg-lowering-neg.f64 59.7

         \[\leadsto k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, \color{blue}{\left(-y\right)} \cdot y4\right)\right) \]

   8. Simplified 59.7%

      \[\leadsto k \cdot \color{blue}{\left(b \cdot \mathsf{fma}\left(y0, z, \left(-y\right) \cdot y4\right)\right)} \]

   if -2.9000000000000001e131 < y0 < -8.19999999999999965e-188

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 42.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(k \cdot y\right)\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(k \cdot y\right)\right) + j \cdot t\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{-1 \cdot \left(k \cdot y\right)} + j \cdot t\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot y} + j \cdot t\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot k, y, j \cdot t\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      10. *-lowering-*.f64 39.5

          \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, \color{blue}{j \cdot t}\right)\right) \]

   8. Simplified 39.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]

   if -8.19999999999999965e-188 < y0 < 2.65e-89

   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 k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 46.0%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right)\right) \]

      7. *-lowering-*.f64 42.8

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

   8. Simplified 42.8%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   if 2.65e-89 < y0 < 2.29999999999999998e128

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 48.1%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot i\right) \cdot x} + y3 \cdot y4\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot i, x, y3 \cdot y4\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      7. *-lowering-*.f64 41.6

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, \color{blue}{y3 \cdot y4}\right)\right) \]

   8. Simplified 41.6%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)} \]

   if 2.29999999999999998e128 < y0

   1. Initial program 18.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 59.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around -inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot t\right) \cdot y4} + x \cdot y0\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot t, y4, x \cdot y0\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      7. *-lowering-*.f64 62.1

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, \color{blue}{x \cdot y0}\right)\right) \]

   8. Simplified 62.1%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.6 \cdot 10^{+226}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -2.9 \cdot 10^{+131}:\\ \;\;\;\;k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, y4 \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -8.2 \cdot 10^{-188}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 2.65 \cdot 10^{-89}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 2.3 \cdot 10^{+128}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -5 \cdot 10^{-307}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 3.7 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+15}:\\ \;\;\;\;k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, y4 \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 8.6 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y0 (fma x (- b) (* y3 y5))))))
   (if (<= y2 -1.9e+73)
     (* c (* y2 (fma (- t) y4 (* x y0))))
     (if (<= y2 -5e-307)
       (* c (* y (fma (- i) x (* y3 y4))))
       (if (<= y2 3.7e-207)
         t_1
         (if (<= y2 7.5e+15)
           (* k (* b (fma y0 z (* y4 (- y)))))
           (if (<= y2 8.6e+120) t_1 (* a (* y2 (fma (- x) y1 (* t 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 = j * (y0 * fma(x, -b, (y3 * y5)));
	double tmp;
	if (y2 <= -1.9e+73) {
		tmp = c * (y2 * fma(-t, y4, (x * y0)));
	} else if (y2 <= -5e-307) {
		tmp = c * (y * fma(-i, x, (y3 * y4)));
	} else if (y2 <= 3.7e-207) {
		tmp = t_1;
	} else if (y2 <= 7.5e+15) {
		tmp = k * (b * fma(y0, z, (y4 * -y)));
	} else if (y2 <= 8.6e+120) {
		tmp = t_1;
	} else {
		tmp = a * (y2 * fma(-x, y1, (t * 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(j * Float64(y0 * fma(x, Float64(-b), Float64(y3 * y5))))
	tmp = 0.0
	if (y2 <= -1.9e+73)
		tmp = Float64(c * Float64(y2 * fma(Float64(-t), y4, Float64(x * y0))));
	elseif (y2 <= -5e-307)
		tmp = Float64(c * Float64(y * fma(Float64(-i), x, Float64(y3 * y4))));
	elseif (y2 <= 3.7e-207)
		tmp = t_1;
	elseif (y2 <= 7.5e+15)
		tmp = Float64(k * Float64(b * fma(y0, z, Float64(y4 * Float64(-y)))));
	elseif (y2 <= 8.6e+120)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(y2 * fma(Float64(-x), y1, Float64(t * 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[(j * N[(y0 * N[(x * (-b) + N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.9e+73], N[(c * N[(y2 * N[((-t) * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5e-307], N[(c * N[(y * N[((-i) * x + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.7e-207], t$95$1, If[LessEqual[y2, 7.5e+15], N[(k * N[(b * N[(y0 * z + N[(y4 * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 8.6e+120], t$95$1, N[(a * N[(y2 * N[((-x) * y1 + N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -1.90000000000000011e73

   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 c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 40.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around -inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot t\right) \cdot y4} + x \cdot y0\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot t, y4, x \cdot y0\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      7. *-lowering-*.f64 46.7

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, \color{blue}{x \cdot y0}\right)\right) \]

   8. Simplified 46.7%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)} \]

   if -1.90000000000000011e73 < y2 < -5.00000000000000014e-307

   1. Initial program 27.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 44.6%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot i\right) \cdot x} + y3 \cdot y4\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot i, x, y3 \cdot y4\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      7. *-lowering-*.f64 37.8

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, \color{blue}{y3 \cdot y4}\right)\right) \]

   8. Simplified 37.8%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)} \]

   if -5.00000000000000014e-307 < y2 < 3.69999999999999984e-207 or 7.5e15 < y2 < 8.6000000000000003e120

   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 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 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in 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. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot x\right)\right)} + y3 \cdot y5\right)\right) \]

      4. *-commutative N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\left(\mathsf{neg}\left(\color{blue}{x \cdot b}\right)\right) + y3 \cdot y5\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{x \cdot \left(\mathsf{neg}\left(b\right)\right)} + y3 \cdot y5\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(x \cdot \color{blue}{\left(-1 \cdot b\right)} + y3 \cdot y5\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(x, -1 \cdot b, y3 \cdot y5\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      10. *-lowering-*.f64 59.6

          \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, \color{blue}{y3 \cdot y5}\right)\right) \]

   8. Simplified 59.6%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)} \]

   if 3.69999999999999984e-207 < y2 < 7.5e15

   1. Initial program 40.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 45.0%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto k \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \left(y \cdot y4\right) + y0 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \left(y \cdot y4\right) + y0 \cdot z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(b \cdot \color{blue}{\left(y0 \cdot z + -1 \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto k \cdot \left(b \cdot \color{blue}{\mathsf{fma}\left(y0, z, -1 \cdot \left(y \cdot y4\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, \color{blue}{\left(-1 \cdot y\right) \cdot y4}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, \color{blue}{\left(-1 \cdot y\right) \cdot y4}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y4\right)\right) \]

      7. neg-lowering-neg.f64 47.8

         \[\leadsto k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, \color{blue}{\left(-y\right)} \cdot y4\right)\right) \]

   8. Simplified 47.8%

      \[\leadsto k \cdot \color{blue}{\left(b \cdot \mathsf{fma}\left(y0, z, \left(-y\right) \cdot y4\right)\right)} \]

   if 8.6000000000000003e120 < y2

   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 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 47.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. *-lowering-*.f64 52.5

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 52.5%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -5 \cdot 10^{-307}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 3.7 \cdot 10^{-207}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+15}:\\ \;\;\;\;k \cdot \left(b \cdot \mathsf{fma}\left(y0, z, y4 \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 8.6 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 21.0% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -7 \cdot 10^{+149}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -3.4 \cdot 10^{+20}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;k \leq 8.6 \cdot 10^{+252}:\\ \;\;\;\;\left(-i\right) \cdot \left(z \cdot \left(k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(y \cdot k\right) \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -7e+149)
   (* k (* i (* y y5)))
   (if (<= k -3.4e+20)
     (* y1 (* y4 (* k y2)))
     (if (<= k 2.8e-60)
       (* c (* x (* y0 y2)))
       (if (<= k 7.5e+120)
         (* a (* y2 (* x (- y1))))
         (if (<= k 8.6e+252)
           (* (- i) (* z (* k y1)))
           (* i (* (* y k) 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 (k <= -7e+149) {
		tmp = k * (i * (y * y5));
	} else if (k <= -3.4e+20) {
		tmp = y1 * (y4 * (k * y2));
	} else if (k <= 2.8e-60) {
		tmp = c * (x * (y0 * y2));
	} else if (k <= 7.5e+120) {
		tmp = a * (y2 * (x * -y1));
	} else if (k <= 8.6e+252) {
		tmp = -i * (z * (k * y1));
	} else {
		tmp = i * ((y * k) * y5);
	}
	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 (k <= (-7d+149)) then
        tmp = k * (i * (y * y5))
    else if (k <= (-3.4d+20)) then
        tmp = y1 * (y4 * (k * y2))
    else if (k <= 2.8d-60) then
        tmp = c * (x * (y0 * y2))
    else if (k <= 7.5d+120) then
        tmp = a * (y2 * (x * -y1))
    else if (k <= 8.6d+252) then
        tmp = -i * (z * (k * y1))
    else
        tmp = i * ((y * k) * y5)
    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 (k <= -7e+149) {
		tmp = k * (i * (y * y5));
	} else if (k <= -3.4e+20) {
		tmp = y1 * (y4 * (k * y2));
	} else if (k <= 2.8e-60) {
		tmp = c * (x * (y0 * y2));
	} else if (k <= 7.5e+120) {
		tmp = a * (y2 * (x * -y1));
	} else if (k <= 8.6e+252) {
		tmp = -i * (z * (k * y1));
	} else {
		tmp = i * ((y * k) * y5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if k <= -7e+149:
		tmp = k * (i * (y * y5))
	elif k <= -3.4e+20:
		tmp = y1 * (y4 * (k * y2))
	elif k <= 2.8e-60:
		tmp = c * (x * (y0 * y2))
	elif k <= 7.5e+120:
		tmp = a * (y2 * (x * -y1))
	elif k <= 8.6e+252:
		tmp = -i * (z * (k * y1))
	else:
		tmp = i * ((y * k) * 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 (k <= -7e+149)
		tmp = Float64(k * Float64(i * Float64(y * y5)));
	elseif (k <= -3.4e+20)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (k <= 2.8e-60)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (k <= 7.5e+120)
		tmp = Float64(a * Float64(y2 * Float64(x * Float64(-y1))));
	elseif (k <= 8.6e+252)
		tmp = Float64(Float64(-i) * Float64(z * Float64(k * y1)));
	else
		tmp = Float64(i * Float64(Float64(y * k) * y5));
	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 (k <= -7e+149)
		tmp = k * (i * (y * y5));
	elseif (k <= -3.4e+20)
		tmp = y1 * (y4 * (k * y2));
	elseif (k <= 2.8e-60)
		tmp = c * (x * (y0 * y2));
	elseif (k <= 7.5e+120)
		tmp = a * (y2 * (x * -y1));
	elseif (k <= 8.6e+252)
		tmp = -i * (z * (k * y1));
	else
		tmp = i * ((y * k) * y5);
	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[k, -7e+149], N[(k * N[(i * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.4e+20], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.8e-60], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.5e+120], N[(a * N[(y2 * N[(x * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.6e+252], N[((-i) * N[(z * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(y * k), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -7.00000000000000023e149

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 63.6%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right)\right) \]

      7. *-lowering-*.f64 58.7

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

   8. Simplified 58.7%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y5 \cdot y\right)}\right) \]

       3. *-lowering-*.f64 42.0

          \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y5 \cdot y\right)}\right) \]

   11. Simplified 42.0%

       \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y\right)\right)} \]

   if -7.00000000000000023e149 < k < -3.4e20

   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 y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y3} + k \cdot y2\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot j, y3, k \cdot y2\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(j\right)}, y3, k \cdot y2\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(j\right)}, y3, k \cdot y2\right)\right) \]

      7. *-lowering-*.f64 47.3

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(-j, y3, \color{blue}{k \cdot y2}\right)\right) \]

   8. Simplified 47.3%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \mathsf{fma}\left(-j, y3, k \cdot y2\right)\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 44.2

          \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot k\right)}\right) \]

   11. Simplified 44.2%

       \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot k\right)}\right) \]

   if -3.4e20 < k < 2.8000000000000002e-60

   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 c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 46.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right)} \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y0} + t \cdot y4\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y0, t \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      10. *-lowering-*.f64 34.4

          \[\leadsto -\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, \color{blue}{t \cdot y4}\right) \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{-\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

       4. *-lowering-*.f64 29.8

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   11. Simplified 29.8%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if 2.8000000000000002e-60 < k < 7.5000000000000006e120

   1. Initial program 21.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 32.2%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. *-lowering-*.f64 37.2

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 37.2%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(x \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(\mathsf{neg}\left(x \cdot y1\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \left(\mathsf{neg}\left(\color{blue}{y1 \cdot x}\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

       4. mul-1-neg N/A

          \[\leadsto a \cdot \left(y2 \cdot \left(y1 \cdot \color{blue}{\left(-1 \cdot x\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot x\right)\right)}\right) \]

       6. mul-1-neg N/A

          \[\leadsto a \cdot \left(y2 \cdot \left(y1 \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right) \]

       7. neg-lowering-neg.f64 37.6

          \[\leadsto a \cdot \left(y2 \cdot \left(y1 \cdot \color{blue}{\left(-x\right)}\right)\right) \]

   11. Simplified 37.6%

       \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y1 \cdot \left(-x\right)\right)}\right) \]

   if 7.5000000000000006e120 < k < 8.6000000000000004e252

   1. Initial program 23.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 48.2%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right)\right) \]

      7. *-lowering-*.f64 48.8

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

   8. Simplified 48.8%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]

       2. neg-lowering-neg.f64 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)}\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)}\right) \]

       6. *-lowering-*.f64 44.2

          \[\leadsto -i \cdot \left(\color{blue}{\left(k \cdot y1\right)} \cdot z\right) \]

   11. Simplified 44.2%

       \[\leadsto \color{blue}{-i \cdot \left(\left(k \cdot y1\right) \cdot z\right)} \]

   if 8.6000000000000004e252 < k

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right)\right) \]

      7. *-lowering-*.f64 58.6

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

   8. Simplified 58.6%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot y5\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot y5\right)} \]

       4. *-lowering-*.f64 71.6

          \[\leadsto i \cdot \left(\color{blue}{\left(k \cdot y\right)} \cdot y5\right) \]

   11. Simplified 71.6%

       \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y\right) \cdot y5\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -7 \cdot 10^{+149}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -3.4 \cdot 10^{+20}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(x \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;k \leq 8.6 \cdot 10^{+252}:\\ \;\;\;\;\left(-i\right) \cdot \left(z \cdot \left(k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(y \cdot k\right) \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.0% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -3.35 \cdot 10^{+128}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.1 \cdot 10^{-253}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 5.4 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 8.2 \cdot 10^{+176}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -3.35e+128)
   (* c (* x (* y0 y2)))
   (if (<= y0 -1.1e-253)
     (* b (* y4 (fma (- k) y (* t j))))
     (if (<= y0 5.4e-71)
       (* a (* y2 (fma (- x) y1 (* t y5))))
       (if (<= y0 8.2e+176)
         (* c (* y (fma (- i) x (* y3 y4))))
         (* (* x c) (* y0 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 (y0 <= -3.35e+128) {
		tmp = c * (x * (y0 * y2));
	} else if (y0 <= -1.1e-253) {
		tmp = b * (y4 * fma(-k, y, (t * j)));
	} else if (y0 <= 5.4e-71) {
		tmp = a * (y2 * fma(-x, y1, (t * y5)));
	} else if (y0 <= 8.2e+176) {
		tmp = c * (y * fma(-i, x, (y3 * y4)));
	} else {
		tmp = (x * c) * (y0 * 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 (y0 <= -3.35e+128)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y0 <= -1.1e-253)
		tmp = Float64(b * Float64(y4 * fma(Float64(-k), y, Float64(t * j))));
	elseif (y0 <= 5.4e-71)
		tmp = Float64(a * Float64(y2 * fma(Float64(-x), y1, Float64(t * y5))));
	elseif (y0 <= 8.2e+176)
		tmp = Float64(c * Float64(y * fma(Float64(-i), x, Float64(y3 * y4))));
	else
		tmp = Float64(Float64(x * c) * Float64(y0 * y2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -3.35e+128], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.1e-253], N[(b * N[(y4 * N[((-k) * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.4e-71], N[(a * N[(y2 * N[((-x) * y1 + N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8.2e+176], N[(c * N[(y * N[((-i) * x + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * c), $MachinePrecision] * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -3.34999999999999996e128

   1. Initial program 19.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 49.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right)} \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y0} + t \cdot y4\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y0, t \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      10. *-lowering-*.f64 37.6

          \[\leadsto -\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, \color{blue}{t \cdot y4}\right) \]

   8. Simplified 37.6%

      \[\leadsto \color{blue}{-\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

       4. *-lowering-*.f64 42.7

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   11. Simplified 42.7%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if -3.34999999999999996e128 < y0 < -1.09999999999999998e-253

   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 y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 41.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(k \cdot y\right)\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(k \cdot y\right)\right) + j \cdot t\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{-1 \cdot \left(k \cdot y\right)} + j \cdot t\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot y} + j \cdot t\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot k, y, j \cdot t\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      10. *-lowering-*.f64 37.3

          \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, \color{blue}{j \cdot t}\right)\right) \]

   8. Simplified 37.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]

   if -1.09999999999999998e-253 < y0 < 5.4000000000000003e-71

   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 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 41.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. *-lowering-*.f64 39.5

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 39.5%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   if 5.4000000000000003e-71 < y0 < 8.1999999999999998e176

   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 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 49.2%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot i\right) \cdot x} + y3 \cdot y4\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot i, x, y3 \cdot y4\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      7. *-lowering-*.f64 41.8

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, \color{blue}{y3 \cdot y4}\right)\right) \]

   8. Simplified 41.8%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)} \]

   if 8.1999999999999998e176 < y0

   1. Initial program 16.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 52.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right)} \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y0} + t \cdot y4\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y0, t \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      10. *-lowering-*.f64 52.6

          \[\leadsto -\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, \color{blue}{t \cdot y4}\right) \]

   8. Simplified 52.6%

      \[\leadsto \color{blue}{-\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{neg}\left(\color{blue}{-1 \cdot \left(c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(\color{blue}{\left(c \cdot x\right) \cdot \left(y0 \cdot y2\right)}\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot x\right) \cdot \left(\mathsf{neg}\left(y0 \cdot y2\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot x\right) \cdot \left(\mathsf{neg}\left(y0 \cdot y2\right)\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot x\right)} \cdot \left(\mathsf{neg}\left(y0 \cdot y2\right)\right)\right) \]

       6. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{neg}\left(\left(c \cdot x\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y0 \cdot y2\right)\right)}\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(c \cdot x\right) \cdot \left(\mathsf{neg}\left(\color{blue}{y2 \cdot y0}\right)\right)\right) \]

       8. *-lowering-*.f64 58.8

          \[\leadsto -\left(c \cdot x\right) \cdot \left(-\color{blue}{y2 \cdot y0}\right) \]

   11. Simplified 58.8%

       \[\leadsto -\color{blue}{\left(c \cdot x\right) \cdot \left(-y2 \cdot y0\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.35 \cdot 10^{+128}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.1 \cdot 10^{-253}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 5.4 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 8.2 \cdot 10^{+176}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y0 \cdot y2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.5% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;y0 \leq -3 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -1.05 \cdot 10^{-254}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 1.35 \cdot 10^{-13}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{+71}:\\ \;\;\;\;y1 \cdot \left(\left(j \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (* y0 y2)))))
   (if (<= y0 -3e+130)
     t_1
     (if (<= y0 -1.05e-254)
       (* b (* y4 (fma (- k) y (* t j))))
       (if (<= y0 1.35e-13)
         (* a (* y2 (fma (- x) y1 (* t y5))))
         (if (<= y0 1.7e+71) (* y1 (* (* j y3) (- 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 = c * (x * (y0 * y2));
	double tmp;
	if (y0 <= -3e+130) {
		tmp = t_1;
	} else if (y0 <= -1.05e-254) {
		tmp = b * (y4 * fma(-k, y, (t * j)));
	} else if (y0 <= 1.35e-13) {
		tmp = a * (y2 * fma(-x, y1, (t * y5)));
	} else if (y0 <= 1.7e+71) {
		tmp = y1 * ((j * y3) * -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(c * Float64(x * Float64(y0 * y2)))
	tmp = 0.0
	if (y0 <= -3e+130)
		tmp = t_1;
	elseif (y0 <= -1.05e-254)
		tmp = Float64(b * Float64(y4 * fma(Float64(-k), y, Float64(t * j))));
	elseif (y0 <= 1.35e-13)
		tmp = Float64(a * Float64(y2 * fma(Float64(-x), y1, Float64(t * y5))));
	elseif (y0 <= 1.7e+71)
		tmp = Float64(y1 * Float64(Float64(j * y3) * Float64(-y4)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3e+130], t$95$1, If[LessEqual[y0, -1.05e-254], N[(b * N[(y4 * N[((-k) * y + N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.35e-13], N[(a * N[(y2 * N[((-x) * y1 + N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.7e+71], N[(y1 * N[(N[(j * y3), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -2.9999999999999999e130 or 1.6999999999999999e71 < y0

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 55.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right)} \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y0} + t \cdot y4\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y0, t \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      10. *-lowering-*.f64 42.4

          \[\leadsto -\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, \color{blue}{t \cdot y4}\right) \]

   8. Simplified 42.4%

      \[\leadsto \color{blue}{-\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

       4. *-lowering-*.f64 44.3

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   11. Simplified 44.3%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if -2.9999999999999999e130 < y0 < -1.04999999999999998e-254

   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 y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 41.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(k \cdot y\right)\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(k \cdot y\right)\right) + j \cdot t\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{-1 \cdot \left(k \cdot y\right)} + j \cdot t\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot y} + j \cdot t\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot k, y, j \cdot t\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(k\right)}, y, j \cdot t\right)\right) \]

      10. *-lowering-*.f64 37.3

          \[\leadsto b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, \color{blue}{j \cdot t}\right)\right) \]

   8. Simplified 37.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, j \cdot t\right)\right)} \]

   if -1.04999999999999998e-254 < y0 < 1.35000000000000005e-13

   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 42.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. *-lowering-*.f64 37.2

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 37.2%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   if 1.35000000000000005e-13 < y0 < 1.6999999999999999e71

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 48.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y3} + k \cdot y2\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot j, y3, k \cdot y2\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(j\right)}, y3, k \cdot y2\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(j\right)}, y3, k \cdot y2\right)\right) \]

      7. *-lowering-*.f64 47.6

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(-j, y3, \color{blue}{k \cdot y2}\right)\right) \]

   8. Simplified 47.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \mathsf{fma}\left(-j, y3, k \cdot y2\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(\mathsf{neg}\left(j \cdot y3\right)\right)}\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(y3\right)\right)\right)}\right) \]

       3. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \left(j \cdot \color{blue}{\left(-1 \cdot y3\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot y3\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \left(j \cdot \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)}\right)\right) \]

       6. neg-lowering-neg.f64 47.9

          \[\leadsto y1 \cdot \left(y4 \cdot \left(j \cdot \color{blue}{\left(-y3\right)}\right)\right) \]

   11. Simplified 47.9%

       \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(j \cdot \left(-y3\right)\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3 \cdot 10^{+130}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.05 \cdot 10^{-254}:\\ \;\;\;\;b \cdot \left(y4 \cdot \mathsf{fma}\left(-k, y, t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 1.35 \cdot 10^{-13}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{+71}:\\ \;\;\;\;y1 \cdot \left(\left(j \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 33.6% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.32 \cdot 10^{+62}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.02 \cdot 10^{-305}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 6.6 \cdot 10^{+121}:\\ \;\;\;\;j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.32e+62)
   (* c (* y2 (fma (- t) y4 (* x y0))))
   (if (<= y2 1.02e-305)
     (* c (* y (fma (- i) x (* y3 y4))))
     (if (<= y2 6.6e+121)
       (* j (* y0 (fma x (- b) (* y3 y5))))
       (* a (* y2 (fma (- x) y1 (* t 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 (y2 <= -1.32e+62) {
		tmp = c * (y2 * fma(-t, y4, (x * y0)));
	} else if (y2 <= 1.02e-305) {
		tmp = c * (y * fma(-i, x, (y3 * y4)));
	} else if (y2 <= 6.6e+121) {
		tmp = j * (y0 * fma(x, -b, (y3 * y5)));
	} else {
		tmp = a * (y2 * fma(-x, y1, (t * 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 (y2 <= -1.32e+62)
		tmp = Float64(c * Float64(y2 * fma(Float64(-t), y4, Float64(x * y0))));
	elseif (y2 <= 1.02e-305)
		tmp = Float64(c * Float64(y * fma(Float64(-i), x, Float64(y3 * y4))));
	elseif (y2 <= 6.6e+121)
		tmp = Float64(j * Float64(y0 * fma(x, Float64(-b), Float64(y3 * y5))));
	else
		tmp = Float64(a * Float64(y2 * fma(Float64(-x), y1, Float64(t * 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[y2, -1.32e+62], N[(c * N[(y2 * N[((-t) * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.02e-305], N[(c * N[(y * N[((-i) * x + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.6e+121], N[(j * N[(y0 * N[(x * (-b) + N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y2 * N[((-x) * y1 + N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.3199999999999999e62

   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 c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 40.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around -inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot t\right) \cdot y4} + x \cdot y0\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot t, y4, x \cdot y0\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      7. *-lowering-*.f64 46.7

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, \color{blue}{x \cdot y0}\right)\right) \]

   8. Simplified 46.7%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)} \]

   if -1.3199999999999999e62 < y2 < 1.01999999999999994e-305

   1. Initial program 27.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 44.6%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot i\right) \cdot x} + y3 \cdot y4\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot i, x, y3 \cdot y4\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      7. *-lowering-*.f64 37.8

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, \color{blue}{y3 \cdot y4}\right)\right) \]

   8. Simplified 37.8%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)} \]

   if 1.01999999999999994e-305 < y2 < 6.59999999999999958e121

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 43.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   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. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot x\right)\right)} + y3 \cdot y5\right)\right) \]

      4. *-commutative N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\left(\mathsf{neg}\left(\color{blue}{x \cdot b}\right)\right) + y3 \cdot y5\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{x \cdot \left(\mathsf{neg}\left(b\right)\right)} + y3 \cdot y5\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(x \cdot \color{blue}{\left(-1 \cdot b\right)} + y3 \cdot y5\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(x, -1 \cdot b, y3 \cdot y5\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(b\right)}, y3 \cdot y5\right)\right) \]

      10. *-lowering-*.f64 44.7

          \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, \color{blue}{y3 \cdot y5}\right)\right) \]

   8. Simplified 44.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \mathsf{fma}\left(x, -b, y3 \cdot y5\right)\right)} \]

   if 6.59999999999999958e121 < y2

   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 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 47.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. *-lowering-*.f64 52.5

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 52.5%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 20: 28.3% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;y0 \leq -1.25 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 9.4 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{+68}:\\ \;\;\;\;y1 \cdot \left(\left(j \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (* y0 y2)))))
   (if (<= y0 -1.25e+125)
     t_1
     (if (<= y0 9.4e-14)
       (* a (* y2 (fma (- x) y1 (* t y5))))
       (if (<= y0 3.5e+68) (* y1 (* (* j y3) (- 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 = c * (x * (y0 * y2));
	double tmp;
	if (y0 <= -1.25e+125) {
		tmp = t_1;
	} else if (y0 <= 9.4e-14) {
		tmp = a * (y2 * fma(-x, y1, (t * y5)));
	} else if (y0 <= 3.5e+68) {
		tmp = y1 * ((j * y3) * -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(c * Float64(x * Float64(y0 * y2)))
	tmp = 0.0
	if (y0 <= -1.25e+125)
		tmp = t_1;
	elseif (y0 <= 9.4e-14)
		tmp = Float64(a * Float64(y2 * fma(Float64(-x), y1, Float64(t * y5))));
	elseif (y0 <= 3.5e+68)
		tmp = Float64(y1 * Float64(Float64(j * y3) * Float64(-y4)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.25e+125], t$95$1, If[LessEqual[y0, 9.4e-14], N[(a * N[(y2 * N[((-x) * y1 + N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.5e+68], N[(y1 * N[(N[(j * y3), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y0 < -1.24999999999999991e125 or 3.49999999999999977e68 < y0

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 54.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right)} \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y0} + t \cdot y4\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y0, t \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      10. *-lowering-*.f64 42.0

          \[\leadsto -\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, \color{blue}{t \cdot y4}\right) \]

   8. Simplified 42.0%

      \[\leadsto \color{blue}{-\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

       4. *-lowering-*.f64 43.9

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   11. Simplified 43.9%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if -1.24999999999999991e125 < y0 < 9.4000000000000003e-14

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-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 44.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. *-lowering-*.f64 31.9

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 31.9%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   if 9.4000000000000003e-14 < y0 < 3.49999999999999977e68

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 48.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y3} + k \cdot y2\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot j, y3, k \cdot y2\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(j\right)}, y3, k \cdot y2\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(j\right)}, y3, k \cdot y2\right)\right) \]

      7. *-lowering-*.f64 47.6

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(-j, y3, \color{blue}{k \cdot y2}\right)\right) \]

   8. Simplified 47.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \mathsf{fma}\left(-j, y3, k \cdot y2\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(\mathsf{neg}\left(j \cdot y3\right)\right)}\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(y3\right)\right)\right)}\right) \]

       3. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \left(j \cdot \color{blue}{\left(-1 \cdot y3\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot y3\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \left(j \cdot \color{blue}{\left(\mathsf{neg}\left(y3\right)\right)}\right)\right) \]

       6. neg-lowering-neg.f64 47.9

          \[\leadsto y1 \cdot \left(y4 \cdot \left(j \cdot \color{blue}{\left(-y3\right)}\right)\right) \]

   11. Simplified 47.9%

       \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(j \cdot \left(-y3\right)\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.25 \cdot 10^{+125}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 9.4 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{+68}:\\ \;\;\;\;y1 \cdot \left(\left(j \cdot y3\right) \cdot \left(-y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.9% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.7 \cdot 10^{+64}:\\ \;\;\;\;c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.8 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.7e+64)
   (* c (* y2 (fma (- t) y4 (* x y0))))
   (if (<= y2 1.8e+14)
     (* c (* y (fma (- i) x (* y3 y4))))
     (* a (* y2 (fma (- x) y1 (* t 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 (y2 <= -1.7e+64) {
		tmp = c * (y2 * fma(-t, y4, (x * y0)));
	} else if (y2 <= 1.8e+14) {
		tmp = c * (y * fma(-i, x, (y3 * y4)));
	} else {
		tmp = a * (y2 * fma(-x, y1, (t * 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 (y2 <= -1.7e+64)
		tmp = Float64(c * Float64(y2 * fma(Float64(-t), y4, Float64(x * y0))));
	elseif (y2 <= 1.8e+14)
		tmp = Float64(c * Float64(y * fma(Float64(-i), x, Float64(y3 * y4))));
	else
		tmp = Float64(a * Float64(y2 * fma(Float64(-x), y1, Float64(t * 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[y2, -1.7e+64], N[(c * N[(y2 * N[((-t) * y4 + N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.8e+14], N[(c * N[(y * N[((-i) * x + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y2 * N[((-x) * y1 + N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -1.7000000000000001e64

   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 c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 40.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around -inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(t \cdot y4\right) + x \cdot y0\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot t\right) \cdot y4} + x \cdot y0\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot t, y4, x \cdot y0\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(t\right)}, y4, x \cdot y0\right)\right) \]

      7. *-lowering-*.f64 46.7

         \[\leadsto c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, \color{blue}{x \cdot y0}\right)\right) \]

   8. Simplified 46.7%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \mathsf{fma}\left(-t, y4, x \cdot y0\right)\right)} \]

   if -1.7000000000000001e64 < y2 < 1.8e14

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 46.4%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{\left(-1 \cdot i\right) \cdot x} + y3 \cdot y4\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot i, x, y3 \cdot y4\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(i\right)}, x, y3 \cdot y4\right)\right) \]

      7. *-lowering-*.f64 36.0

         \[\leadsto c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, \color{blue}{y3 \cdot y4}\right)\right) \]

   8. Simplified 36.0%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \mathsf{fma}\left(-i, x, y3 \cdot y4\right)\right)} \]

   if 1.8e14 < y2

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 48.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. *-lowering-*.f64 47.2

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 47.2%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 21.3% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -9.6 \cdot 10^{+148}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2.15 \cdot 10^{+26}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{-53}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(y \cdot k\right) \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -9.6e+148)
   (* k (* i (* y y5)))
   (if (<= k -2.15e+26)
     (* y1 (* y4 (* k y2)))
     (if (<= k 1.85e-53) (* c (* x (* y0 y2))) (* i (* (* y k) 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 (k <= -9.6e+148) {
		tmp = k * (i * (y * y5));
	} else if (k <= -2.15e+26) {
		tmp = y1 * (y4 * (k * y2));
	} else if (k <= 1.85e-53) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = i * ((y * k) * y5);
	}
	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 (k <= (-9.6d+148)) then
        tmp = k * (i * (y * y5))
    else if (k <= (-2.15d+26)) then
        tmp = y1 * (y4 * (k * y2))
    else if (k <= 1.85d-53) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = i * ((y * k) * y5)
    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 (k <= -9.6e+148) {
		tmp = k * (i * (y * y5));
	} else if (k <= -2.15e+26) {
		tmp = y1 * (y4 * (k * y2));
	} else if (k <= 1.85e-53) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = i * ((y * k) * y5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if k <= -9.6e+148:
		tmp = k * (i * (y * y5))
	elif k <= -2.15e+26:
		tmp = y1 * (y4 * (k * y2))
	elif k <= 1.85e-53:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = i * ((y * k) * 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 (k <= -9.6e+148)
		tmp = Float64(k * Float64(i * Float64(y * y5)));
	elseif (k <= -2.15e+26)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (k <= 1.85e-53)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(i * Float64(Float64(y * k) * y5));
	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 (k <= -9.6e+148)
		tmp = k * (i * (y * y5));
	elseif (k <= -2.15e+26)
		tmp = y1 * (y4 * (k * y2));
	elseif (k <= 1.85e-53)
		tmp = c * (x * (y0 * y2));
	else
		tmp = i * ((y * k) * y5);
	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[k, -9.6e+148], N[(k * N[(i * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.15e+26], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.85e-53], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(y * k), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -9.59999999999999979e148

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 63.6%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right)\right) \]

      7. *-lowering-*.f64 58.7

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

   8. Simplified 58.7%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y5 \cdot y\right)}\right) \]

       3. *-lowering-*.f64 42.0

          \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y5 \cdot y\right)}\right) \]

   11. Simplified 42.0%

       \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y\right)\right)} \]

   if -9.59999999999999979e148 < k < -2.1499999999999999e26

   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 y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y3} + k \cdot y2\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot j, y3, k \cdot y2\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(j\right)}, y3, k \cdot y2\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(j\right)}, y3, k \cdot y2\right)\right) \]

      7. *-lowering-*.f64 47.3

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(-j, y3, \color{blue}{k \cdot y2}\right)\right) \]

   8. Simplified 47.3%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \mathsf{fma}\left(-j, y3, k \cdot y2\right)\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot k\right)}\right) \]

       2. *-lowering-*.f64 44.2

          \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot k\right)}\right) \]

   11. Simplified 44.2%

       \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot k\right)}\right) \]

   if -2.1499999999999999e26 < k < 1.84999999999999991e-53

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 47.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right)} \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y0} + t \cdot y4\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y0, t \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      10. *-lowering-*.f64 34.5

          \[\leadsto -\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, \color{blue}{t \cdot y4}\right) \]

   8. Simplified 34.5%

      \[\leadsto \color{blue}{-\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

       4. *-lowering-*.f64 29.1

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   11. Simplified 29.1%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if 1.84999999999999991e-53 < k

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 49.0%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right)\right) \]

      7. *-lowering-*.f64 39.6

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

   8. Simplified 39.6%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot y5\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot y5\right)} \]

       4. *-lowering-*.f64 32.6

          \[\leadsto i \cdot \left(\color{blue}{\left(k \cdot y\right)} \cdot y5\right) \]

   11. Simplified 32.6%

       \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y\right) \cdot y5\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9.6 \cdot 10^{+148}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -2.15 \cdot 10^{+26}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{-53}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(y \cdot k\right) \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.0% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -7 \cdot 10^{+147}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -4 \cdot 10^{+26}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-53}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(y \cdot k\right) \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -7e+147)
   (* k (* i (* y y5)))
   (if (<= k -4e+26)
     (* k (* y2 (* y1 y4)))
     (if (<= k 8.2e-53) (* c (* x (* y0 y2))) (* i (* (* y k) 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 (k <= -7e+147) {
		tmp = k * (i * (y * y5));
	} else if (k <= -4e+26) {
		tmp = k * (y2 * (y1 * y4));
	} else if (k <= 8.2e-53) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = i * ((y * k) * y5);
	}
	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 (k <= (-7d+147)) then
        tmp = k * (i * (y * y5))
    else if (k <= (-4d+26)) then
        tmp = k * (y2 * (y1 * y4))
    else if (k <= 8.2d-53) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = i * ((y * k) * y5)
    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 (k <= -7e+147) {
		tmp = k * (i * (y * y5));
	} else if (k <= -4e+26) {
		tmp = k * (y2 * (y1 * y4));
	} else if (k <= 8.2e-53) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = i * ((y * k) * y5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if k <= -7e+147:
		tmp = k * (i * (y * y5))
	elif k <= -4e+26:
		tmp = k * (y2 * (y1 * y4))
	elif k <= 8.2e-53:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = i * ((y * k) * 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 (k <= -7e+147)
		tmp = Float64(k * Float64(i * Float64(y * y5)));
	elseif (k <= -4e+26)
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	elseif (k <= 8.2e-53)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(i * Float64(Float64(y * k) * y5));
	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 (k <= -7e+147)
		tmp = k * (i * (y * y5));
	elseif (k <= -4e+26)
		tmp = k * (y2 * (y1 * y4));
	elseif (k <= 8.2e-53)
		tmp = c * (x * (y0 * y2));
	else
		tmp = i * ((y * k) * y5);
	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[k, -7e+147], N[(k * N[(i * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4e+26], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.2e-53], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(y * k), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -6.99999999999999949e147

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 63.6%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right)\right) \]

      7. *-lowering-*.f64 58.7

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

   8. Simplified 58.7%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y5 \cdot y\right)}\right) \]

       3. *-lowering-*.f64 42.0

          \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y5 \cdot y\right)}\right) \]

   11. Simplified 42.0%

       \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y\right)\right)} \]

   if -6.99999999999999949e147 < k < -4.00000000000000019e26

   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 y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. --lowering--.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, t \cdot j - k \cdot y, y1 \cdot \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right)\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto y1 \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y3} + k \cdot y2\right)\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot j, y3, k \cdot y2\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(j\right)}, y3, k \cdot y2\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(j\right)}, y3, k \cdot y2\right)\right) \]

      7. *-lowering-*.f64 47.3

         \[\leadsto y1 \cdot \left(y4 \cdot \mathsf{fma}\left(-j, y3, \color{blue}{k \cdot y2}\right)\right) \]

   8. Simplified 47.3%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \mathsf{fma}\left(-j, y3, k \cdot y2\right)\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   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. *-commutative N/A

          \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

       3. associate-*r* N/A

          \[\leadsto k \cdot \color{blue}{\left(\left(y1 \cdot y4\right) \cdot y2\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto k \cdot \color{blue}{\left(\left(y1 \cdot y4\right) \cdot y2\right)} \]

       5. *-lowering-*.f64 41.1

          \[\leadsto k \cdot \left(\color{blue}{\left(y1 \cdot y4\right)} \cdot y2\right) \]

   11. Simplified 41.1%

       \[\leadsto \color{blue}{k \cdot \left(\left(y1 \cdot y4\right) \cdot y2\right)} \]

   if -4.00000000000000019e26 < k < 8.2000000000000001e-53

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 47.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right)} \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y0} + t \cdot y4\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y0, t \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      10. *-lowering-*.f64 34.5

          \[\leadsto -\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, \color{blue}{t \cdot y4}\right) \]

   8. Simplified 34.5%

      \[\leadsto \color{blue}{-\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

       4. *-lowering-*.f64 29.1

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   11. Simplified 29.1%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if 8.2000000000000001e-53 < k

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 49.0%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right)\right) \]

      7. *-lowering-*.f64 39.6

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

   8. Simplified 39.6%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot y5\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot y5\right)} \]

       4. *-lowering-*.f64 32.6

          \[\leadsto i \cdot \left(\color{blue}{\left(k \cdot y\right)} \cdot y5\right) \]

   11. Simplified 32.6%

       \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y\right) \cdot y5\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -7 \cdot 10^{+147}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -4 \cdot 10^{+26}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-53}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(y \cdot k\right) \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.6% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;y0 \leq -1.1 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 6.4 \cdot 10^{+109}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (* y0 y2)))))
   (if (<= y0 -1.1e+29) t_1 (if (<= y0 6.4e+109) (* k (* i (* y y5))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (y0 <= -1.1e+29) {
		tmp = t_1;
	} else if (y0 <= 6.4e+109) {
		tmp = k * (i * (y * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (x * (y0 * y2))
    if (y0 <= (-1.1d+29)) then
        tmp = t_1
    else if (y0 <= 6.4d+109) then
        tmp = k * (i * (y * y5))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (y0 <= -1.1e+29) {
		tmp = t_1;
	} else if (y0 <= 6.4e+109) {
		tmp = k * (i * (y * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (x * (y0 * y2))
	tmp = 0
	if y0 <= -1.1e+29:
		tmp = t_1
	elif y0 <= 6.4e+109:
		tmp = k * (i * (y * y5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(x * Float64(y0 * y2)))
	tmp = 0.0
	if (y0 <= -1.1e+29)
		tmp = t_1;
	elseif (y0 <= 6.4e+109)
		tmp = Float64(k * Float64(i * Float64(y * y5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (x * (y0 * y2));
	tmp = 0.0;
	if (y0 <= -1.1e+29)
		tmp = t_1;
	elseif (y0 <= 6.4e+109)
		tmp = k * (i * (y * y5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.1e+29], t$95$1, If[LessEqual[y0, 6.4e+109], N[(k * N[(i * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y0 < -1.1000000000000001e29 or 6.4000000000000002e109 < y0

   1. Initial program 21.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 49.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right)} \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y0} + t \cdot y4\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y0, t \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      10. *-lowering-*.f64 40.6

          \[\leadsto -\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, \color{blue}{t \cdot y4}\right) \]

   8. Simplified 40.6%

      \[\leadsto \color{blue}{-\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

       4. *-lowering-*.f64 43.8

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   11. Simplified 43.8%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if -1.1000000000000001e29 < y0 < 6.4000000000000002e109

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right)\right) \]

      7. *-lowering-*.f64 33.4

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

   8. Simplified 33.4%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y5 \cdot y\right)}\right) \]

       3. *-lowering-*.f64 23.3

          \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y5 \cdot y\right)}\right) \]

   11. Simplified 23.3%

       \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y5 \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.1 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 6.4 \cdot 10^{+109}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.7% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;y0 \leq -3.5 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 2.05 \cdot 10^{+110}:\\ \;\;\;\;i \cdot \left(\left(y \cdot k\right) \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (* y0 y2)))))
   (if (<= y0 -3.5e+30) t_1 (if (<= y0 2.05e+110) (* i (* (* y k) y5)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (y0 <= -3.5e+30) {
		tmp = t_1;
	} else if (y0 <= 2.05e+110) {
		tmp = i * ((y * k) * y5);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (x * (y0 * y2))
    if (y0 <= (-3.5d+30)) then
        tmp = t_1
    else if (y0 <= 2.05d+110) then
        tmp = i * ((y * k) * y5)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (y0 <= -3.5e+30) {
		tmp = t_1;
	} else if (y0 <= 2.05e+110) {
		tmp = i * ((y * k) * y5);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (x * (y0 * y2))
	tmp = 0
	if y0 <= -3.5e+30:
		tmp = t_1
	elif y0 <= 2.05e+110:
		tmp = i * ((y * k) * y5)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(x * Float64(y0 * y2)))
	tmp = 0.0
	if (y0 <= -3.5e+30)
		tmp = t_1;
	elseif (y0 <= 2.05e+110)
		tmp = Float64(i * Float64(Float64(y * k) * y5));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (x * (y0 * y2));
	tmp = 0.0;
	if (y0 <= -3.5e+30)
		tmp = t_1;
	elseif (y0 <= 2.05e+110)
		tmp = i * ((y * k) * y5);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.5e+30], t$95$1, If[LessEqual[y0, 2.05e+110], N[(i * N[(N[(y * k), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y0 < -3.50000000000000021e30 or 2.0499999999999999e110 < y0

   1. Initial program 21.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 49.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right)} \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y0} + t \cdot y4\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y0, t \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      10. *-lowering-*.f64 40.6

          \[\leadsto -\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, \color{blue}{t \cdot y4}\right) \]

   8. Simplified 40.6%

      \[\leadsto \color{blue}{-\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

       4. *-lowering-*.f64 43.8

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   11. Simplified 43.8%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if -3.50000000000000021e30 < y0 < 2.0499999999999999e110

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)}\right) \]

      3. associate--l+ N/A

         \[\leadsto k \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto k \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right)\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto k \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto k \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(\mathsf{neg}\left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(-1 \cdot \left(y1 \cdot z\right) + y \cdot y5\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 + -1 \cdot \left(y1 \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 + \color{blue}{\left(\mathsf{neg}\left(y1 \cdot z\right)\right)}\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto k \cdot \left(i \cdot \left(\color{blue}{y \cdot y5} - y1 \cdot z\right)\right) \]

      7. *-lowering-*.f64 33.4

         \[\leadsto k \cdot \left(i \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

   8. Simplified 33.4%

      \[\leadsto k \cdot \color{blue}{\left(i \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot y5\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot y5\right)} \]

       4. *-lowering-*.f64 22.8

          \[\leadsto i \cdot \left(\color{blue}{\left(k \cdot y\right)} \cdot y5\right) \]

   11. Simplified 22.8%

       \[\leadsto \color{blue}{i \cdot \left(\left(k \cdot y\right) \cdot y5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.5 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 2.05 \cdot 10^{+110}:\\ \;\;\;\;i \cdot \left(\left(y \cdot k\right) \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.6% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;y0 \leq -1.5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 1.06 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (* y0 y2)))))
   (if (<= y0 -1.5e+25) t_1 (if (<= y0 1.06e+58) (* a (* t (* y2 y5))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (y0 <= -1.5e+25) {
		tmp = t_1;
	} else if (y0 <= 1.06e+58) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (x * (y0 * y2))
    if (y0 <= (-1.5d+25)) then
        tmp = t_1
    else if (y0 <= 1.06d+58) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (y0 <= -1.5e+25) {
		tmp = t_1;
	} else if (y0 <= 1.06e+58) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (x * (y0 * y2))
	tmp = 0
	if y0 <= -1.5e+25:
		tmp = t_1
	elif y0 <= 1.06e+58:
		tmp = a * (t * (y2 * y5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(x * Float64(y0 * y2)))
	tmp = 0.0
	if (y0 <= -1.5e+25)
		tmp = t_1;
	elseif (y0 <= 1.06e+58)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (x * (y0 * y2));
	tmp = 0.0;
	if (y0 <= -1.5e+25)
		tmp = t_1;
	elseif (y0 <= 1.06e+58)
		tmp = a * (t * (y2 * y5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.5e+25], t$95$1, If[LessEqual[y0, 1.06e+58], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y0 < -1.50000000000000003e25 or 1.05999999999999997e58 < y0

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot c\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + i \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \cdot \left(-1 \cdot c\right)} \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y0, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(i, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right) \cdot \left(-c\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(c \cdot \left(y2 \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right) \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(c \cdot y2\right)} \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y0} + t \cdot y4\right)\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y0, t \cdot y4\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg}\left(\left(c \cdot y2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y0, t \cdot y4\right)\right) \]

      10. *-lowering-*.f64 39.2

          \[\leadsto -\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, \color{blue}{t \cdot y4}\right) \]

   8. Simplified 39.2%

      \[\leadsto \color{blue}{-\left(c \cdot y2\right) \cdot \mathsf{fma}\left(-x, y0, t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

       4. *-lowering-*.f64 40.1

          \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   11. Simplified 40.1%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if -1.50000000000000003e25 < y0 < 1.05999999999999997e58

   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 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 46.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

      6. *-lowering-*.f64 30.2

         \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

   8. Simplified 30.2%

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 14.9

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

   11. Simplified 14.9%

       \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

       4. *-lowering-*.f64 16.3

          \[\leadsto a \cdot \left(\color{blue}{\left(y2 \cdot y5\right)} \cdot t\right) \]

   13. Applied egg-rr 16.3%

       \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.5 \cdot 10^{+25}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.06 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 17.2% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* 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) {
	return a * (t * (y2 * y5));
}

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 * (t * (y2 * y5))
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 * (t * (y2 * y5));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (t * (y2 * y5))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(t * Float64(y2 * y5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (t * (y2 * y5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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 41.3%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in y2 around inf

   \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

   2. associate-*r* N/A

      \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

   3. accelerator-lowering-fma.f64 N/A

      \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

   4. mul-1-neg N/A

      \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

   5. neg-lowering-neg.f64 N/A

      \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

   6. *-lowering-*.f64 26.4

      \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

8. Simplified 26.4%

   \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

9. Taylor expanded in x around 0

   \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]
10. Step-by-step derivation

    1. *-lowering-*.f64 13.6

       \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

11. Simplified 13.6%

    \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]
12. Step-by-step derivation

    1. *-commutative N/A

       \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

    2. associate-*r* N/A

       \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

    3. *-lowering-*.f64 N/A

       \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

    4. *-lowering-*.f64 14.4

       \[\leadsto a \cdot \left(\color{blue}{\left(y2 \cdot y5\right)} \cdot t\right) \]

13. Applied egg-rr 14.4%

    \[\leadsto a \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot t\right)} \]

14. Final simplification 14.4%

    \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]
15. Add Preprocessing

Alternative 28: 16.8% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* 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) {
	return a * (y5 * (t * y2));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y5 * (t * y2))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y5 * (t * y2));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y5 * (t * y2))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y5 * Float64(t * y2)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y5 * (t * y2));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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 41.3%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in y2 around inf

   \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

   2. associate-*r* N/A

      \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

   3. accelerator-lowering-fma.f64 N/A

      \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

   4. mul-1-neg N/A

      \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

   5. neg-lowering-neg.f64 N/A

      \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

   6. *-lowering-*.f64 26.4

      \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

8. Simplified 26.4%

   \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

9. Taylor expanded in x around 0

   \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
10. Step-by-step derivation

    1. *-lowering-*.f64 N/A

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

    2. associate-*r* N/A

       \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot y5\right)} \]

    3. *-lowering-*.f64 N/A

       \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot y5\right)} \]

    4. *-lowering-*.f64 13.6

       \[\leadsto a \cdot \left(\color{blue}{\left(t \cdot y2\right)} \cdot y5\right) \]

11. Simplified 13.6%

    \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2\right) \cdot y5\right)} \]

12. Final simplification 13.6%

    \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right) \]
13. Add Preprocessing

Alternative 29: 16.9% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y2 (* t 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) {
	return a * (y2 * (t * y5));
}

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 * (y2 * (t * y5))
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 * (y2 * (t * y5));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y2 * (t * y5))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y2 * Float64(t * y5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y2 * (t * y5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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 41.3%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in y2 around inf

   \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(x \cdot y1\right) + t \cdot y5\right)\right)} \]

   2. associate-*r* N/A

      \[\leadsto a \cdot \left(y2 \cdot \left(\color{blue}{\left(-1 \cdot x\right) \cdot y1} + t \cdot y5\right)\right) \]

   3. accelerator-lowering-fma.f64 N/A

      \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot x, y1, t \cdot y5\right)}\right) \]

   4. mul-1-neg N/A

      \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

   5. neg-lowering-neg.f64 N/A

      \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(x\right)}, y1, t \cdot y5\right)\right) \]

   6. *-lowering-*.f64 26.4

      \[\leadsto a \cdot \left(y2 \cdot \mathsf{fma}\left(-x, y1, \color{blue}{t \cdot y5}\right)\right) \]

8. Simplified 26.4%

   \[\leadsto a \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-x, y1, t \cdot y5\right)\right)} \]

9. Taylor expanded in x around 0

   \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]
10. Step-by-step derivation

    1. *-lowering-*.f64 13.6

       \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]

11. Simplified 13.6%

    \[\leadsto a \cdot \left(y2 \cdot \color{blue}{\left(t \cdot y5\right)}\right) \]
12. Add Preprocessing

Developer Target 1: 27.5% 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 2024204 
(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)))))